High Pressure Phase Equilibria of the CO2 ... - ACS Publications

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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High Pressure Phase Equilibria of the CO2/Saturated Ethyl Esters Homologous Series Cara E. Schwarz* Department of Process Engineering, Private Bag X1, Matieland, 7602, South Africa ABSTRACT: A systematic study on the phase behavior of saturated ethyl esters with supercritical CO2 is presented. High pressure phase behavior measurements for the systems CO2/ethyl decanoate, CO2/ethyl dodecanoate, CO2/ethyl tetradecanoate, and CO2/ethyl hexadecanoate were conducted in a static synthetic view cell in the temperature range 308−358 K. Phase transition pressures were measured in the range 5.86−23.01 MPa for ethyl ester mass fractions in the range 0.0174−0.657 and complement existing literature data. Throughout the temperature and compositional range measured, which encompassed the liquid phase, mixture critical region, and vapor phase, an increase in temperature leads to an increase in phase transition pressure with no temperature inversions or three phase regions observed. Additionally, an increase in hydrocarbon backbone length leads to an ever-increasing phase-transition pressure, suggesting fractionation of ethyl esters according to molecular mass with supercritical CO2 is possible. Finally, the measured and previously published CO2/ethyl ester data were successfully correlated with a modified Chrastil models and the MT model. While these models cannot easily be used predictively and depend on the data sets used for correlation, these are simple and easy methods that can be used to interpolate data. state approached. While Gücļ ü-Ü stündağ and Temelli,15 Fornari et al.16 and Hernández et al.,17 among others, have applied the approach, in part, to CO2/fatty acid esters systems, it has to date not been fully applied to both the solubility of CO2 in esters and esters in CO2 simultaneously, thus justifying further investigation. Two additional models, namely that of MéndezSantiago and Teja18 and that of Narayan et al.19 were also considered. These two models are similar in structure and complexity to that of the model of Chrasil and are comparative in correlating solubility of components in supercritical CO2,19 thus warranting investigation. The aim of this contribution is to present results on a systematic study of the phase behavior of homologous series of saturated ethyl ester in supercritical CO2. To achieve this aim, the following objective were realized: (1) After evaluation of literature data, where required, additional phase equilibria measurements were conducted and the measurements are presented. (2) Analysis of previously published and newly measured experimental data was conducted to consider the effect of temperature and hydrocarbon backbone chain length on the phase behavior. (3) The modeling of previously published and newly measured data was done with the Chrastil,14 the Méndez-Santiago and Teja18 and the Narayan et al.19 models to determine the suitability of the models and whether any of these three models are superior.

1. INTRODUCTION Supercritical fluid extraction and fractionation is a viable alternative to processing plant and animal oils and fats. Such oils and fats typically consists of mixed triglycerides. To modify the fatty acid profile of such oils and fats, the triglycerides need to be esterified, after which the individual esters can be fractionated. Typically, esterification occurs with a low molecular mass alcohol, with ethanol being favorable due to its suitable properties. Therefore, a need exists to fractionate a mixture of fatty acid ethyl esters. Supercritical CO2 is a suitable method to fractionate these fatty acid ethyl esters due to their reasonably good solubility in supercritical CO2 (below 30 MPa), the mild operating temperature (below 373 K), and the fact that CO2 is generally regarded as a safe solvent. To design a supercritical CO2 fractionation process, details regarding the solubility/phase behavior of the fatty acid ethyl esters in supercritical CO2 are required. In particular, information regarding the effect of temperature, hydrocarbon backbone length, and the degree of saturation on the phase behavior is required. Phase equilibria data are available;1−7 however, in many cases only a limited temperature and/or compositional range is studied. In addition, a simple yet reliable method to correlate or interpolate the phase behavior data is useful. A number of previous studies have applied cubic equations of state to model the phase behavior of esters in supercritical CO2.5,6,8−13 While equations of state are able to model the data successfully, they require either a process simulator or in-house developed software. The approach of Chrastil,14 based on association laws and entropy, presents a mathematically simple alternative to the traditional equation of © XXXX American Chemical Society

Special Issue: In Honor of Cor Peters Received: August 31, 2017 Accepted: December 22, 2017

A

DOI: 10.1021/acs.jced.7b00780 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

The analysis was limited to saturated ethyl esters with eight or more carbon atoms in the hydrocarbon backbone and in the temperature range of 304−360 K. Typically, the fats and oils have reasonably high molecular masses (generally 10 or more carbon atoms per fatty acid segment) and the selected temperature range is suitable for both supercritical CO2 processing (just above the critical temperature of CO2) as well as for the processing of temperature sensitive compounds. The effect of the degree of saturation on the phase behavior of fatty acids is beyond the scope of the current study and will be attended to in a future study.

313.2, 323.2, and 333.2 K. The data cover the liquid phase and the mixture critical range with selected measurements in the vapor phase. Perusal of their verification system (CO2/methyl oleate) showed that in the mixture critical region their measurements were approximately 1 MPa lower than that of some of the previously measured data (data of Zou et al.20). However, except for stating that measurements in this region are difficult, no further explanation was given. To extend the temperature range, clarify the mixture critical region, and possibly contribute additional vapor phase measurements, additional measurements were conducted. • Ethyl hexadecanoate (ethyl palmitate, C16EE): The study of Crampon et al.4 also included the system CO2/ethyl hexadecanoate, again only at temperatures of 313.2, 323.2, and 333.2 K. Gaschi et al.5 also measured the CO2/ethyl hexadecanoate system and also in a static synthetic view cell, with their measurements covering 303.2 to 353.2 at 10 K intervals. While the data of Gaschi et al. and that of Crampon et al. are generally in agreement, the data of Gaschi et al. were measured using ethyl hexadecanoate of 95% purity. It is known that impurities may influence the phase behavior and act as cosolvents therefore reducing the pressure (see, e.g., the effect of small amounts of n-dodecane or n-tetradecane on 1-decanol phase behavior in CO221,22). Considering the difficulties mentioned by Crampon et al., and the low purity components used by Gaschi et al., additional measurements were thus justified. • Ethyl octadecanoate (ethyl stearate, C18EE): Bharath et al.,1 Brandalize et al.,2 (from the same group at Gaschi et al.5) and Crampon et al.4 all measured phase behavior data for the system CO2/ethyl octadecanoate. Bharath et al. and Crampon et al. measured data at 313.2, 323.2, and 333.2 K, while Brandalize et al. covered the range 303.2 to 353.2 K in 10 K increments. Their data cover the majority of the compositional range and, except for selected data-points of Crampon et al., are generally in agreement. No additional measurements are thus justified. In addition to phase behavior studies of pure ethyl esters with CO2, phase behavior measurements for various fatty acid ethyl ester mixtures have been conducted. Examples include biodiesel,23 fish oil,24−26 and soybean and caster oil.27 However, as these measurements entail mixtures and there may be significant interactions between the various fatty acid ethyl esters, these studies cannot provide an outcome for the phase behavior of pure fatty acid ethyl esters in CO2. However, at a later stage, beyond the scope of the current project, data for pure component fatty acid ethyl esters could be used to understand the phase behavior of mixtures and aid in the prediction thereof. To summarize, this work thus measured phase behavior data for the systems CO2/ethyl decanoate, CO2/ethyl dodecanoate, CO2/ethyl tetradecanoate, and CO2/ethyl hexadecanoate in the temperature range 308 to 358 K in the liquid phase, mixture critical, and vapor phase region. The measurements complemented current phase behavior data available and aimed to clarify concerns with selected data sets.

2. LITERATURE DATA The current study focuses on the phase behavior of long chain saturated ethyl esters in supercritical CO2. The focus is mainly on ethyl decanoate and higher homologues but for the purpose of evaluating literature information, ethyl esters from ethyl octanoate and higher were considered. The literature data are plotted together with the experimental measurements later in this contribution. Outlined below is a brief summary of the data available in the literature and justification for additional measurements conducted. • Ethyl octanoate (ethyl caprylate, C8EE): Hwu et al.6 used a flow type apparatus to measure the vapor−liquid equilibrium data at 308.2, 318.2, and 328.2 K. The data appear to be consistent and true and describes the liquid phase well but have limited resolution in the vapor phase (only a single significant figure for some vapor phases ethyl octanoate compositions with no or very little change as a function of pressure). In addition, Juntarachat et al.7 determined the critical loci of ethyl esters up to ethyl decanoate. Their critical data for the ethyl octanoate system cannot directly be compared to the phase equilibria data of Hwu et al. as the temperature ranges do not overlap. However, the data of Juntarachat et al. and that of Hwu et al. do not contradict each other. While additional data may prove valuable to clarify the critical region and provide information on higher temperatures, no additional measurements were conducted as the focus of this work is primarily on higher ethyl esters. • Ethyl decanoate (ethyl caprate, C10EE): The work of Hwu et al.6 also included the system CO2/ethyl decanoate. As for the CO2/ethyl octanoate system, vapor−liquid equilibrium type of data were measured at 308.2, 318.2, and 328.2 K, again showing limited resolution in the vapor phase. Juntarachat et al.7 also measured part of the critical curve for this system. However, Juntarachat et al. only measured a limited part of the curve and in the temperature range which is well outside the scope of this work, thus negating any direct comparison. To extend the temperature range and cover the mixture critical region additional measurements were conducted. • Ethyl dodecanoate (ethyl laurate, C12EE): Cheng et al.,3 from the same group at Hwu et al.,6 conducted a similar study of the CO2/ethyl dodecanoate system. Data were also measured at 308.2, 318.2, and 328.2 K with good resolution in the liquid phase and also limited resolution in the vapor phase. Again additional measurements were conducted to cover a wider temperature range and the mixture critical region. • Ethyl tetradecanoate (ethyl myristate, C14EE): Crampon et al.4 used a static synthetic method to measure data at

3. EXPERIMENTAL AND CORRELATION METHODS 3.1. Experimental Setup and Method. High pressure phase behavior measurements were conducted on one of two previously constructed and verified static synthetic view cells.28,29 The view cells work on the same principle with the major difference B



Article

being they have a maximum volume of 4528 and 8029 cm3, respectively. The two cells can be used interchangeably with generally the higher ethyl ester compositional measurements being conducted on the smaller of the two cells and higher CO2 compositional measurements being conducted on the larger of the two cells. In both cells the pressure was measured using a regularly in-house calibrated (with a Barnett dead weight tester) OneHalf20 transducer and temperature was measured with a regularly calibrated (by a SANAS accredited facility) 4-wire PT100. The phase transition is observed with the aid of a Stryker 1188 HD endoscope camera coupled to a light source with the image projected onto a 25 in. HD television monitor. The experimental measurements were conducted as follows: A gravimetrically measured known amount of ethyl ester was transferred to the view cell. The cell was closed and repeatedly flushed with CO2. A known amount of CO2 was then gravimetrically added to the view cell, after which it was sealed, pressurized into the single phase region, and heated to the first experimental temperature. Once thermal equilibrium was attained, the pressure is slowly released until the phase transition pressure is observed. The pressure was then increased again, and the process was repeated until the highest pressure in which two phases are present was determined within an accuracy of 0.02 MPa. This point was taken as the phase transition pressure. The temperature (T), phase transition pressure (P), and type of phase transition (bubble-point, dew-point, or mixture critical region transition) was noted, after which the temperature was increased to the next experimental temperature. The experimental measurements therefore resulted in a collection of phase transition pressures at various temperatures at constant composition. Further details regarding the experimental setup and method are given by Schwarz and Nieuwoudt28 for the smaller of the two units and by Fourie et al.29 for the larger unit. To verify the measurements, data measured using these setups have been repeatedly compared to other reliable sources.28−32 3.2. Accuracy of Data. On the basis of the accuracy of the calibration, the absolute uncertainty in the temperature measurements (u(T)) is 0.2 K; that is, u(T) = 0.2 K. The uncertainty of the pressure measurement (u(P)) is a combination of the uncertainty associated with the phase transition observation and the uncertainty in the phase transition measurement. The phase transition pressure is observed accurately to 0.02 MPa, and through accurate calibration the uncertainty in the phase transition measurement was 0.05 MPa. The total absolute uncertainty in the pressure measurement is therefore 0.07 MPa; that is, u(P) = 0.07 MPa. The compositional (mass fraction) uncertainty u(wEE) arises from the accuracy with which the components were gravimetrically added to the view cell. The ethyl esters were accurately weighed off to ±0.0001 g and the CO2 to ±0.01 g. The maximum relative uncertainty in the composition is therefore 0.01 times the ethyl ester mass fraction (wEE); that is, u(wEE) = 0.01 × wEE. 3.3. Materials Used. All materials used are listed in Table 1 together with their specified purity. The fatty acid ethyl esters were check with GC−MS for impurities, and purities higher than that quoted by the supplier were observed. 3.4. Correlation of Data. The data generated, as well as literature data, were correlated with three models: A modified Chrastil model,14,16,17 the model of Méndez-Santiago and Teja,18 and the model of Narayan et al.19 The first model considered in this work was a modified Chrastil model. In 1982 Chrastil14 developed a model for the solubility of solids and liquids in supercritical gases based on

Table 1. Materials Used, Their Suppliers, Product Numbers, and Purities (As Provided by Suppliers) component

CASRN

supplier

product number

purity

carbon dioxide ethyl decanoate (ethyl caprate) ethyl dodecanoate (ethyl laurate) ethyl tetradecanoate (ethyl myristate) ethyl hexadecanoate (ethyl palmitate)

124-38-9 110-38-3

Airproducts Aldrich

K243C S45941

99.995% ≥99%

106-33-2

Aldrich

61630

≥98%

124-06-1

Aldrich

70090

≥99%

628-97-7

Sigma

P9009

≥99%

associations laws and entropies of the components. Essentially, the model states that at constant temperature a linear relationship exists between the natural logarithm of the solubility and the natural logarithm of the density of the supercritical gas. Gücļ üÜ stündağ and Temelli15 noted that the gradient of this linear relationship reflects the density dependence of the solubility and the intercept incorporates a temperature dependence. In their publication Gücļ ü-Ü stündağ and Temelli applied the approach to, among others, the solubility of fatty acid esters in supercritical CO2 and, while successful applied, showed that the approach is dependent on the quality of the data used in the correlation. In 2009 Fornari et al.16 applied the same approach to determine the solubility of a supercritical fluid in a liquid. They also proposed an alternative form of the model whereby the term containing the natural logarithm of the density of the supercritical fluid is divided by the pressure, with this alternative approach yielding good results for among others the solubility of CO2 in methyl oleate and ethyl oleate. Recently, in 2011 Hernández et al.17 applied the alternative approach of Fornari et al. to predict among others the solubility of CO2 in methyl esters with reasonable success. From the various models based on the concept proposed by Chrastil, two main approaches can be identified. First, the natural logarithm of the mole fraction of the solute (xi) is correlated against the natural logarithm of the density of CO2 (ρCO2), as described in eq 1 and eq 2 for the liquid and the vapor phase, respectively, where ACO2, BCO2, AEE and BEE are correlation parameters: ln xCO2 = A CO2 ln ρCO + BCO2

(1)

ln x EE = AEE ln ρCO + BEE

(2)

2

2

Second, the natural logarithm of the mole fraction of the solute is correlated against the natural logarithm of the density of CO2 divided by the phase transition pressure, as described in eq 3 and eq 4 for the liquid and the vapor phase, respectively, where aCO2, bCO2, aEE, and bEE are correlation parameters: ln xCO2 =

aCO2 ln ρCO

2

P

+ bCO2

(3)

aEE ln ρCO

2 + bEE (4) P To date, these two approaches in their entirety have not been compared on an equal basis, and their application to the systems CO2/ethyl esters has not been fully investigated. This work first compared the two approaches, and then second, for the more suitable approach, determined the model parameters and their

ln x EE =

C



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Table 2. Experimental Phase Transition Pressure (P/MPa) at Various Measured Temperatures (T/K) and Correlation of the Measured Data for the System CO2/Ethyl Decanoatea P−T correlation: P = AT2 + BT + C (P/MPa, T/K)

composition xC10EE

wC10EE

0.275

0.633

0.212

0.551

0.162

0.467

0.125

0.394

0.0875

0.304

0.0622

0.232

0.0469

0.183

0.0287

0.118

0.0187

0.080

0.0129

0.0562

0.00642

0.0286

0.00395

0.0177

experimental phase transition pressure (P/MPa) as at the various measured temperatures (T/K) T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa

308.5 5.86b 308.4 6.49b 308.5 6.93b 308.4 7.14b 308.4 7.39b 308.5 7.59b 308.5 7.58b 308.5 7.72b 308.5 7.84b 308.1 7.67c 308.4 7.85c 308.6 7.91c

318.6 6.91b 318.4 7.76b 318.5 8.29b 318.3 8.64b 318.3 9.02b 318.6 9.30b 318.4 9.26b 318.5 9.51c 318.5 9.61c 318.6 9.37c 318.6 9.39c 318.2 9.20d

328.7 8.00b 328.6 9.12b 328.5 9.78b 328.3 10.34b 328.4 10.88b 328.5 11.26c 328.5 11.33c 328.5 11.42c 328.5 11.44c 328.6 11.18d 328.6 10.96d 328.7 10.71d

338.7 9.12b 338.7 10.46b 338.6 11.40b 338.2 12.13b 338.4 12.80b 338.6 13.30c 338.6 13.31c 338.6 13.32c 338.6 13.26d 338.7 12.93d 338.7 12.38d 338.6 11.82d

348.7 10.20b 348.7 11.84b 348.6 13.01b 348.2 13.80b 348.5 14.69b 348.6 15.12c 348.8 15.11c 348.8 15.04d 348.7 14.85d 348.5 14.38d 348.4 13.53d 348.4 12.74d

358.5 11.29b 358.7 13.25b 358.6 14.52b 358.5 15.46b 358.4 16.43c 358.7 16.77c 358.8 16.72c 358.8 16.56d 358.8 16.21d 358.5 15.52d 358.4 14.38d 358.5 13.47d

B

C

R2

0.10887

−27.759

1.000

0.13441

−35.016

1.000

0.15312

−40.419

0.999

0.16815

−44.795

1.000

0.18292

−49.118

1.000

0.18626

−49.911

0.999

−2.8413 × 10−04

0.37453

−81.014

0.999

−3.9822 × 10−04

0.44358

−91.284

1.000

−5.5900 × 10−04

0.54163

−106.111

1.000

−6.4498 × 10−04

0.58928

−112.757

0.999

−8.6138 × 10−04

0.70743

−128.462

0.999

−9.2321 × 10−04

0.72873

−129.105

0.999

A

a

xC10EE and wC10EE denote mole and mass fractions of ethyl decanoate in the mixture, respectively, and A, B, and C are correlations parameter. u(T) = 0.2 K, u(P) = 0.7 MPa and u(wC10EE) = 0.01 · wC10EE. bBubble-point phase transition. cPhase transition in the mixture critical region. dDew point phase transition.

temperature and data set dependence. Originally, Chrastil14 included a temperature term in his approach, but Gücļ ü-Ü stündağ and Temelli15 found that if fitted to various constant temperature data sets the values of ACO2 and AEE are not necessary constant. As such, in this work the parameters were fitted at a specific temperature and the temperature dependence thereof was investigated. The second model considered in this work is that of MéndezSantiago and Teja18 (MT model). They also correlated the solubility of solids in supercritical fluids with a simple model relating the mole fraction ethyl ester, the system pressure and temperature, and the pure CO2 density at the system temperature and pressure to one another. The development of their model was based on the assumption of dilute solutions and a classical Helmhotlz energy expansion, together with the Clausius− Clapeyron type expression for the sublimation pressure. While the model was developed for the solubility of solids in supercritical fluids, it is believed the assumptions may also hold true for liquids in supercritical fluids and possibly for supercritical fluids in liquids. In fact, Narayan et al.19 applied the MT model to the solubility of liquids in supercritical CO2. The model, applied to the solubility of the ethyl ester in supercritical CO2, is expressed ′ 2, BCO ′ 2 and CCO ′ 2 are the model parameters: as per eq 5, where ACO ′ + BEE ′ ρCO + C EE ′ T T ln(x EEP) = AEE 2

liquid ethyl ester phase can be expressed as per eq 7: ′ T = AEE ′ + BEE ′ ρCO T ln(x EEP) − C EE

(6)

2

′ 2T = A CO ′ 2 + BCO ′ 2 ρCO T ln(xCO2P) − CCO

2

(7)

18

While Méndez-Santiago and Teja did not apply their model to systems involving CO2 and esters, Narayan et al.19 did and obtained reasonably good fits for the MT-model. However, except for the CO2/ethyl octadecanoate system, Narayan et al. did not consider the ethyl esters investigated in this work and generally the temperature range they fitted their data to was smaller than that investigated here. Thus, the ability of the MT model to describe the data was investigated by evaluating how well the data can be linearized according to eq 6 and eq 7 with fitted parameters AEE ′ , BEE ′ , and CEE ′ , and ACO ′ 2, BCO ′ 2, and CCO ′ 2, respectively, and how well the resultant model can predict the data. Third, the last model considered was that of Narayan et al.19 Their model originates from the equality of fugacities, and together with a number of simplifying assumptions, used the Wilson model to describe the liquid activity coefficients. Their model is expressed as per eq 8 with E1, E2, and E3 being model parameters and ϕ being the product of the density of the supercritical fluid and the molar volume of the pure liquid (VEE), as stated in eq 9.

(5)

ln(x 2ϕ) = E1 + E2ϕ +

According to Méndez-Santiago and Teja,18 eq 5 can be linearized by plotting T ln(xEEP) − C′EET versus ρCO2, as per eq 6. Analogous to the Chrastil model, the solubility of CO2 in the

ϕ= D

E3 T

(8)

ρCO

2

VEE

(9) DOI: 10.1021/acs.jced.7b00780 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Table 3. Experimental Phase Transition Pressure (P/MPa) at Various Measured Temperatures (T/K) and Correlation of the Measured Data for the System CO2/Ethyl Dodecanoatea P−T correlation: P = AT2 + BT + C (P/MPa, T/K)

composition xC12EE

wC12EE

0.261

0.647

0.195

0.557

0.145

0.469

0.107

0.383

0.080

0.309

0.055

0.233

0.044

0.191

0.026

0.123

0.018

0.085

0.0108

0.0534

0.0054

0.0276

0.0035

0.0178

experimental phase transition pressure (P/MPa) as at the various measured temperatures (T/K) T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa

308.4 6.09b 308.5 6.74b 308.5 7.25b 308.5 7.54b 308.5 7.61b 308.6 7.87b 308.7 7.97b 308.5 7.85b 308.4 7.83b 308.6 7.89c 308.3 7.87c 308.5 7.89c

318.1 7.16b 318.4 8.07b 318.5 8.85b 318.5 9.33b 318.5 9.55b 318.6 9.85b 318.7 10.14c 318.6 10.01c 318.5 9.87d 318.2 9.71d 318.2 9.57d 318.5 9.47d

328.7 8.42b 328.6 9.59b 328.6 10.62b 328.7 11.38b 328.6 11.82b 328.7 12.24c 328.7 12.48c 328.7 12.34c 328.6 12.09d 328.7 11.92d 328.7 11.54d 328.6 11.18d

338.7 9.62b 338.6 11.11b 338.6 12.40b 338.9 13.48b 338.4 14.00b 338.4 14.38c 338.4 14.62c 338.4 14.39c 338.4 14.11d 338.8 13.82d 338.8 13.15d 338.8 12.66d

348.7 10.84b 348.7 12.62b 348.5 14.16b 348.7 15.37b 349.0 16.13b 348.5 16.40c 348.6 16.68c 348.8 16.41c 349.0 16.04d 348.4 15.46d 348.4 14.44d 348.6 13.85d

358.7 12.08b 358.7 14.05b 358.7 15.90b 358.7 17.11b 358.8 17.93c 358.3 18.20c 358.3 18.37c 358.6 18.11c 358.6 17.54d 358.6 16.89d 358.4 15.62d 358.8 14.81d

B

C

R2

0.11942

−30.797

1.000

0.14698

−38.666

1.000

0.17367

−46.401

1.000

0.19351

−52.199

0.999

−2.5903 × 10−04

0.38125

−85.449

0.999

−3.8998 × 10−04

0.47119

−100.503

0.999

−6.0912 × 10−04

0.61865

−125.035

1.000

−6.1637 × 10−04

0.61804

−124.216

1.000

−6.6387 × 10−04

0.63898

−126.168

0.999

−7.4262 × 10−04

0.67831

−130.799

0.999

−8.6194 × 10−04

0.73120

−135.698

0.999

−9.1054 × 10−04

0.74739

−136.090

0.999

A

a

xC12EE and wC12EE denote mole and mass fractions of ethyl dodecanoate in the mixture, respectively, and A, B, and C correlations parameters. u(T) = 0.2 K, u(P) = 0.7 MPa and u(wC12EE) = 0.01·wC12EE. bBubble-point phase transition. cPhase transition in the mixture critical region. dDew point phase transition.

tetradecanoate, and CO2/ethyl hexadecanoate were conducted at 308 to 358 K at approximately 10 K intervals. For each loaded composition, at various temperatures the phase transition pressure was determined and the type of transition noted. In the proximity of the mixture critical point (point of the critical curve at the experimental temperature) it is difficult, if not impossible to detect the type of phase transition. Here critical opalescence and the similar density of the coexiting phases prevents reliable determination of the type of phase transition. As such, such transitions are noted as being in the mixture critical region. The resultant composition−temperature−phase transition pressure data are presented in Table 2 to Table 5. In all cases it was observed that at constant composition an increase in temperature leads to an increase in phase transition pressure. Additionally, no three phase behavior was noted nor does the data indicate the presence thereof. However, while no three phase regions were observed, it may be that they are present in these systems, only at composition−temperature conditions not considered in this work. Brandalize et al.2 and Gaschi et al.5 observed liquid−liquid immiscibility and vapor−liquid−liquid equilibria at temperatures close to the critical point of CO2 for the systems CO2/ethyl hexadecanoate and CO2/ethyl octadecanoate. For each composition loaded to the view cell, six phase transition points were measured, each being approximately 10 K apart. However, the data were not measured at exactly the same temperatures. A method to generate isothermal data is thus required. Previous studies of phase behavior of supercritical fluids with high molecular mass components have indicated that in most cases the relationship between the phase transition pressure and temperature can be described by a simple linear, or second or

Equation 8 can be linearized through rearrangements, as per E eq 10. Thus, a plot of ln(x 2ϕ) − T3 vs ϕ should yield a straight line if the model assumptions hold, the model is suitable for the system considered and E3 is fitted correctly. ln(x 2ϕ) −

E3 = E1 + E2ϕ T

(10)

Unlike the modified Chrastil and the MT model, the Narayan et al. model cannot easily be applied to the liquid phase. The assumptions in deriving the model will not hold true for describing the solubility of CO2 in the liquid phase. Therefore, for the Narayan model, only the vapor phase correlation will be considered. Narayan et al.19 compared the fit of their model with the Chrastil and MT models for esters in supercritical CO2. However, with exception of ethyl stearate, none of the esters considered in their work are studied in their work. In general, the models performed very similarly with the Narayan et al. model performing marginally better than the other two. In this work, all three models were compared on an equal basis using the same data sets. The density of CO2, in kg·m−3, was obtained from NIST at the experimental temperature and phase transition pressure, and the fitting of the model parameters was conducted in MS Excel.

4. RESULTS AND DISCUSSION 4.1. Experimental Results and Observed Phase Behavior. Experimental phase behavior measurements for the systems CO2/ethyl decanoate, CO2/ethyl dodecanoate, CO2/ethyl E



Article

Table 4. Experimental Phase Transition Pressure (P/MPa) at Various Measured Temperatures (T/K) and Correlation of the Measured Data for the System CO2/Ehyl Tetradecanoatea P−T correlation: P = AT2 + BT + C (P/MPa, T/K)

composition xC14EE

wC14EE

0.247

0.657

0.188

0.574

0.135

0.476

0.0947

0.379

0.0699

0.305

0.0499

0.234

0.0397

0.194

0.0381

0.188

0.0237

0.124

0.0152

0.0826

0.00976

0.0543

0.00458

0.0261

0.00309

0.0178

experimental phase transition pressure (P/MPa) as at the various measured temperatures (T/K) T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa

308.5 6.36b 308.5 7.01b 308.4 7.50b 308.5 7.81b 308.5 7.95b 308.5 8.16c 308.5 8.20c 308.3 8.16c 308.4 8.07c 308.3 7.96c 308.3 7.99c 308.2 7.90c 308.1 7.93c

318.4 7.56b 318.5 8.50b 318.5 9.35b 318.5 10.20b 318.6 10.78c 318.5 11.04c 318.5 11.08c 318.4 11.03c 318.4 10.87c 318.2 10.54d 318.4 10.39d 318.2 9.96d 318.2 9.80d

328.6 8.83b 328.7 10.07b 328.6 11.49b 328.6 12.77b 328.7 13.44c 328.5 13.67c 328.5 13.70c 328.4 13.67c 328.6 13.50c 328.4 13.14d 328.4 12.76d 328.3 12.00d 328.6 11.76d

338.2 10.02b 338.3 11.63b 338.6 13.61b 338.7 15.11b 338.9 15.87c 338.4 15.99c 338.3 15.95c 338.2 15.93c 339.0 15.90c 338.3 15.34d 338.4 14.80d 338.9 13.84d 338.7 13.45d

348.7 11.39b 348.8 13.32b 348.7 15.67b 348.9 17.31b 348.4 17.92c 348.7 18.24c 348.9 18.18c 348.6 18.13c 348.6 17.85d 348.6 17.39d 348.3 16.65d 348.6 15.31d 348.3 14.83d

358.5 12.49b 358.6 14.79b 358.3 17.48b 358.5 19.20b 358.6 19.91c 358.6 20.17c 358.6 20.06c 358.5 20.04c 358.2 19.59d 358.1 19.00d 358.5 18.29d 358.7 16.73d 358.4 15.96d

B

C

R2

0.12363

−31.788

1.000

0.15647

−41.306

1.000

0.20276

−55.106

1.000

−6.4582 × 10−04

0.66034

−134.497

1.000

−1.1001 × 10−03

0.97278

−187.464

1.000

−1.1448 × 10−03

1.00293

−192.280

1.000

−1.2056 × 10−03

1.04006

−197.895

1.000

−1.1860 × 10−03

1.02693

−195.711

1.000

−1.2671 × 10−03

1.07608

−203.284

1.000

−1.2073 × 10−03

1.02734

−194.051

1.000

−1.0437 × 10−03

0.90214

−170.969

1.000

−9.2957 × 10−04

0.79503

−148.848

1.000

−9.7013 × 10−04

0.80839

−149.106

1.000

A

a

xC14EE and wC14EE denote mole and mass fractions of ethyl tetradecanoate in the mixture, respectively, and A, B and C correlations parameters. u(T) = 0.2 K, u(P) = 0.7 MPa and u(wC14EE) = 0.01·wC14EE. bBubble-point phase transition. cPhase transition in the mixture critical region. d Dew point phase transition.

third order polynomial relationship.21,28−30 The same approach was used here. A linear relationship was considered acceptable if the Pearson R2 value is 0.99 or greater, the phase transition pressure could be replicated with an accuracy of 0.15 MPa or less, and if the error in the phase transition pressure replication is less than 2% of the measured value. Should these constraints not hold true, a second order polynomial was tested and in all such cases was sufficient. The resultant linear or second order polynomials are included in Table 2 to Table 5 with the experimental data. It should be noted that the linear correlations are merely used to interpolate between data and should not be used as a predictive or correlative model and not extrapolated beyond a few K. From the experimental measurements the influence of temperature and pressure on the phase behavior is observed. At constant temperature, an increase in pressure leads to the compositions of the coexisting phases becoming more similar until the compositions are identical and the mixture critical point is reached, after which at higher pressures single phase behavior is present. Similarly, at constant pressure as temperature decreases, the compositions also become more similar again until the mixture critical point is reached, whereafter single phase behavior is present. These mixture critical points at the various temperatures are located on the critical loci and help define the type of phase behavior present. Van Konynenburg and Scott33 and more recently Bolz et al.34 have classified systems according to their type of phase behavior. Unfortunately, for the CO2/ethyl ester homologous series insufficient information is available for a

definitive classification. Very little low temperature behavior studies have been conducted. Gaschi et al.5 and Brandalize et al.2 both observed low temperature vapor−liquid−liquid and liquid−liquid equilibria for the systems CO2/ethyl hexadecanoate and CO2/ ethyl octadecanote, respectively. However, no critical end point or further three phase behavior is currently available. Thus, a definitive classification can not be made according to either of the classification systems save to require that for the CO2/ethyl hexadecanoate and CO2/ethyl octadecanote systems the type of phase behavior needs to include low temperature three phase behavior. Further studies focusing specifically on the low temperature phase behavior and determination of possible critical end points are required to provide a definitive outcome regarding the type of phase behavior; such studies are beyond the scope of the current work. 4.2. Comparison with Literature Data. The experimental measurements are compared to literature data in Figure 1 and Figure 2. All experimental data were generated using the correlations in Table 2 to Table 5. All comparisons are presented on a mass fraction basis so that the plots show a significant part of the vapor-like and critical region. The CO2/ethyl decanoate measured data is compared to data of Hwu et al.6 in Figure 1a. While limited overlap exists, the overlapping data corresponds well and the newly measured data complements previous experimental measurements. Similar observation exists of the CO2/ethyl dodecanoate system, presented in Figure 1b, where the experimental measurements compare well to the literature data of Cheng et al.3 F



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Table 5. Experimental Phase Transition Pressure (P/MPa) at Various Measured Temperatures (T/K) and Correlation of the Measured Data for the System CO2/Ethyl Hexadecanoatea P−T correlation: P = AT2 + BT + C (P/MPa, T/K)

Composition xC16EE

wC16EE

0.219

0.644

0.162

0.556

0.117

0.463

0.0932

0.399

0.0637

0.305

0.0477

0.244

0.0324

0.178

0.0202

0.118

0.0135

0.0812

0.00767

0.0476

0.00507

0.0319

0.00273

0.0174

Experimental phase transition pressure (P/MPa) as at the various measured temperatures (T/K) T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa T/K P/MPa

308.5 6.70b 308.6 7.36b 308.6 7.91b 309.1 9.04b 308.6 10.09c 308.6 10.71c 308.3 10.38c 308.6 10.29c 308.5 9.54c 308.4 8.76d 308.7 8.48d 308.3 8.06d

318.5 7.93b 318.7 8.99b 318.6 10.37b 318.3 11.62b 318.1 12.85c 319.2 13.78c 318.4 13.36c 318.3 13.20c 318.7 12.65c 318.8 11.74d 318.7 11.17d 318.6 10.53d

328.5 9.40b 328.8 11.00b 328.7 13.00b 328.2 14.17b 328.2 15.65c 328.8 16.31c 328.3 15.95c 328.3 15.86c 328.5 15.36c 328.6 14.28d 328.8 13.45d 328.5 12.64d

338.7 10.93b 338.8 13.01b 338.9 15.34b 338.5 16.65b 338.7 18.18c 338.3 18.63c 338.5 18.44c 338.3 18.29c 338.2 17.71c 338.3 16.32d 338.4 15.42d 338.3 14.47d

348.2 12.38b 348.5 14.88b 348.4 17.46b 348.8 18.75b 349.0 20.55c 348.7 20.95c 348.8 20.69c 348.3 20.39c 348.6 20.02c 348.5 18.43d 348.4 17.23d 348.6 15.91d

358.3 13.82b 358.4 16.67b 358.5 19.47b 358.6 20.61b 359.6 22.72c 358.4 23.01c 358.6 22.60c 358.4 22.37c 358.3 21.88c 358.4 20.57d 358.5 19.17d 358.5 17.49d

B

C

R2

0.14492

−38.130

0.999

1.3513 × 10−04

0.09996

−36.444

0.993

−6.9069 × 10−04

0.69395

−140.514

1.000

−1.1903 × 10−03

1.02847

−195.145

1.000

−1.0733 × 10−03

0.96467

−185.392

1.000

−9.9971 × 10−04

0.91296

−175.803

1.000

−1.1910 × 10−03

1.03690

−196.076

1.000

−1.3275 × 10−03

1.12711

−211.095

1.000

−1.4063 × 10−03

1.18520

−222.245

1.000

−1.0197 × 10−03

0.91281

−175.691

0.999

−1.0127 × 10−03

0.88732

−168.864

0.999

−1.2495 × 10−03

1.01899

−187.277

0.999

A

a

xC16EE and wC16EE denote mole and mass fractions of ethyl ester in the mixture, respectively, and A, B and C correlations parameters. u(T) = 0.2 K, u(P) = 0.7 MPa and u(wC16EE) = 0.01·wC16EE. bBubble-point phase transition. cPhase transition in the mixture critical region. dDew point phase transition.

Figure 1. Experimental phase transition pressure (P) as a function of ethyl ester mass fraction (wi) with comparison to literature data at 308.2 to 348.2 K in 10 K intervals: (a) CO2/ethyl decanoate system, literature data from Hwu et al.;6 (b) CO2/ethyl dodecanoate system, literature data from Chang et al.3 (key: ○ = 308.2 K, △ = 318.2 K, □ = 328.2 K, ◊ = 338.2 K, + = 348.2 K, × = 358.2 K; nonfilled markers this work from correlations in Table 2 and Table 3, gray filled markers indicate literature data).

The CO2/ethyl tetradecanoate measured data are compared to the measured data of Crampon et al.4 in Figure 2 (a). In general the data compares well, with the measurements in the current work being slightly higher than that of Crampon et al. As mentioned in the literature data discussion above, the verification data of Crampon et al. for the system CO2/ethyl oleate is up to 1 MPa lower than that of Zou et al.20 in the mixture critical region. Crampon et al. also correctly mentioned that measurements in the mixture critical region are difficult and as such some scatter is expected. The data of Crampon et al. thus seems to be on the lower end of the general scatter noted in the

mixture critical region. It should also be noted that the medical endoscope system used in the current work allows extremely detailed observation of the interior of the view cell contents. The entire view cell content is viewed on a 25 in. HD television monitor and observed at high resolution. Detection of the first signs of the phase transition, often not detected at lower definition or with the naked eye, is thus possible. The difference between the CO2/ethyl tetradecanoate data of Crampon et al. and that measured in this work is less than 1 MPa and therefore the data presented here can be regarded to compare well to that of Crampon et al. G



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Figure 2. Experimental phase transition pressure (P) as a function of ethyl ester mass fraction (wi) with comparison with literature data at 313.2 to 353.2 K in 10 K intervals: (a) CO2/ethyl tetradecanoate system, literature data from Crampon et al.;4 (b) CO2/ethyl hexadecanoate system, literature data from Crampon et al.4 and Gaschi et al.5 (key: ○ = 313.2 K, △ = 323.2 K, □ = 333.2 K, ◊ = 343.2 K, + = 353.2 K; nonfilled markers this work from correlations in Table 4 and Table 5, gray filled markers indicate data from Crampon et al., black markers and × = 353.2 K data from Gaschi et al.).

CO2/ethyl octadecanoate. As seen, although the data sets generally agree, there appears to be some scatter between the different data set. Figure 3 thus provides perspective on the difficulty of the measurements at high pressures and possible scatter present in the data. 4.3. Effect of Molecular Mass of Ethyl Ester. A comparison of the measured and literature data sets shows that as the length of the hydrocarbon backbone of the ethyl ester increases, so does the phase transition pressure. This can clearly be seen in Figure 4 where the experimental measurements and selected literature data are compared at 318.2, 333.2, and 348.2 K. This increase in phase transition pressure with hydrocarbon backbone length suggests that supercritical CO2 can separate saturated ethyl esters based on their molecular mass. Furthermore, it is noted that, unlike for the ethyl esters in ethane and propane,35 the increase is not linear with respect to the number of carbon atoms (carbon number). This can be seen more clearly in Figure 5, where at ethyl ester mass fractions of 0.10 and 0.35, the phase transition pressure is plotted as a function of carbon number (CN) at various temperatures. As the number of carbon atoms increases, so the increase in phase transition pressure becomes larger. Similar, nonlinear relationships are noted for the homologous series CO2/saturated acids36 and CO2/n-alkanes37 and collectively suggest complex molecular interactions. 4.4. Correlation of Data. The measured and literature data were correlated with the three models discussed above with the aim to test the suitability of the models and to determine if any of the models are superior to the others. The first model to be evaluated is that of the modified Chrastil model. Two approaches for correlation with the modified Chrastil model were suggested. The first approach (eq 1 and eq 2) correlates ln xCO2 and ln xEE with ln ρCO2 while the second approach

Comparison of the CO2/ethyl hexadecanoate measured data with that of Crampon et al.4 and Gaschi et al.5 is presented in Figure 2 (b). While the data generally compares well, it is observed that the data from this work is at times up to 1 MPa higher than that of Crampon et al. and Gaschi et al. As noted above, the verification data of Crampon et al. is at times 1 MPa lower than that of Zou et al.20 Crampon et al. also found that for the CO2/ethyl octadecanoate system their data is also slightly lower than that of Bharath et al.1 While the data of Gaschi et al. compares well with that of Crampon et al., the phase transition pressures noted by Gaschi et al. are at times slightly higher than that of Crampon et al. Additionally, Gaschi et al. used ethyl hexadecanoate of 95% purity. It is known that small amounts of impurities can notably lower than phase transition pressure.21,22 Therefore, the impurities in the ethyl hexadecanoate of Gaschi et al. could have lowered their data and in reality pure ethyl hexadecanoate data would have been closer to that measured in the current work. The difference between the measured CO2/ ethyl hexadecanoate data and that of Crampon et al. and Gaschi et al. can thus be explained. To substantiate the possible scatter in data, Figure 3 shows a plot data from three different literature sources1,2,4 for the system

ln ρ

(eq 3 and eq 4) correlates ln xCO2 and ln xEE with CO2 . The first P step in correlating the data was to compare the two approaches and decide which approach is most suitable, with the most suitable approach being that which most closely mimics a linear relationship. Both approaches were evaluated for the entire compositional range for the systems CO2/ethyl dodecanoate and CO2/ethyl tetradecanoate and both approaches gave a regular shape plot indicating good correlation between the parameters. However, the approach correlating against ln ρCO2 gives a linear relationship outside the critical region, whereas that correlating

Figure 3. Phase transition pressure (P) as a function of ethyl octadecanoate mass fraction (wC18EE) at 313.2, 323.2, and 333.2 at 10 K intervals for the system CO2/ethyl octadecanoate (key: ○ = 313.2 K, △ = 323.2 K, □ = 333.2 K, nonfilled markers from Bharath et al.,1 Gray filled markers from Brandalize et al.,2 and black filled markers from Crampon et al.4). H



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Figure 4. Comparison of experimental phase transition pressure (P) as a function of ethyl ester mass fraction (wEE) for CO2/ethyl esters system from ethyl octanoate to ethyl octadecanoate at (a) 318.2 K, (b) 333.2 K, and (c) 348.2 K (key × = C8EE, ○ = C10EE, △ = C12EE, □ = C14EE, ◊ = C16EE, + = C18EE; CO2/ethyl octanoate data from Hwu et al.6 and CO2/ethyl octadecanoate data from Bharath et al.,1 Brandalize et al.,2 and Crampon et al.4).

Figure 5. Phase transition pressure (P) as a function of carbon number (CN) at various temperatures and constant ethyl ester mass fraction (wi) for (a) wi = 0.35 and (b) wi = 0.10. Data obtained via interpolation from this work (key: ○ = 308.2 K, △ = 318.2 K, □ = 328.2 K, ◊ = 338.2 K, + = 348.2 K, × = 358.2 K; dashed line shows trend in data). ln ρ

against CO2 does not. Therefore, the first approach, correlating P against ln ρCO2, was chosen as the preferred approach (called the modified Chrastil model in this work). During the preliminary evaluation it was noted that neither approach was able to correlate the data in the mixture critical region. Here, at constant temperature, the phase transition pressure remains reasonably constant yet the mole fraction changes significantly. Therefore, the density of CO2 also remains relatively constant while the mole fraction changes, thus making correlation of the mole fraction with density virtually impossible

in this region. From a fundamental point of view in the mixture critical region the phase transition changes in nature from a liquid-like phase where CO2 is dissolved in a liquid to a vapor-like phase where a liquid is dissolved in CO2. The modified Chrastil model is thus not able characterize this transition and therefore model the mixture critical region. As such, it was decided to limit the correlation of the data to the liquid phase and vapor phase regions. Liquid phase data was limited to data with CO2 mole fractions less than 0.9 and the vapor phase to ethyl ester mole fractions less I



Article

Table 6. Correlation Results for the Modified Chrastil Model Using Measured and Literature Data for Both Liquid and Vapor Phasesa liquid phase correlation data sets

a b

T/K

ACO2

BCO2

R

2

lit. data6 lit. data6 lit. data6

308.2 318.2 328.2

0.5882 0.5995 0.6064

−3.246 −3.383 −3.494

0.981 0.982 0.979

lit. data6 and this work lit. data6 and this work lit. data6 and this work this work only this work only this work only this work only this work only this work only

308.2 318.2 328.2 308.2 318.2 328.2 338.2 348.2 358.2

0.5968 0.5660 0.5515 0.4800 0.3561 0.3315 0.3405 0.3588 0.3785

−3.334 −3.286 −3.287 −2.728 −2.165 −2.082 −2.164 −2.289 −2.418

0.989 0.979 0.980 0.999 0.999 1.000 0.999 0.998 0.996

lit. data3 and this work lit. data3 and this work lit. data3 and this work this work only this work only this work only this work only this work only this work only

308.2 318.2 328.2 308.2 318.2 328.2 338.2 348.2 358.2

0.5990 0.5740 0.5615 0.3740 0.2639 0.2710 0.2960 0.3227 0.3478

−3.387 −3.362 −3.395 −2.194 −1.683 −1.763 −1.930 −2.102 −2.261

0.983 0.977 0.971 0.994 0.988 0.996 0.999 0.999 0.999

lit. data4 and this work lit. data4 and this work lit. data4 and this work this work only this work only this work only this work only this work only

313.2 323.2 333.2 313.2 323.2 333.2 343.2 353.2

0.4027 0.3815 0.3888 0.2033 0.2088 0.2359 0.2627 0.2883

−2.488 −2.442 −2.523 −1.340 −1.413 −1.591 −1.761 −1.922

0.975 0.972 0.978 0.963 0.993 0.998 0.997 0.995

lit. data4,5 and this work lit. data4,5 and this work lit. data4,5 and this work lit. data5 and this work lit. data5 and this work this work only this work only this work only this work only this work only

313.2 323.2 333.2 343.2 353.2 313.2 323.2 333.2 343.2 353.2

0.3953 0.3483 0.3269 0.3155 0.3357 0.1281 0.1643 0.2006 0.2354 0.2691

−2.394 −2.216 −2.150 −2.098 −2.226 −0.921 −1.159 −1.390 −1.609 −1.819

0.962 0.940 0.942 0.980 0.981 0.963 0.995 0.997 0.996 0.991

lit. data1,2,4 lit. data1,2,4 lit. data1,2,4 lit. data1,2 lit. data1,2

313.2 323.2 333.2 343.2 353.2

0.2940 0.3013 0.3288 0.2632 0.2894

−1.945 −1.993 −2.164 −1.807 −1.968

0.880 0.877 0.927 0.996 0.997

%AAD

vapor phase correlation highest xCO2

C8EE System 4.249 all data 4.266 all data 5.021 all data C10EE System 3.205 0.875 4.803 0.875 5.221 0.875 0.191 0.875 0.177 0.875 0.119 0.875 0.189 0.875 0.289 0.875 0.360 0.875 C12EE System 4.413 0.893 5.512 0.855 6.778 0.855 0.525 0.893 0.728 0.893 0.359 0.893 0.229 0.893 0.203 0.893 0.211 0.893 C14EE System 3.185 0.872 4.201 0.872 3.633 0.872 1.333 0.905 0.462 0.905 0.300 0.905 0.299 0.905 0.380 0.905 C16EE System 3.887 0.867 4.971 0.867 4.675 0.898 1.954 0.898 1.989 0.898 0.867 0.907 0.369 0.907 0.228 0.093 0.357 0.907 0.518 0.907 C18EE System 7.944 0.900 7.490 0.900 6.576 0.900 0.716 0.900 0.673 0.900

AEE

BEE

R2

%AAD

highest xEE

21.3 19.0

0.0064 0.0129

18.9 7.22 5.27 4.52 4.68

0.0187 0.0187 0.0187 0.0187 0.0187

b b b

4.192 4.930

−30.35 −34.57

11.099 8.731 7.333 6.393 5.642

−71.37 −57.40 −48.88 −43.06 −38.39

9.603 4.804 3.734

−61.00 −34.45 −28.39

10.760 9.269 8.227 7.494 6.792

b 0.972 0.972 b 0.850 0.981 0.990 0.992 0.993

7.46 17.6 20.4

0.0108 0.0108 0.0054

−70.75 −61.86 −55.35 −50.69 −46.21

0.998 0.988 0.968 b 0.970 0.980 0.983 0.986 0.987

10.3 8.74 8.08 7.16 6.80

0.0175 0.0175 0.0175 0.0175 0.0175

7.798 8.311 7.986 8.745 8.740 8.303 7.855 7.571

−53.49 −57.00 −54.88 −59.37 −59.78 −56.93 −53.93 −51.94

0.981 0.889 0.922 0.981 0.994 0.996 0.996 0.996

10.7 11.9 8.00 8.31 4.62 3.59 3.04 3.10

0.0180 0.0152 0.0152 0.0152 0.0152 0.0152 0.0152 0.0152

3.216 3.349 3.067 8.869 8.480 7.136 8.141 7.867 7.767 7.336

−25.27 −26.07 −24.19 −61.31 −58.58 −50.92 −57.27 −55.34 −54.45 −51.48

0.386 0.367 0.333 0.880 0.883 0.996 0.999 0.989 0.996 0.990

34.8 36.2 37.2 19.0 18.8 3.70 1.65 5.03 3.46 5.34

0.0192 0.0192 0.0192 0.0192 0.0192 0.0135 0.0135 0.0135 0.0135 0.0135

5.987 4.219 5.765

−44.35 −32.72 −42.44

0.808 0.666 0.756 b b

25.7 36.2 29.7

0.0140 0.0150 0.0150

ACO2, BCO2, AEE and BEE are correlation parameters for eq 1 and eq 2 with the Pearson’s R2 value and the % AAD indicating the quality of the fit. No correlation of vapor phase due to insufficient data.

than 0.02. These cutoff points are partly arbitrary but for both phases generally indicate the region where the correlations appear to hold true. Additionally, the liquid phase cutoff is similar to that of Fornari et al.16 and Hernández et al.17 At times this

cutoff was relaxed slightly to ensure at least four data points are used, provided the fit was still good. All systems studied in this work as well as the CO2/ethyl octanoate and CO2/ethyl octadecanoate systems were correlated J



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Figure 6. Modified Chrastil model correlation of the experimental phase transition pressure (P) as a function of mole fraction ethyl ester (xEE) at 308.2, 328.2, and 348.2 K for the systems (a) CO2/ethyl decanoate, (b) CO2/ethyl dodecanoate, and at 313.2, 333.2, and 353.2 K for the systems (c) CO2/ ethyl tetradecanoate and (d) CO2/ethyl hexadecanoate (key: ○ = 308.2 or 313.2 K, □ = 328.2 or 333.2 K, + = 348.2 or 353.2 K; dashed line modified Chrastil model prediction using parameters based on all data for the system, solid line modified Chrastil model prediction using parameters based on experimental data only).

do not predict the phase transition of the data measured in this work as accurately the solid lines (based on the data generated in this work). Conversely, the parameters based on all the data do, as expected, predict the combined data sets better. Importantly, it is noted that the correlation parameters are sensitive to the data set used and the correlations should not be extrapolated beyond the compositional range to which they were fitted. If one considers the fundamental origin of the model, the gradient of the relationship should be temperature independent. However, perusal of Table 6 shows that this is clearly not the case. Within a system the ACO2 and the AEE values differ significantly. To compare the effect of temperature of the model parameters on a fair basis, only parameters based only on data measured in this work are compared, as shown in Figure 7. For the liquid phase there appears to be a regular and similar, although not linear, trend in the parameter with respect to temperature and ester carbon number (see Figure 7a,b). However, for the vapor phase (Figure 7c,d) more scatter in the parameters is observed. It is clearly noted that the parameters are functions of temperature and carbon number, yet too little data are available to make definitive trends. As it is clear that the degree of correlation is dependent on the data sets used, for correlation of the data with the MT and the Narayan et al. models, the data measured in this work as well as the complete data sets was used. Additionally, to ensure comparison on an equal basis, the same data set were used for correlation purposes.

using the modified Chrastil model (eq 1 and eq 2). At each temperature where data are available, the model parameters were correlated using two data sets: First, all available data were used and then second, only data measured in this work were used. The resultant correlation parameters and their fitting ability, as well as the cutoff for that particular correlation, are given in Table 6. From the correlation results in Table 6 it is noted that the liquid phase was generally well correlated. At low temperatures it was difficult and at times impossible to correlate the vapor phase due to limited data. As such, when less than four data points were available, correlation was omitted. In general, reasonable correlation of the vapor phase was obtained. It is also noted that when using a single set of data for correlation, albeit data measured data from this work or from a literature source, improved correlation is attained than when using all available data. This observation can be explained by the fact that a single data set generally has less scatter and at times only encompasses a limited compositional range. Comparing the resultant parameters attained from the two sets of correlation data, it is noted that different values, albeit of the same order of magnitude, are attained. The same observation can be noted when studying the application of the Chrastil model by Narayan et al. for the solubility of ester in supercritical CO2 fitted to various data sets. When the data set used for correlation is limited to the data measured in this work, a smaller compositional range is used therefore focusing the data on a limited part of the phase transition curve. These observations are re-enforced when considering Figure 6. The dashed lines (based on all data) K



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Figure 7. Modified Chrastil model parameters fitted to experimental data as a function of temperature (T): (a) ACO2, (b) BCO2, (c) AEE and (d) BEE (key ○ = C10EE, △ = C12EE, □ = C14EE, ◊ = C16EE, dashed line shows trend in data).

Table 7. Correlation Results for the MT-Model Using Measured and Literature Data for Both Liquid and Vapor Phasesa liquid phase correlation data set

a

A′CO2

B′CO2

C′CO2

this work only lit. data6 and this work

−830.4 1260

1.057 3.026

17.48 9.54


−1010 1864

0.8094 2.876

18.21 7.68


−1382 339.1

0.6215 1.682

19.48 13.05

this work only lit. data4,5 and this work

−1709 −184.5

0.5065 1.350

20.60 14.99

vapor phase correlation R

2

%AAD

C10EE System 0.979 3.11 0.879 32.8 C12EE System 0.956 4.21 0.859 42.2 C14EE System 0.942 4.41 0.794 35.0 C16EE System 0.906 5.36 0.820 26.8

AEE ′

BEE ′

CEE ′

R2

%AAD

−4771 −4594

6.285 5.633

18.14 18.14

0.930 0.978

12.2 13.3

−4894 −4356

6.545 5.403

17.09 17.09

0.957 0.983

12.8 18.5

−5114 −5060

5.381 5.290

18.47 18.47

0.934 0.921

15.2 16.2

−7027 −5725

4.856 2.929

23.86 23.86

0.987 0.483

6.1 45.1

AEE ′ , BEE ′ , CEE ′ , A′CO2, B′CO2 and C′CO2, are correlation parameters for eq 6 and eq 7 with the Pearson’s R2 value indicating the quality of the fit.

illustrated for the system CO2/ethyl decanoate in Figure 8, with the overall pressure prediction shown in Figure 8a. For the vapor phase it is noted that a good fit was obtained ′ when using the data obtained in the current work. The same CEE parameters were then transferred to the data set containing all the data, and it is observed a very good fit was obtained with A′EE and B′EE from that fit. While it was found that the A′EE, B′EE, and C′EE parameters are strongly intercorrelated, changing the C′EE does not result in a significant change in fitting ability. Figure 8b illustrates how well the models fit the data (the correlations lie on-top of each other). One advantage of the MT model is that the model already incorporates temperature and therefore parameters are not required for each temperature. Figure 8c suggests that

The second model evaluated was the MT model. As the model was derived for dilute solutions, it was not be applied in the mixture critical region. Additionally, as the composition is essentially correlated against density the same issues in the critical region were expected as noted for the modified Chrastil model. Although developed for the vapor phase, the MT model was tested here for the liquid phase as well, similar to that of the modified Chrastil model for the liquid phase. The vapor phase data were plotted as T ln(xEEP) − CEE ′ T versus ρCO2 and the value of C′EE changed to obtain the best linear fit. From this linear fit the A′EE and B′EE values were then obtained. The same approach was followed for the liquid phase and the fitted parameters are given in Table 7 and the ability of the model to fit the data is L



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Figure 8. Correlation of the CO2/ethyl decanoate system with the MT model: (a) phase transition pressure prediction for the entire compositional range, (b) detail of the vapor phase pressure prediction, (c) correlation of the vapor phase data as per eq 6, and (d) correlation of the liquid phase data as per eq 7 (key: ○ = 308.2 K, △ = 318.2 K, □ = 328.2 K, ◊ = 338.2 K, + = 348.2 K, × = 358.2 K; dashed line MT model prediction using parameters based on all data for the system, solid line MT model prediction using parameters based on experimental data only).

Lastly, the model of Narayan et al. is considered. The same approach as for the MT model was used. From a plot of E ln(x EEϕ) − T3 vs ϕ the values of E3 were obtained using the data measured in this work. Again, when fitting the data measured in this work in combination with literature data, the E3 value fitted to the data measured in this work was retained as good fits resulted, and the E1 and E2 values were obtained from the fit. The parameters obtained from the correlation (Table 8) are similar in magnitude and sign to that of Narayan et al.

for the vapor phase the model temperature dependence is correct as data points from the various temperatures lie approximately on the same line. The correlation of the liquid phase data was, unfortunately, not as successful as that of the vapor phase. When considering the correlation of the data generated in this work acceptable results are obtained (see Figure 8d, lower data set, solid line in Figure 8a, and the low %AAD values in Table 7). However, if the entire ′ 2 value is data set is used, the correlation ability is poor. If a CCO selected to ensure the data at the various temperatures falls onto one another, a nonlinear shape is obtained. Conversely, if C′CO2 is fitted to minimize the error, a strong temperature dependence is noted (see Figure 8b, upper data set). Additionally, when using the fitted parameters to predict the data, incorrect xCO2 values are often obtain. At times xCO2 values greater than unity are predicted at higher pressures and lower densities. At the same time, for lower pressures and higher densities the values of xCO2 move toward a minimum and then increase again resulting in a sideways parabolic shape. It is therefore clear that the MT model is not able to predict the solubility of CO2 in ethyl esters data in the broad liquid compositional range considered in this work. The model was developed under the assumption of a dilute solution. It is thus possible that in the compositional range considered here the solution is not sufficiently dilute for the assumption and its implication to hold true. Overall, the MT model performed well in the region for which it was developed, that is, for solute in a supercritical solvent. However, extension to solvation of supercritical CO2 in a solute is generally not successful except for within a small compositional range.

Table 8. Correlation Results for the Narayan et al. Model Using Measured and Literature Data for the Vapor Phase Onlya data set this work only lit. data6 and this work this work only lit. data3 and this work this work only lit. data4 and this work this work only lit. data4,5 and this work

E1

E2

C10EE System −12.56 83.49 −12.38 80.89 C12EE System −13.17 73.53 −12.54 67.98 C14EE System −9.798 59.41 −9.770 59.55 C16EE System −8.947 44.17 −5.301 28.02

E3

R2

−823 −823

0.917 0.992

59.0 51.7

−923 −923

0.945 0.990

107 88.4

−2086 −2086

0.994 0.955

784 839

−2137 −2137

0.991 0.516

1730 1784

%AAD

a

E1, E2, and E3 are correlation parameters for eq 10 with the Pearson’s R2 value indicating the quality of the fit.

M



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Figure 9. Correlation of the CO2/ethyl decanoate system with the Narayan et al. model: (a) correlation of the vapor phase data as per eq 10 and (b) vapor phase transition pressure correlation (key: ○ = 308.2 K, △ = 318.2 K, □ = 328.2 K, ◊ = 338.2 K, + = 348.2 K, × = 358.2 K; dashed line MT model prediction using parameters based on all data for the system, solid line MT model prediction using parameters based on experimental data only).

Figure 9a shows that a good, temperature independent fit was obtained and Figure 9b shows that visually the correlations fit the data well. However, while Table 8 re-enforces the good fit of the data during correlation (good Pearsons R2 values), the % AAD suggests that the parameters are not able to predict the data as well, especially at higher molecular mass ethyl esters. Narayan et al. only reported the fit of the correlation equation (eq 10) and did not comment on the ability of their model (or the Chrastil or MT models) to predict the phase behavior data, nor did they plot the prediction (i.e phase transition pressure as a function of composition or vice versa). The poor ability of the model to predict current systems may cause the compositions to be a result of the method used to fit the parameters. As for the MT model, intercorrelation of the data was observed. Alternatively, the inability of the Narayan et al. model to predict the data may also be due to model structure. More advanced techniques and a more detailed investigation of the Narayan et al. model, beyond the scope of the current work, may provide a more definitive outcome of the true ability of the model to predict the data. Overall, the simple correlations considered provide a method to correlate the vapor-like data with reasonable accuracy. All models fitted the vapor phase data well, with the modified Chrastil and MT models giving good correlations. The modified Chrastil model provided a better correlation but required parameters that need to be fitted at each temperature. Conversely, the MT-model provided a model that can be used throughout the temperature range in which it was correlated. On the other hand, the liquid phase correlations were not as successful. Only the modified Chrastil model provided partially reliable fits and correlation. It may be that the range of compositions used for correlation were ambitious, as the correlations using only a limited compositional range, such as the data from this work, were significantly more successful. However, the underlying assumption of dilute CO2 in a solute may not hold true. Therefore, if the correlation of a large compositional range in the liquid phase is required, a more fundamental approach, such as equations of state, may be necessary to obtain sufficiently good correlation.

critical, and vapor phase regions were obtained in the temperature range 308 to 358 K. The measured data compare well to and complement previously published data. The data show that an increase in temperature leads to an increase in pressure, which is not necessarily linear but can be described well with a polynomial relationship. At higher temperatures the mutual solubility of the components is lower. Conversely, the mutual solubility increases at constant temperature with an increase in pressure and at constant pressure with a decrease in temperature. Additionally, an increase in carbon number of the ethyl ester showed an ever increasing increase in phase transition pressure, indicating complex molecular interactions. This increase in phase transition pressure with carbon number also indicates that supercritical CO2 has the ability to fractionate ethyl esters based on its hydrocarbon backbone length. A modified Chrastil model, the MT model, and the model of Narayan et al. were fitted to the data. For the modified Chrastil model, the results show that ln xi vs ln ρCO2 provides an approximately linear relationship for both the liquid-like and vapor-like phases, thus yielding good results for this model. The modified Chrastil model parameters are both functions of temperature and ethyl ester carbon number, and are sensitive to the data set to which they are correlated. While the MT and Narayan et al. models provided good fits, for these two models only the MT model applied to the vapor phase provided good correlation of the results. Therefore, the modified Chrastil model for both vapor and liquid phases as well as the MT model for the vapor phase is able to provide fair correlation of the data. While predictive use of these model is limited, their simple structure allows for easy correlation of data making such models a useful tool for interpolation of phase transition data for these type of systems.

5. CONCLUSIONS This work achieved its aim by conducting a systematic study of the phase behavior of the homologous series of CO2/saturated ethyl esters. Additional phase behavior data for the systems CO2/ ethyl decanoate, CO2/ethyl dodecanoate, CO2/ethyl tetradecanoate, and CO2/ethyl hexadecanoate in the liquid phase, mixture

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AUTHOR INFORMATION

Corresponding Author

*Email: [email protected]. Tel: +27 21 8084487. Fax: +27 21 8082059.

Cara E. Schwarz: 0000-0001-5513-2105 Funding

This work is based on the research supported in part by the National Research Foundation (NRF) of South Africa. The author acknowledges that opinions, findings, and conclusions or N



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recommendations expressed herein are that of the authors and that the NRF accepts no liability whatsoever in this regard. Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS The assistance of Mr. B.J. Daniels with some of the experimental measurements is hereby acknowledged. REFERENCES

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