Solubility of Ethylene Glycol in Supercritical Carbon Dioxide at

Article pubs.acs.org/jced

Solubility of Ethylene Glycol in Supercritical Carbon Dioxide at Pressures up to 19.0 MPa Chun-yue Jiang,† Zhi-juan Sun,*,† Qin-min Pan,‡ and Jian-biao Pi† †

The Zhejiang Province Key Laboratory of Biofuel, College of Chemical Engineering and Materials Science, Zhejiang University of Technology, Hangzhou, Zhejiang Province (310014), China ‡ Department of Polymer Science and Engineering, Soochow University, Suzhou, Jiangsu Province (215123), China S Supporting Information *

ABSTRACT: The experimental equilibrium solubility of ethylene glycol in supercritical carbon dioxide was measured by the static method at temperatures between (313.15 and 353.15) K and pressures up to 19.0 MPa, and the effects of temperature and pressure on the solubility were investigated. The experimental results show that the solubility ranged from ethylene glycol mole fraction of 0.83·10−2 (353.15 K, 7.0 MPa) to 4.29·10−2 (353.15 K, 19.0 MPa), and the solubility increased with increasing pressure at a constant temperature, but a crossover pressure point (about 16.0 MPa) has been observed in the solubility isotherms at the temperature range from (313.15 to 353.15) K. Moreover, the experimental results were correlated with the Peng−Robinson equation of state using the quadratic mixing rules of the two-fluid van der Waals (vdW2) as well as the modified associative model; both correlations demonstrated satisfactory results, with an average absolute relative deviation (AARD) less than 5 %.

1. INTRODUCTION The utilization of supercritical carbon dioxide (SCCO2) has attracted significant attention because of its nontoxicity, nonflammability, low cost, and abundance, and it has moderate critical constants (Tc = 304.15 K, Pc = 7.38 MPa). Previous studies1,2 have shown that SCCO2 has adjustable solvent power, enhanced mass transfer characteristics, and low surface tension. Because of these attributes, SCCO2 is promising to be an environmentally benign replacement for the organic solvents currently used in various synthesis or separation processes, such as melt/solid phase polymerization, supercritical fluid extraction, and so on.3−6 In most application fields, step-growth polymerization based on SCCO2 becomes a spotlight in the research of green chemical engineering. Although the traditional process of stepgrowth polymerization like melt/solid phase polymerization without solvent can avoid the use of environmentally detrimental solvent mixtures, it is difficult to attain the polymer products with a high molecular weight because of the high viscosity of the polymer melt near the end of the polymerization.7 Fortunately, SCCO2 as a continuous phase or sweep fluid in step-growth polymerization is able to swell or plasticize the polymer, thus producing both a reduction in melt viscosity and an increase both chain mobility and free volume in the melt phase. Additionally, the enhancement of condensate removal is a key step to keep the polymerization continuing for the stepgrowth polymerization, compared to the conventional vacuum © 2012 American Chemical Society

method that requires tedious process controls and extensive capital investment; SCCO2 as sweep fluid may carry out condensates of step-growth reactions from the reaction mix and drive the polymerization by condensate removal.8,9 The use of SCCO2 as a continuous phase for step-growth polymerization has been extensively investigated, like polyesters, polyamides, and polycarbons.10−12 However, the enhancing mechanism of SCCO2 for step-growth polymerization in the high viscosity melt/solid-phase polymerization process is not addressed in the previous work, which is closely related to the thermodynamics of the process; the solubility of small molecules (condensates or byproducts) in SCCO2 is important basis data to predict the phase equilibrium of these compounds in the polymerization process and provide key information in supercritical fluid technology.13,14 Therefore, solubility data of condensates in SCCO2 are among the most important thermophysical properties that are essential to the efficient design of supercritical processes for step-growth polymerization, and more investigations for the solubility of condensates in SCCO2 are still needed. Poly(ethylene terephthalate) (PET) is an important engineering plastic with a wide range of applications in industry,15,16 and ethylene glycol (EG) is the condensate in Received: February 23, 2012 Accepted: May 2, 2012 Published: May 9, 2012 1794

dx.doi.org/10.1021/je3002249 | J. Chem. Eng. Data 2012, 57, 1794−1802

Journal of Chemical & Engineering Data

Article

Figure 1. Schematic diagram of the experimental apparatus. (1) CO2 cylinder, (2) pressure-regulating valve, (3) electric contact pressure gauge, (4) low-temperature thermostat bath, (5) digital thermometer, (6) pressure-regulating valve, (7) syringe pump, (8) electric contact pressure gauge, (9) safety valve, (10) pressure-regulating valve, (11) preheater, (12) temperature probe, (13) pressure-regulating valve, (14) precision pressure gauge, (15) pressure transducer and indicator, (16) high-pressure equilibrium cell, (17) magnetic stirrer, (18) magneton, (19) electric heating rods, (20) temperature controller, (21) outlet valve, (22) sampling valve, (23) fidelity sampler, (24) sampling valve, (25) gas chromatography, (26) computer.

In the feed system of CO2, pure CO2 was cooled to liquid by a low-temperature thermostat bath and then pressured by a syringe pump (2J-XZ20/40), and the syringe pump stopped automatically when the system pressure was larger than the set values ((7.0 to 19.0) MPa). After that, the liquid CO2 was preheated to gasification and feed CO2 to the high-pressure equilibrium cell. In the equilibrium system, the high-pressure equilibrium cell (200 mL) equipped with four electric heating rods was designed to allow the measurements at pressures up to 40 MPa and temperatures up to 573.15 K. In this system, CO2 flow and EG were stirred adequately by a magnetic stirrer for a certain period until the dissoving equilibrium was reached. The time needed to reach the equilibrium for all of the systems studied was found to be within 2 h; thus, the equilibrium time of 2 h was adopted in this work. The equilibrium pressure was measured using a pressure transducer (HQ-1000), which is fixed in pipe just before the equilibrium cell to avoid its channel was jammed. The temperature inside the cell was measured and adjusted to the set values by a temperature controller with a temperature probe (XMTA-7512). The resolutions of the pressure transducer and the temperature probe are 0.2 MPa and 0.1 K, respectively. In the sampler system, a fidelity sampler with two sampling valves (22 and 24) was connected to the high-pressure equilibrium cell by an outlet valve (21), and the designed volume of the fidelity sampler was 10 mL. When CO2 flow and EG achieved the dissolving equilibrium in the equilibrium cell, the outlet valve and sampling valve (22) were opened gradually to start sampling, but the other sampling valve (24) was closed, and the mixed air phase was fed to the fidelity sampler. The process of sampling was slow-operating, and meanwhile the syringe pump was restarted to feed some fresh CO2 to maintain constant pressure of the equilibrium cell. When the system pressure rises steeply, that means the fidelity sampler is filled with the sample of the mixed air phase, the syringe pump was stopped immediately, and the system was left for some minutes to achieve equilibrium in the cell and fidelity sampler again. Then the outlet valve (21) and sampling valve (22) were closed, and the sample with high fidelity was obtained and placed in a refrigerator for analysis by the gas chromatographic

the step-growth polymerization of PET, so it is important to measure the solubility of EG in SCCO2 when SCCO2 is used as a continuous phase in step-growth polymerization. However, to the best of our knowledge, no detailed experimental solubility data of EG in SCCO2 at various temperatures and pressures are available in the literature. Although the DeSimone group17 once described simply that the weight solubility of EG in SCCO2 is (2 to 3) wt %, the experimental conditions and their detailed results of the solubility of EG in SCCO2 are not disclosed as much as we know. Recently, Galvao et al. reported solubility data of carbon dioxide in ethylene glycol, but its measurements were performed at the temperatures of (303, 323, 373, 398, and 423.15) K and pressures up to 6.3 MPa for mixtures containing carbon dioxide and ethylene glycol.18 In this work, an apparatus based on a static-analytic method was utilized to perform high pressure equilibrium measurements with uncertainties estimated less than 5 %; the solubility of EG in SCCO2 was investigated at temperatures between (313.15 and 353.15) K and pressures up 19.0 MPa, and the experimental results were correlated by the Peng−Robinson equation of state and the modified associative model. It is expected that this study will be of benefit to insight the high-pressure equilibrium of EG in SCCO2 and design effectively the melt/solid state polymerization processes of PET based on SCCO2 technology in industry.

2. EXPERIMENTAL SECTION 2.1. Materials. Carbon dioxide with a minimum purity of 0.9999 was purchased from Hangzhou Jingong Industrial Gas Co. Ltd. Analytical grade styrene, ethanol, and EG were supplied by J&K Scientific Ltd., with a minimum purity of 0.997 mass fraction. 2.2. Equipment and Procedures. The experimental apparatus (shown in Figure 1) based on a static-analytic method assembled in this work was utilized to measure the solubility of EG in SCCO2. The whole system of the apparatus was composed of a CO2 feed system, an equilibrium unit with a high-pressure equilibrium cell, a sampler system with high fidelity (fidelity sampler), and a gas chromatographic analysis system, which are described in detail as follows. 1795



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method (see Section 2.4). Because the volume of the fidelity sampler is much less than that of the equilibrium cell, the pressure drop is very small, and the system pressure can return quickly to the original set values, thereby the fidelity sampler and slow-operating sampling could ensure that the obtained sample and the mixed air phase in the equilibrium cell are same in this work. 2.3. Solubility Measurement. Prior to operating experiments, the whole apparatus was cleaned, and gas tightness at the connection was checked; the fidelity sampler, the outlet line, and valves were flushed with ethanol. At first, a suitable amount of EG (about 50 mL) and a magneton were loaded into the high-pressure equilibrium cell, and then the cell was sealed tightly. The system was heated to the desired temperature and pressurized with CO2 from the syringe pump until the pressure increased gradually to a set value. The magnetic stirrer was turned on, and CO2 flow and EG were mixed adequately for a period of time of about 2 h until the system achieved the dissolving equilibrium of CO2 and EG. Second, after the equilibrium is reached in the cell, the fidelity sampler was used to start sampling (see Section 2.1), and the sample with high fidelity was obtained. Before sampling, the fidelity sampler was preheated to the same temperature of the cell in an air bath to avoid precipitating of EG from CO2 in the process of sampling. Third, the fidelity sampler filled with the sample was moved away from the apparatus and placed in a refrigerator to cool for 20 min, and the mixture in the fidelity sampler was passed into ethanol solution slowly to collect EG in the sample; after that the fidelity sampler were flushed with ethanol several times until no obvious EG traces (< 0.1 ppm) were detected, and all above ethanol solution were collected together and dried to get enriched EG−ethanol solution. Finally, the enriched EG−ethanol solution was diluted to the specific volume with ethanol, the EG concentration in the final solution was analyzed by a gas chromatographic method (see Section 2.4), and then the solubility of EG in SCCO2 was determined. At each condition, the experiment was repeated at least three times to make sure the experimental results are reliable. 2.4. Gas Chromatographic Analysis. For the analysis of the solubility of EG in SCCO2, a gas chromatograph (type Trace GC 2000 Series, Thermo-Quest CE Instruments) with a flame ionization detector was used. The detector and injector temperatures were set to (553.15 and 490.15) K, respectively. First, mixtures of fixed concentrations of EG in ethanol were used to establish a calibration curve (shown in Figure 2), and the square of correlation coefficient of the calibration curve was 0.9993. According to the calibration curve, the ethylene glycol− ethanol mixtures (obtained samples) were analyzed, and the concentration (C) of EG in SCCO2 was determined by eq 1: C=

m ·f m2 = s V V

Figure 2. Calibration curve of gas chromatographic analysis (A is the peak area of the obtained sample).

Table 1. Solubility of EG in SCCO2 together with the Density of CO2 at Each Operating Condition T/K

P/MPa

C/g·L−1

ρ/g·L−1

y2·102

F2/%

313.15

7.0 9.0 11.0 13.0 15.0 17.0 19.0 7.0 9.0 11.0 13.0 15.0 17.0 19.0 7.0 9.0 11.0 13.0 15.0 17.0 19.0 7.0 9.0 11.0 13.0 15.0 17.0 19.0 7.0 9.0 11.0 13.0 15.0 17.0 19.0

3.70 10.36 17.40 21.37 25.41 29.00 30.53 2.61 5.37 10.78 16.56 22.03 28.09 31.50 2.34 4.07 7.67 12.69 18.55 26.34 32.50 1.90 3.26 5.63 9.30 14.60 24.81 33.49 1.66 2.62 4.40 7.09 11.69 23.33 35.97

207 490 677 749 779 805 831 178 291 495 637 704 736 768 161 230 364 501 604 668 707 149 207 296 403 505 585 639 140 190 257 340 428 507 569

1.25 1.48 1.79 1.98 2.26 2.49 2.54 1.03 1.29 1.52 1.81 2.17 2.63 2.83 1.02 1.24 1.47 1.76 2.13 2.72 3.16 0.90 1.10 1.33 1.61 2.01 2.92 3.58 0.83 0.97 1.20 1.46 1.90 3.16 4.29

1.76 2.07 2.51 2.77 3.16 3.48 3.54 1.45 1.81 2.13 2.53 3.03 3.68 3.94 1.43 1.74 2.06 2.47 2.98 3.79 4.39 1.26 1.55 1.87 2.26 2.81 4.07 4.98 1.17 1.36 1.68 2.04 2.66 4.40 5.95

323.15

333.15

343.15

353.15

(1)

Here m2 is the weight of EG in the sample, f is the weight fraction of EG in the sample, and ms and V are the weight and volume of the sample, respectively. Each reported datum was an average of at least three replicated sample measurements, and the relative deviation between the measurements and the average of at least three replicated sample measurements was always less than ± 5 % in terms of EG concentration. The resulting weight solubilities of EG in SCCO2 have been shown in Table 1.

2.5. Reliability Compliance Test. To guarantee the accuracy of the measured solubility data, experimental measurements had been done with careful calibration of the 1796



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equation (shown in eq 7) to predict the density of CO2 at the temperature range of (272.05 to 355.35) K and the pressure range of (7.6 to 24.8) MPa. According to the regression equation and the experimental conditions in this work, the regression equation coefficients of a, b, c, d, e, f, and g at each operating condition were obtained from the data given by McCollum and Ogden (shown in the Supporting Information, part B), and thus the densities of CO2 at each operating condition in this work were calculated (shown in Table 1) and compared to those of the reported experimental data.21 The maxima of RD and AARD for the density of CO2 between the calculated values and the reported experimental data are only 1.86 % and 0.65 %, respectively.

measuring devices like pressure transducers, temperature probes, and the volume of the fidelity sampler by the considerable repeatability measurements. To calibrate the temperature controller with a temperature probe (XMTA7512) and pressure transducer (HQ-1000), a Pt-100 thermometer (resolution 0.001 K) and a precision pressure gauge (resolution 0.05 MPa) were used as references, respectively. The results show that the relative deviations of the measurement value from the reference value for the temperature controller with a temperature probe (XMTA7512) and pressure transducer (HQ-1000) are less than 1 %, and the relative deviation of the volume of the fidelity sampler is less than 0.5 %. To provide accurate and reliable equilibrium solubility, the solubility of liquid solute (styrene) in SCCO2 over the pressure range of 7.0 to 18.0 MPa and at temperature of 323.15 K was measured. The measured solubility of styrene in SCCO2 was compared to the reported values (shown in the Supporting Information, part A).19 The results are quantitatively similar to those reported previously, and the relative deviation between this experimental results and the reported values is less than 10 %. To set the margin of error within acceptable defined deviations and test the accuracy of the correlation results, the relative deviation (RD) and the average absolute relative deviation (AARD) for the mole fractions of EG in the SCCO2 between experimental and calculated values are defined by eqs 2 and 3, respectively. ycal − yexp RD% = · 100 % yexp (2)

ρ = aP 6 + bP 5 + cP 4 + dP 3 + eP 2 + fP + g

With the above results of the weight solubility of EG in SCCO2 and the density of CO2, the mole fraction and mass fraction solubility of EG in SCCO2 were calculated and shown in Table 1. Over the entire range of experimental conditions, it can be seen that the mole fraction solubility (y2) and the mass fraction solubility of EG (F2) are in the range of 0.83·10−2 to 4.29·10−2 and 1.17 wt % to 5.95 wt %, respectively. According to the reported results from the DeSimone group,17 the mass fraction solubility of EG in SCCO2 is (2 to 3) wt %. Although the experimental conditions and their detailed results of the solubility of EG in SCCO2 are unpublished as we know, their results are quantitatively similar to our experimental data at the temperature range from (313.15 to 353.15) K and the pressure range of (9.0 to 15.0) MPa, which indicates that the measured solubility data of EG in SCCO2 are reliable. Moreover, the measured solubility data of EG in SCCO2 at the wide range of experimental temperature (313.15 to 353.15 K) and pressure (7.0 to 19.0 MPa) in this work would provide important basis data and key information to predict the phase equilibrium of EG in SCCO2 and benefit the research of the enhancing mechanism of SCCO2 for the high viscosity melt/solid-phase polymerization process in step-growth polymerization of PET. 3.2. Effect of Experimental Conditions on the Solubility of EG in SCCO2. The relationship between the mole fraction solubility (y2) of the EG in SCCO2 and the total pressure of the system (P) is illustrated in Figure 3. From

N

AARD% =

∑N = 1 |RD| N

·100 %

(3)

where yexp is the experimental data for the mole fraction of EG in the SCCO2, ycal is the correlated result by the models, and N is the total number of data points. In this work, the accepted absolute values of relative deviations for the calculated mole fractions of EG in the SCCO2 are considered to be within 20 % according to the capabilities of the models for this purpose.

3. RESULTS AND DISCUSSION 3.1. Solubility of EG in SCCO2. The solubility of EG is expressed in terms of the mole fraction (mole fraction solubility, y2) and mass fraction of EG (mass fraction solubility, F2) in SCCO2 when the equilibrium is reached as follows: y2 =

n2 (m 2 / M 2 ) = n2 + n1 (m2 /M 2) + (m1/M1)

(4)

F2 =

m2 ·100 % m2 + m1

(5)

m1 = ρV

(7)

(6)

where n1(n2), m1(m2), and M1(M2) are the mole number, weight, and mole mass of CO2 (EG) in sample, respectively; V is the volume of the sample, which equals to 10 mL; ρ is the density of carbon dioxide, which is determined with the regression method of McCollum and Ogden.20 Based on many reported data of the density of CO2, McCollum and Ogden considered that the density of CO2 was a function of temperature and pressure, and they then proposed a regression

Figure 3. Solubility isotherms of EG in SCCO2 as a function of pressure: ■, T = 313.15 K; ●, T = 323.15 K; ⧫, T = 333.15 K; ★, T = 343.15 K; ▲, T = 353.15 K. 1797



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Figure 3, it is clear that the solubility increased with increasing pressure at a constant temperature, which exhibits trends that are typical of the solubility of nonvolatile organic molecules in SCCO2.22−24 For example, the solubility increased from 0.83·10−2 to 4.29·10−2 at the temperature of 353.15 K when the pressure increased from (7.0 to 19.0) MPa. It is mainly due to the fact that the density and solubility parameter of SCCO2 increase with the increase of pressure at a constant temperature, and thus the solvent power of SCCO2 is stronger at higher pressures, accordingly the solubility of solute in SCCO2 increase with increasing density of CO2 (data from Table 1), as shown in Figure 4. These results indicate that the solubility of the EG in SCCO2 obeys the universal rules of the binary system for phase equilibrium.22

Figure 5. Relationship between the solubility of EG in SCCO2 and temperature: ■, P = 7.0 MPa; ●, P = 9.0 MPa; ★, P = 11.0 MPa; ⧫, P = 13.0 MPa; ▲, P = 15.0 MPa; □, P = 17.0 MPa; ○, P = 19.0 MPa.

(EG) vapor pressure increases and solvent's (CO2) density decreases with increasing temperature. At the crossover point, these two competitive factors affect balance. In this work, when the experimental pressure is less than the crossover pressure (16.0 MPa), the effect of the density of CO2 on the solubility dominates and that of solute's (EG) vapor pressure is minor, the solubility decreases with increasing temperature as the density of CO2 decreases with increasing temperature; however, when the experimental pressure is higher than the crossover pressure (16.0 MPa), the effect of solute's (EG) vapor pressure on the solubility dominates, so the solubility increases with increasing temperature. Such results illuminate that the solubility of EG in SCCO2 is dependent on the experimental pressure, temperature, and the density of CO2, and the solubility of EG in SCCO2 can be enhanced by improving the temperature above the crossover pressure or reducing the temperature below the crossover pressure. 3.3. Correlation of the Experimental Solubility Data. Usually, the equation of state (EOS) model can be applied to correlate solubility of high boiling compounds in supercritical fluid. In this work, the Peng−Robinson equation of state was used for the correlation of the experimental results of the EG solubility in SCCO2, in the view of its widespread use in highpressure phase equilibrium and the confirmed accuracy.27 The Peng−Robinson equation of state28 (seen in eqs 8 to 12) and its characteristic terms of the equations are given in relation to pure component critical state constants such as the thermodynamic critical temperature (Tc,i) and pressure (Pc,i) as well as the molecular acentric factors (ωi). Furthermore, a and b are the attraction and covolume parameters of the equation of state, respectively. The constants for EG and CO2 are shown in Table 2.29

Figure 4. Relationship between the solubility of EG in SCCO2 and the density of CO2: ■, T = 313.15 K; ●, T = 323.15 K; ⧫, T = 333.15 K; ★, T = 343.15 K; ▲, T = 353.15 K.

In addition, a crossover pressure point has been observed in solubility isotherms from Figure 3; it is about 16.0 MPa for EG in SCCO2 at the temperature range of (313.15 to 353.15) K. Below the crossover pressure, the solubility decreases with increasing temperature, whereas an opposite trend is exhibited at pressures higher than the crossover pressure. To explain the effect of temperature on the solubility of EG in SCCO2 at various pressures in detail, the solubility isobars of EG in SCCO2 are shown in Figure 5. From Figure 5, it is found that the solubility increases with increasing temperature at the pressure range of (17.0 to 19.0) MPa, but the solubility decreases with increasing temperature at the pressure range of (7.0 to 15.0) MPa, that is to say that the crossover pressure region is between (15.0 and 17.0) MPa, which agrees with the crossover pressure point of 16.0 MPa in Figure 3. Because the solute (EG) vapor pressure and solvent (CO2) density are affected by the system temperature, then the affected results contributions to the solubility of EG vary with the system temperature. Moreover, the crossover region can also been observed in other SCCO2 systems, such as the ethanamideSCCO2 and 2-propenamide-SCCO2 systems studied by Coelho et al.; the solubility isotherms for both ethanamide and 2propenamide exhibit crossover behavior at around 12 MPa.25 The crossover phenomena could be mainly attributed to the competitions between solute's (EG) vapor pressure and solvent's (CO2) density,26 where their temperature dependences are in opposite directions, which means that the solute's

P=

RT a − V−b V (V + b) + b(V − b)

⎛ 0.4572R2T 2 ⎞ c, i ⎟⎟αi(T ) ai = ⎜⎜ Pc, i ⎝ ⎠ ⎡ ⎛ ⎛ T ⎞0.5⎞⎤2 αi(T ) = ⎢1 + mi⎜⎜1 − ⎜⎜ ⎟⎟ ⎟⎟⎥ ⎢⎣ ⎝ ⎝ Tc, i ⎠ ⎠⎥⎦ 1798

(8)

(9)

(10)



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mi = f (ωi) = 0.37464 + 1.54226ωi − 0.26992ωi 2

b=

(11)

∑ ∑ yyi j (bi + bj)(1 − lij)/2 i

0.0778RTc, i

bi =

Pc, i

where yi and yj designate the gas mole fractions of the component i (CO2) and j (EG), respectively. kij and lij are the binary interaction parameters obtained by fitting the experimental solubility data through the minimization of an objective function (F) defined as eq 15

(12)

Table 2. Physical Properties of EG and CO2 substance

critical temperature Tc/K

critical pressure Pc/MPa

acentric factor ω

j (EG) i (CO2)

719.7 304.2

7.70 7.38

0.487 0.224

⎛ y cal − y exp ⎞2 j j ⎟ F = ∑⎜ exp ⎜ ⎟ yj ⎝ ⎠

∑ ∑ yyi j i

aiaj (1 − kij) (13)

j

(15)

exp where ycal stands for the calculated and experimental j and yj mole fraction values of EG in gas phase, respectively, while n denotes the number of experimental data. The experimental data were correlated by the Peng− Robinson equation of state, and the binary interaction parameters were determined for this system; the experimental and calculated solubilities of EG together with the RD between them are shown in Table 3. From Table 3, the absolute value of

For the calculation of the mixture properties, the two-fluid van der Waals (vdW2) mixing rules with the binary interaction parameter are used as follows: a=

(14)

j

Table 3. Correlation Results of the Solubility of EG in SCCO2 by the Peng−Robinson Equation of State and the Modified Associative Model correlation using the Peng−Robinson equation of state

correlation using the modified associative model

T/K

P/MPa

yexp·102

kij

lij

ycal·102

RD/%

ycal·102

RD/%

313.15

7.0 9.0 11.0 13.0 15.0 17.0 19.0 7.0 9.0 11.0 13.0 15.0 17.0 19.0 7.0 9.0 11.0 13.0 15.0 17.0 19.0 7.0 9.0 11.0 13.0 15.0 17.0 19.0 7.0 9.0 11.0 13.0 15.0 17.0 19.0

1.25 1.48 1.79 1.98 2.26 2.49 2.54 1.03 1.29 1.52 1.81 2.17 2.63 2.83 1.02 1.24 1.47 1.76 2.13 2.72 3.16 0.90 1.10 1.33 1.61 2.01 2.92 3.58 0.83 0.97 1.20 1.46 1.90 3.16 4.29

0.1139

0.1524

0.0956

0.1743

0.1252

0.1925

0.0718

0.1495

0.0810

0.1141

1.18 1.56 1.88 2.03 2.23 2.52 2.59 1.01 1.14 1.46 1.76 2.08 2.45 2.71 1.01 1.12 1.38 1.73 2.09 2.59 3.04 0.96 1.07 1.30 1.66 2.12 2.92 3.74 0.87 0.97 1.18 1.52 2.06 3.18 4.61

−5.71 5.62 5.04 2.38 −1.35 1.18 2.02 −1.84 −11.73 −3.99 −2.76 −4.17 −7.01 −4.10 −0.98 −9.61 −6.25 −1.94 −1.93 −4.77 −3.69 7.14 −3.11 −2.30 3.11 5.54 0.03 4.38 4.35 0.18 −1.61 4.32 8.43 0.65 7.46

1.23 1.52 1.79 2.01 2.22 2.42 2.61 0.98 1.30 1.57 1.85 2.17 2.52 2.89 0.93 1.20 1.55 1.88 2.24 2.64 3.10 0.85 0.96 1.22 1.69 2.31 2.93 3.42 0.89 0.85 1.01 1.42 2.17 3.18 4.20

−1.70 2.85 −0.23 1.54 −1.83 −3.00 2.69 −4.74 0.98 3.04 1.96 −0.07 −4.18 2.10 −8.42 −2.77 5.13 6.56 5.03 −2.75 −1.85 −5.05 −13.41 −8.12 4.81 14.85 0.53 −4.56 6.76 −11.86 −15.78 −2.25 14.16 0.67 −1.99

323.15

333.15

343.15

353.15

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In this expression, a′0, a′1, a′2, and a′3 are four model parameters, ΔH0 is the standard heat of solvation, ΔS0 is the standard entropy change of solvation, p03 and V3 are the saturated vapor pressure and molar volume of the pure solute (EG), and B, Bii, Bij are the second virial coefficient of the mixture, pure component, and the intercross components, respectively. The modified associative model was applied to correlate the solubility of EG in SCCO2, and the four model parameters were obtained from regression analysis with the experimental solubility data (seen in Table 1) by Polymath for ln y2 as a function of 1/T, ρ, and ln P. The values of the model parameters and the correlation coefficients are tabulated in Table 4; moreover, the calculated solubility of EG by the

RD between the experimental and the calculated solubility of EG is the range of 0.03 % to 11.73 %, and the value of AARD is 4.01 % by calculating from eq 3. It is implied that the Peng− Robinson equation of state is able to represent the data of solubility of EG in SCCO2 within the acceptable RD and AARD. Moreover, the calculated results using the Peng− Robinson equation of state are compared with the experimental solubility values in Figure 6; with respect to the experimental data, the curves correlated by the Peng−Robinson equation of state at all temperatures show no apparent deviation and follow the same trend of solubility behavior. This suggests that the correlation results by the Peng−Robinson equation of state show agreement with the experimental data, and the best agreement is given in the middle range of (11.0 to 15.0) MPa. Furthermore, the experimental results were also correlated by the modified associative model, which was reported by our group previously.19 Based on the supposition that each molecule of a solute associates with κ molecules of supercritical solvent to form a solvato-complex, the associative model was presented first by Chrastil (shown in eq 16),30 which correlates the solubility of a solute in a supercritical solvent to the density and temperature. C = ρ κ exp(a /T + b)

Table 4. Calculated Model Parameters of the Modified Associative Model

(16)

T/K

a′0·10−3

a′1·103

a′2

a′3

correlation coefficient

313.15 323.15 333.15 343.15 353.15

−0.9097 −1.1401 −1.2686 −0.7243 −0.3574

0.1742 0.3920 0.5470 3.5704 7.4657

0.6433 1.3129 1.6130 −0.3589 −1.6526

1.8242 1.0230 0.5757 2.1156 3.0662

0.9950 0.9963 0.9896 0.9869 0.9932

−1

Here C (g·L ) is the solubility of the solute in the supercritical phase, ρ (g·L−1) is the density of the pure supercritical fluid, T (K) is the operating temperature, κ is the associative constant, and a and b are constants. The Chrastil equation was modified by our group previously,19 and the resulting expression contains four parameters as follows: ln y2 =

a′0 + a′1ρ + a′2 ln p + a′3 T

(17)

a′0 = −(ΔH 0 + p30 V3)/R

(18)

a′1 = −[2(B12 − kB22 ) + (k − 1)B] + V3

(19)

a′2 = k − 1

(20)

a′3 = ΔS 0/R + ln p30

(21) Figure 7. Solubility of EG in SCCO2 correlated by the modified associative model (solid curve) and experimental results (points: ■, T = 313.15 K; ●, T = 323.15 K; ⧫, T = 333.15 K; ★, T = 343.15 K; ▲, T = 353.15 K).

modified associative model are shown in Table 3 and Figure 7 according to the regression analysis results. Compared to the experimental solubility values, the absolute value of RD between the experimental solubility of EG and the calculated solubility of EG by the modified associative model ranges from 0.07 % to 15.78 %, and the value of AARD is 4.81 % by calculated from eq 3. As it can be seen, the correlation result of the Peng−Robinson equation of state is in better agreement with experimental solubility data than that of the modified associative model, but the latter still has the acceptable values of AARD less than 5 % and show no apparent deviation with respect to the experimental data in Figure 7. This fact may demonstrate the experimental data of the solubility of EG in SCCO2 could also be successfully correlated by the modified associative model.

Figure 6. Solubility of EG in SCCO2 correlated by the Peng− Robinson equation of state (solid curve) and the experimental results (points: ■, T = 313.15 K; ●, T = 323.15 K; ★, T = 333.15 K; ▲, T = 343.15 K; ⧫, T = 353.15 K). 1800



Article

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4. CONCLUSIONS In this work, the introduced apparatus based on a static-analytic method was suitable for the high-pressure equilibrium measurements with uncertainties estimated less than 5 %, and the equilibrium solubilities of EG in SCCO2 were determined at the temperature range of (313.15 to 353.15) K and the pressure range of (7.0 to 19.0) MPa. The mole fraction solubility (y2) and the weight solubility of EG (F2) are in the range of 0.83·10−2 to 4.29·10−2 and 1.17 % to 5.95 % over the entire range of experimental conditions, respectively. In addition, the solubility of EG in SCCO2 shows a significant temperature and pressure dependence, and the crossover pressure point for the binary system of EG and SCCO2 is about 16.0 MPa; thereby the solubility of EG in SCCO2 can be enhanced by improving the temperature above the crossover pressure or reducing the temperature below the crossover pressure. The measured equilibrium solubility data in SCCO2 were well-correlated by the Peng−Robinson equation of state using the quadratic mixing rules of the two-fluid van der Waals (vdW2) with two appropriate binary interaction parameters and the modified associative model. The values of AARD from the Peng−Robinson equation of state and the modified associative model are 4.01 % and 5.09 %, respectively.

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ASSOCIATED CONTENT

S Supporting Information *

Measured solubility of styrene and reported values (Table S1) and regression equation coefficient for the density of CO2. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +86-571-88320892. E-mail: [email protected]. Funding

The authors would like to thank the National Science Foundation of China (NSFC) for Award No. 20576123 and No. 21104066. This material is also based upon work funded by Zhejiang Provincial Natural Science Foundation of China under Grant No. Y12B060031. Notes

The authors declare no competing financial interest.

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Solubility of Ethylene Glycol in Supercritical Carbon Dioxide at

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