Phase Behavior of the System (Carbon Dioxide + n-Heptane +

Article pubs.acs.org/jced

Phase Behavior of the System (Carbon Dioxide + n‑Heptane + Methylbenzene): A Comparison between Experimental Data and SAFT-γ-Mie Predictions Saif Z. S. Al Ghafri,†,‡ Geoffrey C. Maitland,† and J. P. Martin Trusler*,† †

Qatar Carbonates and Carbon Storage Research Centre, Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom ‡ Fluid Science and Resources Division, School of Mechanical and Chemical Engineering, University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia 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 298−423 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.

1. INTRODUCTION

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 Dohrn,10 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 co-workers13,14 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.

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, nonflammable, and readily available,7 and thus is used as a supercritical solvent to separate complex mixtures such as aromatic components. © 2017 American Chemical Society

Special Issue: Memorial Issue in Honor of Ken Marsh Received: February 8, 2017 Accepted: April 19, 2017 Published: May 1, 2017 2826

DOI: 10.1021/acs.jced.7b00145 J. Chem. Eng. Data 2017, 62, 2826−2836

Journal of Chemical & Engineering Data

Article

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 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 refs 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 co-workers,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 semiempirical 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 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 that 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 multicomponent (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 SECTION 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 coexisting phases inside the equilibrium cell under conditions of known overall composition. The apparatus supported working pressures and 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 preprepared 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 four 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 2827



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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 color indicates gas paths, red color indicates liquid paths, and blue color indicates mixture paths.

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 nonuniformity 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 ref 53 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 x1 of CO2 ≤ 0.0017x1(1 − x1). The mole fractions of x2 of heptane and x3 of methylbenzene are given by x2 =

(1 − x1)Y (1 − Y )

(1)

(1 − x1) (1 − Y )

(2)

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. Table 1. Description of Chemical Samples source

purity as supplied

additional purification

carbon dioxide heptane methylbenzene

BOC Sigma-Aldrich Sigma-Aldrich

0.99995 0.990 0.998

none none none

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 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 homogeneous phase was obtained at a fixed temperature. The system was then allowed to equilibrate under continued stirring for at least 1 h. 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

and x3 =

chemical name

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 2828



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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 subsystems 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, eqs 4 and 6, while the source and values of the cross parameters εkl and λr,kl are given in Table 3.

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 nonassociating segments k and l present in two different molecules is given by ⎛ λr, klεkl ⎞⎛ λr, kl ⎞ λa, kl /(λ r, kl − λa, kl)⎡⎛ σ ⎞ λ r, kl ⎛ σ ⎞ λa, kl ⎤ ⎢⎜ kl ⎟ ⎟⎟⎜⎜ ⎟⎟ − ⎜ kl ⎟ ⎥ ukl(rkl) = ⎜⎜ ⎢⎝ rkl ⎠ ⎝ rkl ⎠ ⎥⎦ ⎝ λr, kl − λa, kl ⎠⎝ λa, kl ⎠ ⎣

Table 3. Unlike Group Cross Interaction Energies, ε, and Lambda Repulsive, λra

,

(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 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 σkl =

εkl =

1 (σkk + σll) 2

σkk3 σll3 σkl3

λkl = 3 +

a

(5)

(λkk − 3)(λll − 3)

group 2

(ε/kB)/K

λr

CH3 CH3 CH3 CH3 CH2 CH2 CH2 aCH aCH aCCH3

CH2 aCH aCCH3 CO2 aCH aCCH3 CO2 aCCH3 CO2 CO2

350.77 305.81 CR 205.70 415.64 CR 276.45 471.23 224.33 309.36

CR CR CR CR CR CR CR CR 14.155 CR

reference 58 61 current 60 61 current 60 60 current current

work

work

work work

CR denotes parameters obtained with a combining rule.

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 298,62 313,62 353,25 373,25 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 (283,18 311,19 353,19 394,19 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:

(4)

εkkεll

group 1

⎡ p (Ti , xi) − p (Ti , xi) ⎤2 i ,exp i ,calc ⎥ χ = ∑ ⎢⎢ ⎥⎦ N i=1 ⎣ pi ,exp (Ti , xi)

(6)

2

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

Wp

+

Wy N

N

N

∑ [yi ,exp (Ti , xi) − yi ,calc (Ti , xi)]2

(7)

i=1

Table 2. Like Group Parameters Used CH3 CH2 aCH aCCH3 CO2

Sk

(ε/kB)/K

σ × 1010/m

λr

λa

reference

0.5725 0.2293 0.3218 0.3166 0.8468

256.77 473.39 371.53 651.41 207.89

4.077 4.880 4.058 5.487 3.050

15.050 19.871 14.756 23.627 26.408

6.00 6.00 6.00 6.00 5.06

58 58 61 60 60

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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 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).

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 = 353 K (squares),19 T = 394 K (circles),19 and T = 413 K (triangles).21

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 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 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.

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 2830



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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 Pointa p/MPa 0.503 1.052 1.755 3.313 4.352 4.874 5.254 5.631 5.892 5.968 6.062 6.085 6.126 6.210 6.223 6.186 6.256 0.437 0.695 1.425 2.901 4.206 5.250 5.475 5.625 5.725 5.792 5.910 6.175 6.172 0.473 1.241 2.205 3.825 4.501 4.850 5.355 5.525 5.712 5.805 6.135 6.230 6.255 0.782 1.465 2.319 2.837 3.575 4.221 4.762 4.930 5.012 5.101

x1 0.0532 0.1215 0.2083 0.4163 0.5968 0.7108 0.8127 0.8972 0.9504 0.9588 0.9736 0.9769 0.9818 0.9893 0.9909 0.9909 0.9954 0.0479 0.0731 0.1705 0.3572 0.5627 0.8068 0.8661 0.8977 0.9172 0.9275 0.9546 0.9775 0.9897 0.0484 0.1507 0.2767 0.5000 0.6244 0.7152 0.8460 0.8825 0.9157 0.9292 0.9743 0.9836 0.9865 0.0946 0.1847 0.2985 0.3652 0.4619 0.5680 0.6861 0.7325 0.7593 0.7822

x2

x3

T = 298.15 K 0.1149 0.8319 0.1066 0.7719 0.0961 0.6956 0.0708 0.5129 0.0489 0.3543 0.0351 0.2541 0.0227 0.1646 0.0125 0.0903 0.0060 0.0436 0.0050 0.0362 0.0032 0.0232 0.0028 0.0203 0.0022 0.0160 0.0013 0.0094 0.0011 0.0080 0.0011 0.0080 0.00055 0.0040 0.2576 0.6945 0.2508 0.6761 0.2245 0.6050 0.1739 0.4689 0.1183 0.3190 0.0523 0.1409 0.0362 0.0977 0.0277 0.0746 0.0224 0.0604 0.0196 0.0529 0.0123 0.0331 0.0061 0.0164 0.0028 0.0075 0.4586 0.4930 0.4093 0.4400 0.3486 0.3747 0.2410 0.2591 0.1810 0.1946 0.1373 0.1476 0.0742 0.0798 0.0566 0.0609 0.0406 0.0437 0.0341 0.0367 0.0124 0.0133 0.0079 0.0085 0.0065 0.0070 0.6793 0.2261 0.6117 0.2036 0.5263 0.1752 0.4763 0.1585 0.4037 0.1344 0.3241 0.1079 0.2355 0.0784 0.2007 0.0668 0.1806 0.0601 0.1634 0.0544

status bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble

Table 4. continued p/MPa

Y 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.930 0.930 0.930 0.930 0.930 0.930 0.930 0.930 0.930 0.930 0.930 0.930 0.930 3.004 3.004 3.004 3.004 3.004 3.004 3.004 3.004 3.004 3.004 2831

x1

5.222 5.405 5.585 5.636 5.875 5.953 6.045 6.072 6.123

0.8038 0.8583 0.8951 0.9163 0.9451 0.9592 0.9696 0.9732 0.9748

0.297 1.245 2.400 2.650 3.742 4.815 6.581 7.497 8.114 8.775 8.852 8.965 8.925 8.824 8.756 8.217 0.254 0.676 1.678 4.005 6.015 7.395 8.142 8.423 8.625 8.865 8.916 8.895 8.652 8.091 0.201 1.285 2.785 4.115 5.550 6.402 7.275 7.650 8.415 8.645 8.767 8.852 8.885 8.675 8.264 0.234 0.550

0.0218 0.0976 0.1867 0.2082 0.3081 0.4161 0.5956 0.7098 0.8122 0.9070 0.9297 0.9537 0.9669 0.9793 0.9816 0.9860 0.0196 0.0482 0.1372 0.3401 0.5433 0.7143 0.8210 0.8669 0.8972 0.9256 0.9476 0.9660 0.9801 0.9856 0.0199 0.1028 0.2288 0.3567 0.4995 0.6022 0.7035 0.7620 0.8722 0.8992 0.9154 0.9568 0.9716 0.9743 0.9801 0.0235 0.0535

x2

x3

T = 298.15 K 0.1472 0.0490 0.1063 0.0354 0.0787 0.0262 0.0628 0.0209 0.0412 0.0137 0.0306 0.0102 0.0228 0.0076 0.0201 0.0067 0.0189 0.0063 T = 323.15 K 0.1188 0.8594 0.1096 0.7928 0.0987 0.7146 0.0961 0.6957 0.0840 0.6079 0.0709 0.5130 0.0491 0.3553 0.0352 0.2550 0.0228 0.1650 0.0113 0.0817 0.0085 0.0618 0.0056 0.0407 0.0040 0.0291 0.0025 0.0182 0.0022 0.0162 0.0017 0.0123 0.2653 0.7151 0.2576 0.6942 0.2335 0.6293 0.1786 0.4813 0.1236 0.3331 0.0773 0.2084 0.0484 0.1306 0.0360 0.0971 0.0278 0.0750 0.0201 0.0543 0.0142 0.0382 0.0092 0.0248 0.0054 0.0145 0.0039 0.0105 0.4723 0.5078 0.4324 0.4648 0.3717 0.3995 0.3100 0.3333 0.2412 0.2593 0.1917 0.2061 0.1429 0.1536 0.1147 0.1233 0.0616 0.0662 0.0486 0.0522 0.0408 0.0438 0.0208 0.0224 0.0137 0.0147 0.0124 0.0133 0.0096 0.0103 0.7326 0.2439 0.7101 0.2364

status

Y

bubble bubble bubble bubble bubble bubble bubble bubble bubble

3.004 3.004 3.004 3.004 3.004 3.004 3.004 3.004 3.004

bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble dew dew dew bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble dew dew dew bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble dew dew dew bubble bubble

0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.930 0.930 0.930 0.930 0.930 0.930 0.930 0.930 0.930 0.930 0.930 0.930 0.930 0.930 0.930 3.004 3.004



Article


x1

1.889 3.205 3.910 4.921 5.950 7.107 7.536 8.015 8.395 8.635 8.736 8.765 8.795 8.707 8.230

0.1694 0.2777 0.3425 0.4415 0.5472 0.6836 0.7582 0.8238 0.8767 0.9067 0.9251 0.9275 0.9508 0.9648 0.9784

1.025 2.441 3.765 3.885 4.115 6.017 7.768 7.875 10.162 10.951 12.547 13.747 13.890 13.678 13.052 11.872 0.497 1.922 3.786 7.175 10.435 11.694 13.256 13.562 13.532 13.256 12.752 11.653 0.110 0.750 3.501 5.432 8.080 10.880 11.950 13.040 13.170 13.100 12.250 10.761 0.933

0.0437 0.1138 0.1864 0.1937 0.2079 0.3091 0.4136 0.4199 0.5502 0.5955 0.7097 0.8122 0.8447 0.8861 0.9207 0.9417 0.0219 0.0925 0.1966 0.3850 0.5764 0.6627 0.7760 0.8337 0.8683 0.9011 0.9234 0.9408 0.0000 0.0376 0.1878 0.2947 0.4473 0.6180 0.6919 0.7765 0.8510 0.8730 0.9297 0.9502 0.0534

Table 4. continued x2

x3

T = 323.15 K 0.6232 0.2074 0.5419 0.1804 0.4933 0.1642 0.4190 0.1395 0.3397 0.1131 0.2374 0.0790 0.1814 0.0604 0.1322 0.0440 0.0925 0.0308 0.0700 0.0233 0.0562 0.0187 0.0544 0.0181 0.0369 0.0123 0.0264 0.0088 0.0162 0.0054 T = 373.15 K 0.1161 0.8402 0.1076 0.7786 0.0987 0.7149 0.0979 0.7084 0.0961 0.6960 0.0839 0.6070 0.0712 0.5152 0.0704 0.5097 0.0546 0.3952 0.0491 0.3554 0.0352 0.2551 0.0228 0.1650 0.0189 0.1364 0.0138 0.1001 0.0096 0.0697 0.0071 0.0512 0.2647 0.7134 0.2456 0.6619 0.2174 0.5860 0.1664 0.4486 0.1146 0.3090 0.0913 0.2460 0.0606 0.1634 0.0450 0.1213 0.0356 0.0961 0.0268 0.0721 0.0207 0.0559 0.0160 0.0432 0.4819 0.5181 0.4638 0.4986 0.3914 0.4208 0.3399 0.3654 0.2664 0.2863 0.1841 0.1979 0.1485 0.1596 0.1077 0.1158 0.0718 0.0772 0.0612 0.0658 0.0339 0.0364 0.0240 0.0258 0.7102 0.2364

Y

p/MPa

x1

bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble dew dew

3.004 3.004 3.004 3.004 3.004 3.004 3.004 3.004 3.004 3.004 3.004 3.004 3.004 3.004 3.004

2.256 4.450 6.825 9.351 11.250 12.160 12.653 12.812 12.702 12.431 12.152 11.735 10.576

0.1298 0.2567 0.3987 0.5497 0.6744 0.7449 0.7938 0.8503 0.8818 0.9115 0.9227 0.9316 0.9472

bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble dew dew dew bubble bubble bubble bubble bubble bubble bubble bubble bubble dew dew dew bubble bubble bubble bubble bubble bubble bubble bubble bubble dew dew dew bubble

0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.930 0.930 0.930 0.930 0.930 0.930 0.930 0.930 0.930 0.930 0.930 0.930 3.004

1.258 3.454 4.905 5.415 7.946 10.364 12.726 14.287 15.997 16.065 16.021 15.275 14.672 14.276 13.050 1.425 4.323 6.153 9.956 11.813 14.225 15.243 15.536 15.075 14.052 13.832 13.032 11.957 0.405 1.256 2.962 4.545 6.625 10.320 13.250 14.595 14.755 13.950 13.200 11.587 2.150 4.421 7.615

0.0335 0.1257 0.1860 0.2075 0.3092 0.4134 0.5221 0.5954 0.7096 0.7699 0.7996 0.8328 0.8527 0.8596 0.8792 0.0482 0.1672 0.2491 0.4167 0.5003 0.6215 0.7026 0.7779 0.8067 0.8411 0.8478 0.8667 0.8792 0.0000 0.0378 0.1170 0.1875 0.2868 0.4512 0.6018 0.7085 0.7702 0.8206 0.845 0.8620 0.0875 0.1980 0.3490

status

2832

x2

x3

T = 373.15 K 0.6529 0.2173 0.5577 0.1856 0.4511 0.1502 0.3378 0.1125 0.2443 0.0813 0.1914 0.0637 0.1547 0.0515 0.1123 0.0374 0.0887 0.0295 0.0664 0.0221 0.0580 0.0193 0.0513 0.0171 0.0396 0.0132 T = 423.15 K 0.1173 0.8492 0.1061 0.7682 0.0988 0.7152 0.0962 0.6963 0.0839 0.6069 0.0712 0.5154 0.0580 0.4199 0.0491 0.3555 0.0352 0.2552 0.0279 0.2022 0.0243 0.1761 0.0203 0.1469 0.0179 0.1294 0.0170 0.1234 0.0147 0.1061 0.2576 0.6942 0.2254 0.6074 0.2032 0.5477 0.1578 0.4255 0.1352 0.3645 0.1024 0.2761 0.0805 0.2169 0.0601 0.1620 0.0523 0.1410 0.0430 0.1159 0.0412 0.1110 0.0361 0.0972 0.0327 0.0881 0.4819 0.5181 0.4637 0.4985 0.4255 0.4575 0.3916 0.4209 0.3437 0.3695 0.2645 0.2843 0.1919 0.2063 0.1405 0.1510 0.1107 0.1191 0.0865 0.0929 0.0747 0.0803 0.0665 0.0715 0.6846 0.2279 0.6017 0.2003 0.4884 0.1626

status

Y

bubble bubble bubble bubble bubble bubble bubble bubble dew dew dew dew dew

3.004 3.004 3.004 3.004 3.004 3.004 3.004 3.004 3.004 3.004 3.004 3.004 3.004

bubble bubble bubble bubble bubble bubble bubble bubble bubble bubble dew dew dew dew dew bubble bubble bubble bubble bubble bubble bubble dew dew dew dew dew dew bubble bubble bubble bubble bubble bubble bubble bubble dew dew dew dew bubble bubble bubble

0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.138 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.930 0.930 0.930 0.930 0.930 0.930 0.930 0.930 0.930 0.930 0.930 0.930 3.004 3.004 3.004



Article

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 4−6 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.


x1

11.532 13.625 13.853 13.792 13.350 12.375 11.052

0.5420 0.6833 0.7198 0.7745 0.7982 0.8310 0.8587

x2

x3

T = 423.15 K 0.3436 0.1144 0.2376 0.0791 0.2102 0.0700 0.1692 0.0563 0.1514 0.0504 0.1268 0.0422 0.1060 0.0353

status bubble bubble bubble dew dew dew dew

Y 3.004 3.004 3.004 3.004 3.004 3.004 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.

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 unweighted 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.

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.

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. 2833



Article

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.

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.

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 consequence, in addition to a liquid−gas critical surface a liquid−liquid critical plane exists at low temperatures and a critical end point curve exists at low pressure connecting upper critical end points. 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 8−11 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 9−11 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.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

J. P. Martin Trusler: 0000-0002-6403-2488 2834



Article

Funding

(16) Wu, W.; Ke, J.; Poliakoff, M. Phase Boundaries of CO2 + Toluene, CO2 + Acetone, and CO2 + Ethanol at High Temperatures and High Pressures. J. Chem. Eng. Data 2006, 51, 1398−1403. (17) Peng, D.-Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 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. GasLiquid 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 k ij 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. (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.

This work was carried out as part of the activities of the Qatar Carbonates and 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. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

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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Phase Behavior of the System (Carbon Dioxide + n-Heptane +

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