High-Pressure Phase Equilibria of Carbon Dioxide + 1-Octanol Binary

Article pubs.acs.org/jced

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

High-Pressure Phase Equilibria of Carbon Dioxide + 1‑Octanol Binary System Sergiu Sima,† Simona Ioniţa,̆ † Catinca Secuianu,*,†,‡ Viorel Feroiu,*,† and Dan Geană† †

Department of Inorganic Chemistry, Physical Chemistry and Electrochemistry, Faculty of Applied Chemistry and Materials Science, University Politehnica of Bucharest, 1-7 Gh. Polizu Street, S1, 011061 Bucharest, Romania ‡ Department of Chemical Engineering, Imperial College London, South Kensington Campus, SW7 2AZ London, United Kingdom ABSTRACT: New isothermal vapor−liquid equilibrium (VLE) and vapor−liquid−liquid equilibrium data for the carbon dioxide + 1-octanol system are reported at several temperatures, 303.15, 310.15, 315.15, 323.15, and 333.15 K, and pressures up to 145 bar. A staticanalytical method with phase sampling was used. The experimental results of this study are compared with literature data when available and discussed. The new and all available literature data for the carbon dioxide +1-octanol binary system are modeled with the cubic general equation of state and Peng−Robinson equations of state (EoS) with classical van der Waals mixing rules. The aforementioned EoS’s were used to model the phase behavior of the carbon dioxide + 1-octanol binary system (critical curves, the three-phase equilibrium curve, isothermal VLE, and vapor−liquid−liquid equilibria), using a semipredictive approach. The results of the calculations are compared to the new data reported in this work and to all available literature data. The results show a satisfactory level of agreement between the models and the experimental data.

1. INTRODUCTION Phase equilibria of carbon dioxide + alcohols have been the focus of many researchers for a long time, either because of scientific interest or industrial applications.1−5 In our group, binary6−25 or ternary26 systems containing CO2 and alcohols have also been studied extensively. Herein we present results for the CO2 (1) + 1-octanol (2) binary system. Although the system has been studied since the 1990s due to its multiple uses in industry, such as model liquids for supercritical fluid extraction of natural oils or model liquids for the lipid region of biological membranes,27 the available literature data are scattered. Our careful literature search revealed that Ke et al.,28 Byun and Kwak,29 Scheidgen,30 and Ziegler et al.31 reported critical data, while Lam et al.32 measured vapor−liquid−liquid equilibrium (VLLE) data, the upper critical end point (UCEP), and the quadruple point (Q-point), as can be seen in Table 1. Scheidgen30 also measured two isobars (101 and 150 bar), two vapor−liquid equilibrium (VLE) isotherms (313.0 and 392.9 K), and two liquid−liquid equilibrium (LLE) isotherms (298.4 and 303.3 K), Weng et al.33 published two isotherms (348.15 and 403.15 K), Lee and Chen34 determined vapor−liquid equilibrium data at three temperatures (348.15, 403.15, and 453.15 K), and Gregorowicz and Chylinki35 and Schlichting36 measured only the composition of the vapor phase at 313.0 and 293.18 K, and 313.15 and 338.14 K, respectively. Furthermore, Weng and Lee37 presented equilibrium data at 315.15, 328.15, and 348.15 K, Chrisochoou et al.38 measured one isotherm (313.15 K) using two different methods, Feng et al.39 determined VLE data at 328.15 K, Chang et al.40 reported three isotherms (308.15, 318.19, and 328.15 K), and Hwu et al.41 measured VLE data at 328.2 K. In addition, Chiu et al.42 measured isothermal VLE data © XXXX American Chemical Society

at 313.15, 328.15, and 348.15 K, but the phase compositions were not determined at the same pressure, Fourie et al.43 reported similar isothermal data at 308.0, 318.0, 328.0, 338.0, and 348.0 K, Li et al.44 measured a few solubilities at 303.5 K, and Byun and Kwak29 presented correlations between pressure and composition of the liquid phase at 313.15, 333.15, 353.15, 373.15, and 393.15 K. The VLE literature data are summarized in Table 2. The experimental methods used in the references cited in Table 2 are not discussed in this study as they have already been extensively presented in a series of papers by Dohrn and co-workers.4,45−47 However, the experimental methods of these references are mentioned in Table 2 using the same designation of Dohrn and co-workers.4,45−47 It should also be mentioned that there are a few additional papers reporting solubilities at atmospheric pressure or excess properties.48−52 Here we report vapor−liquid equilibrium and vapor−liquid− liquid equilibrium data for the carbon dioxide + 1-octanol system at several temperatures, 303.15, 310.15, 315.15, 323.15, and 333.15 K, and pressures up to 145 bar. The cubic general equation of state (GEOS)54,55 and Peng− Robinson (PR)56 EoSs coupled with quadratic classical van der Waals mixing rules (two-parameter conventional mixing rules, 2PCMR) were used in this study to model the carbon dioxide + 1-octanol system. These EoSs have the capability to represent the complex phase behavior (critical curves, equilibrium LLV line, isothermal VLE and VLLE, isobars) of the carbon dioxide + 1-octanol Special Issue: In Honor of Cor Peters Received: September 30, 2017 Accepted: January 9, 2018

A

DOI: 10.1021/acs.jced.7b00865 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Literature Critical Data for CO2 (1) + 1-Octanol (2) Binary System T or Trange/K

prange/bar

NEXP

observations

method

reference

389.07−295.23 308.70 300.00−333.00 300.10−309.10 353.15−393.15 304.25−523.15 255.15−306.15

216.4−989.3 79.10 22.9−17.1 65.70−79.80 187.20−219.70 73.90−200 20.86−74.77

74 1 12 4 4 21 11

LL critical curve VLE critical curve LL critical curve LLV equilibrium line VLE critical curve VLE critical curve LLV equilibrium line

AnT SynNonPcTc SynNonPcTc SynNonPcTc SynVis AnOth SynVis

Scheidgen, 199730 Ke et al., 200728 Ke et al., 200728 Ke et al., 200728 Byun and Kwak, 200229 Ziegler et al., 199531 Lam et al., 199032

Table 2. Literature VLE and VLLE data for CO2 (1) + 1-Octanol (2) Binary System T or Trange/K 293.18 298.40 298.40 303.15 303.30 303.30 308.00 308.00 308.15 313.00 313.00 313.15 313.15 313.15 313.15 313.15 313.15 315.15 318.00 318.00 318.19 328.00 328.00 328.15 328.15 328.15 328.15 328.15 328.20 333.15 338.00 338.00 338.14 348.00 348.00 348.15 348.15 348.15 348.15 348.15 353.15 353.15 373.15 373.15 392.90 393.15 393.15 403.15 403.15 453.15

prange/bar 10.7−44.85 51.2 80.3−239.0 2.57−9.27 51.4 78.0−181.2 68.4−163.4 79.8−160.9 15.1−77.4 53.1−155.3 12.5−78.7 13.5−69.5 59.0−152.0 5.0−42.0 32.5−161.2 95.6−160.3 29.3−123.8 70.0−155.0 79.8−153.1 93.8−153.4 21.7−97.8 91.1−156.9 107.7−157.5 40.0−170.0 30.0−133.8 28.9−151.1 39.2−162.5 122.1−162.3 30.0−133.0 36.2−149.3 102.5−167.5 121.7−167.9 15.05−100.8 113.9−177.3 135.6−179.4 10.0−50.0 65.0−190.0 40.0−190.0 48.6−182.9 147.9−182.3 41.7−187.2 174.5 44.1−209.3 191.4−203.8 49.1−213.2 46.6−219.7 199.7−218.3 10.0−50.0 65.0−185.0 10.0−50.0

NEXP 5 1 8 6 1 7 7 7 12 6 6 6 9 8 11 6 11 6 7 7 9 7 7 7 6 16 10 6 6 11 7 7 8 7 7 5 7 7 11 5 10 1 9 2 8 9 2 5 9 5

observations p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p

− − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − −

y x, y xL1, xL2 x x, y xL1, xL2 x y x, y x, y y y x, y x x y x x, y x y x, y x y x, y x, y x, y x y x, y x x y y x y x, y x, y x, y x y x y x y x, y x y x, y x, y x, y B

method

reference a

not available AnT AnT not availablea AnT AnT SynVisVar SynVisVar SynMatLcir AnT not availablea not availablea AnPTVisVal AnPTVisVal SynVisVar SynVisVar SynVis AnPTSem SynVisVar SynVisVar SynMatLcir SynVisVar SynVisVar AnPTSem AnPTSemXY SynMatLcir SynVisVar SynVisVar AnPTSemXY SynVis SynVisVar SynVisVar not availablea SynVisVar SynVisVar AnPTSemVal AnPTSem AnPTSem SynVisVar SynVisVar SynVis SynVis SynVis SynVis AnT SynVis SynVis AnPTSemVal AnPTSem AnPTSemVal

Schlichting, 199136,53 Scheidgen, 199730 Scheidgen, 199730 Li et al., 201244,53 Scheidgen, 199730 Scheidgen, 199730 Fourie et al., 200843 Fourie et al., 200843 Chang et al., 199840 Scheidgen, 199730 Gregorowicz and Chylinski, 199835,53 Schlichting, 199136 Chrisochou et al., 199738 Chrisochou et al., 199738 Chiu et al., 200842 Chiu et al., 200842 Byun and Kwak, 200229 Weng and Lee, 199237 Fourie et al., 200843 Fourie et al., 200843 Chang et al., 199840 Fourie et al., 200843 Fourie et al., 200843 Weng and Lee, 199237 Feng et al., 200139 Chang et al., 199840 Chiu et al., 200842 Chiu et al., 200842 Hwu et al., 200441 Byun and Kwak, 200229 Fourie et al., 200843 Fourie et al., 200843 Schlichting, 199136,53 Fourie et al., 200843 Fourie et al., 200843 Lee and Chen, 199434 Weng et al., 199433 Weng and Lee, 199237 Chiu et al., 200842 Chiu et al., 200842 Byun and Kwak, 200229 Byun and Kwak, 200229 Byun and Kwak, 200229 Byun and Kwak, 200229 Scheidgen, 199730 Byun and Kwak, 200229 Byun and Kwak, 200229 Lee and Chen, 199434 Weng et al., 199433 Lee and Chen, 199434 DOI: 10.1021/acs.jced.7b00865 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


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Table 2. continued T or Trange/K 287.10−342.67 292.93−313.19 a

prange/bar 150.0 101.0

NEXP 8 5

observations

method

T − x, y T − x, y

reference Scheidgen, 199730 Scheidgen, 199730

AnP AnP

Experimental data collected from Detherm database53

about 35 cm3 from the vapor phase and 15 cm3 from the liquid phase. The experimental uncertainty of the measured volume is smaller than ±0.02%. The liquid samples separated in the glass traps are weighed with a precision balance (A&D Instruments Ltd., type HM-200, Tokyo, Japan) with an accuracy of ±0.0001 g. The platinum temperature probe connected to a digital indicator was calibrated against the calibration system Digital Precision Thermometer with PT 100 sensor (Romanian Bureau of Legal Metrology-BRML). The temperature uncertainty of the platinum probe is estimated to be ±0.1 K using a similar procedure as described in our previous paper.24 The pressure gauge connected to the cell is a HEISE model 3089 digital pressure indicator for 500 bar and 0.05% accuracy. It was calibrated at 323.15 K with a precision hydraulic dead-weight tester (model 580C, DH-Budenberg SA, Aubervilliers, France). The pressure uncertainty is estimated to be ±0.15 bar using the same procedure as described previously24 for a pressure range of 5.0−200.0 bar.

system, using a semipredictive approach. The results of the calculations are compared to the new data reported in this work, as well as to all available literature data.

2. EXPERIMENTAL SECTION 2.1. Materials. Carbon dioxide (mass fraction purity >0.999) was provided by Linde Gaz Romania, and 1-octanol (mass fraction purity >0.990) was purchased from Merck, as presented in Table 3. The chemicals were used without further purification, Table 3. Description of Materials

compound carbon dioxide 1-octanol

chemical formula

CAS registry number

CO2

124-38-9

C8H18O

111-87-5

source Linde Gaz Romania Merck

purification method

minimum mass fraction purity

none

>0.999

none

≥0.990

except for drying and degassing of 1-octanol. The purity of 1-octanol was also checked and confirmed by gas chromatography. 2.2. Apparatus and Procedure. The apparatus used for phase equilibrium measurements, based on the static-analytical method with liquid and vapor phase sampling, was previously presented in detail.23,24,57 The high-pressure visual cell with constant volume, built by SEPAREX Supercritical Fluid Technology, project 4261 type SC350,58 is the main component. The visual equilibrium cell consists of a sapphire tube, closed by two metallic lids, which provides a complete view of the full cell volume. The cell is placed on a thermostation, has a protection jacket, and is equipped with appropriate instrumentation, such as pressure gauge and thermocouple, for accurate measurements of both pressure and temperature. The temperature of the cell is controlled by a circulatory thermostat (Lauda E 110) connected to the heating jacket. The setup was completed with a syringe pump Teledyne ISCO model 500D. The experimental procedure is the same as described in our previous papers.23,24,57 The entire internal loop of the apparatus, including the equilibrium cell, is rinsed several times with carbon dioxide, followed by emptying with a vacuum pump. Then the cell is charged with liquid (in this case 1-octanol), and it is slightly pressurized with carbon dioxide to the desired pressure, using the syringe pump. The next operation consists in heating the cell to the experimental temperature and then maintaining it constant. The mixture in the cell is stirred for several hours, to facilitate the approach to an equilibrium state. The average stirring time is about 4 h. Then the stirrer is switched off and about 2 h are allowed to pass before the coexisting phases become completely separated. Samples of the liquid and vapor phases are collected by depressurization and expansion into glass traps using manually operated valves. The valves are operated in such a way as to keep the pressure in the visual cell almost constant (Δp < 0.5 bar). The total amounts of organic substance (1-octanol, in this case) in the glass trap are about 0.05 and 0.1 g for the vapor and liquid phases, respectively. The amount of carbon dioxide in the liquid phase is obtained by expansion in a glass bottle of calibrated volume. In a typical experiment, the volumes of carbon dioxide measured are

3. MODELING The phase behavior of the carbon dioxide (1) + 1-octanol (2) binary system was modeled with the cubic GEOS54,55 and PR56 EoS, coupled with classical van der Waals mixing rules (twoparameter conventional mixing rules, 2PCMR). The cubic GEOS has the form P=

a(T ) RT − V−b (V − d)2 + c

(1)

The four parameters a, b, c, d are given by the following relations for a pure component ⎧ R2Tc2 ⎪ a(T ) = acβ(Tr) ac = Ωa Pc ⎪ ⎨ ⎪ R2Tc2 RT d = Ωd c ⎪ c = Ωc 2 Pc Pc ⎩

b = Ωb

RTc Pc

(2)

The temperature function used in cubic GEOS is

β(Tr) = Tr−m

(3)

where Tr is the reduced temperature, Tr = T/Tc. The expressions of the parameters Ωa, Ωb, Ωc, and Ωd are Ωa = (1 − B)3 ; Ωd = Zc −

Ωb = Zc − B ;

Ωc = (1 − B)2 (B − 0.25);

(1 − B) 2

(4)

with B=

1+m , where αc is Riedel’s criterion αc + m

(5)

The a, b, c, d coefficients of the cubic GEOS equation are in fact functions of the critical data (Tc,, Pc, and Vc), m, and αc parameters. As pointed out previously,59 GEOS is a general form for all the cubic equations of state with two, three, and four parameters. The parameters of the PR equations of state can be obtained C



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from the eqs 2−4 by setting the following restrictions: Ωc = −2(Ωb)2 and Ωd = −Ωb. It follows that 1 ⎛⎜ 1 − 3B ⎞⎟ ; 8⎝ 1 − B ⎠ 2

B = 0.25 −

Zc(PR) =

1+B 4

Table 6. Mole Fraction of Component 1 in the Liquid 1 Phase, x1,L1, Mole Fraction of Component 1 in the Liquid 2 Phase, x1,L2, and Mole Fraction of Component 1 in the Vapor Phase, y1 at 303.15 K and at Various Pressures, P, for the Binary System Carbon Dioxide (1) + 1-Octanol (2)a

(6)

giving B(PR) = 0.2296 and Zc(PR) = 0.3074. The original temperature function β(Tr) was used for PR EoS.56 The first eq 6 for B can be solved iteratively, starting with an initial approximation of B in the right-hand term. The corresponding value for Ωa, Ωb, Ωc, Ωd are given by eq 4 and are shown in Table 4. The Ωa, Ωb, Ωc, Ωd parameters are

P/bar

EoS

GEOS

PR

CO2

1-octanol

CO2, 1-octanol

B Zc Ωa Ωb Ωc Ωd

0.1785 0.2743 0.5545 0.0958 −0.0483 −0.1365

0.1741 0.2510 0.5633 0.0769 −0.0517 −0.1619

0.2296 0.3074 0.4572 0.0778 −0.0121 −0.0778

∑ ∑ xixjaij ; i

d=

b=

j

∑ ∑ xixjbij ; i

c=

i

Table 7. Mole Fraction of Component 1 in the Liquid Phase, x1, and Mole Fraction of Component 1 in the Vapor Phase, y1 at Various Temperatures, T, and Pressures, P, for the Binary System Carbon Dioxide (1) + 1-Octanol (2)a

(7)

i

aij = (aiaj)1/2 (1 − kij); cij = ± (|ci||cj|)1/2

P/bar

j

∑ xidi bij =

bi + bj 2

(1 − lij)

(with “+” for ci , cj > 0 and “−” for ci or cj < 0)

0.9909 0.9926 0.9929 0.9931 0.9933 0.9932

Standard uncertainties: u(T) = 0.1 K, u(p) = 0.1 bar, u(x1,L1) = 0.005, u(x1,L2) = u(y1) = 0.015.

∑ ∑ xixjcij ;

j

y1

a

compound-dependent for GEOS, whereas for PR they are universal. It must also be pointed out that in GEOS the value of Zc is the experimental one. The coefficients a, b, c, d were obtained for mixtures using the classical van der Waals twoparameter conventional mixing rules (2PCMR for a, b) extended correspondingly for c and d a=

xL2

T/K = 303.15 ± 0.1 0.2538 0.3471 0.4238 0.5151 0.6184 0.6526 0.9847 0.6621 0.9842 0.6834 0.9838 0.7095 0.9813

22.96 34.78 45.36 54.17 66.25 70.22 75.60 85.20 105.50

Table 4. Critical Compressibility Factor (Zc), and GEOS Parameters (Ωa, Ωb, Ωc, Ωd, B) substance

xL1

(8)

Generally, negative values are common for the c parameter of pure components. The geometric mean in eq 8 for cij was explained in previous papers.15,18 For PR EoS a, b are given by eqs 7 and 8 and c, d are calculated by the restrictions c = −2b2 and d = −b.59 The GEOS parameters, m and αc, of each component were estimated by constraining the EoS to reproduce the experimental vapor pressure and liquid volume on the saturation curve between the triple point and the critical point. The values of critical data and GEOS parameters of the pure components are given in Table 5. The calculations were made using our in-house61 software package “PHEQ” (phase equilibria database and applications), and GPEC62 (global phase equilibrium calculations). The module for calculating the critical curve, called CRITHK in our software, is using the method proposed by Heidemann and Khalil63 with the numerical derivatives given by Stockfleth and Dohrn.64 The modeling is approached similar to our recent papers,24,25 describing the entire phase behavior of the binary system with simple models, rather than just regressing the experimental data at specified temperatures.

x1

y1

13.87 22.03 31.10 41.31 49.54 59.57 68.18 79.03 83.18 87.87

0.1074 0.1809 0.2713 0.3402 0.3832 0.4488 0.4975 0.5712 0.5925 0.6174

7.99 15.81 25.66 36.16 45.72

0.0605 0.1348 0.2104 0.2675 0.3294

13.66 24.17 33.76 40.92 44.36 50.07

0.1046 0.1785 0.2435 0.2814 0.2944 0.3296

10.16 23.34 33.22 46.13 55.75

0.0596 0.1503 0.2059 0.2695 0.3275

p/bar

T/K = 310.15 ± 0.1 0.9908 94.76 0.9921 108.78 0.9928 114.65 0.9938 117.28 0.9941 123.32 0.9944 126.94 0.9945 131.61 0.9932 135.94 0.9918 137.16 0.9912 144.69 T/K = 315.15 ± 0.1 0.9898 55.47 0.9929 64.64 0.9935 75.43 0.9949 87.90 0.9957 T/K = 323.15 ± 0.1 0.9935 59.99 0.9951 69.73 0.9962 77.52 0.9967 81.79 0.9968 91.97 0.9966 100.04 T/K = 333.15 ± 0.1 0.9955 65.23 0.9975 75.65 0.9983 84.37 0.9984 93.02 0.9987

x1

y1

0.6508 0.6973 0.7212 0.7272 0.7476 0.7498 0.7679 0.7764 0.7785 0.7989

0.9902 0.9853 0.9849 0.9848 0.9839 0.9822 0.9814 0.9795 0.9794 0.9783

0.3725 0.4178 0.4941 0.5663

0.9954 0.9949 0.9937 0.9919

0.3734 0.4358 0.4849 0.5116 0.5667 0.6057

0.9965 0.9956 0.9945 0.9940 0.9929 0.9909

0.3822 0.4251 0.4767 0.5267

0.9979 0.9974 0.9952 0.9943

a

Standard uncertainties: u(T) = 0.1 K, u(p) = 0.1 bar, u(x1) = 0.005, u(y1) = 0.015

Table 5. Critical Data (Tc, Pc, Vc),60 Acentric Factor (ω),60 and GEOS Parameters (αc, m) for Pure Compounds compounds

Tc/K

Pc/bar

Vc/cm3·mol−1

ω

αc

m

carbon dioxide 1-octanol

304.21 652.5

73.83 27.77

93.90 490.0

0.2236 0.5829

7.0517 9.0977

0.3146 0.7075

D



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parameters, restrictions were imposed in the critical curve calculations for the experimental critical minimum temperature and pressure to be reproduced. Because this is a single point, no optimization algorithm was used. Fine modification of the binary interaction parameters can lead even to a different type of phase diagram.12 These new sets of parameters were also used to predict all isothermal data, both measured in this work and reported in the literature, the three-phase VLLE curve, and isobars.

4. RESULTS AND DISCUSSION The carbon dioxide (1) + 1-octanol (2) binary system exhibits type III phase behavior,65,66 having three critical curves: one vapor−liquid critical curve starting from the heavier component, in this case 1-octanol, and continuing with another liquid−liquid curve toward high pressure, and the third one, again a vapor− liquid critical curve, starting from CO2 and ending in an upper critical end point (UCEP) where it intersects the three-phase equilibrium curve (LLV). Vapor−liquid and vapor−liquid−liquid equilibrium compositions for the carbon dioxide +1-octanol binary system were measured at five temperatures (303.15, 310.15, 315.15, 323.15, and 333.15 K), and pressures up to 145 bar. The data are presented in Tables 6 and 7 and, as is the norm in the literature, mole fractions are reported to four decimal places. It must be pointed out that four isotherms (Table 7) are located at higher temperatures than the UCEP temperature (309.12 K32). Figure 1 illustrates the data measured in this study, while Figure 2 shows comparisons with literature data at 315.15 K (a) and 333.15 K (b). It can be observed that our data at 333.15 K (Figure 2b) are in very good agreement with those of Byun and Kwak,29 while our liquid curve at 315.15 K is different as compared to that measured by Weng and Lee37 (Figure 2a). The scatter of other literature data will be discussed further. First, the new and all available literature data were correlated with GEOS and PR EoSs coupled with quadratic mixing rules. The optimized binary interaction parameters for both models are given in Table 8. The average values of the binary interaction parameters are k12 = 0.066 and l12 = −0.008 for GEOS and k12 = 0.101 and l12 = −0.011 for PR, respectively. These two sets of

Figure 1. Pressure composition data for carbon dioxide (1) + 1-octanol (2) system: orange diamond, 303.15 K; maroon square, 310.15 K; green triangle, 315.15 K; purple circle, 323.15 K; blue asterisk, 333.15 K.

First, we regressed the new experimental data with GEOS and PR EoS at each temperature. The optimized binary interaction parameters, k12 and l12, were averaged for each EoS, resulting in two unique sets of k12 and l12. These sets were then used to calculate semipredictively the phase behavior of the system (critical curves, three-phase equilibrium line, VLE and VLLE isotherms, isobars). To improve the calculation of the critical curves, we then obtained by a trial and error procedure for the models used (GEOS and PR) new sets of binary interaction parameters that reproduce the experimental critical lines (liquid−liquid and vapor−liquid) of the system, especially the minimum in temperature. Starting with the average value of the binary interaction

Figure 2. Comparison of measured and literature data for carbon dioxide (1) + 1-octanol system at (a) T = 315.15 K: green triangle, this work; red open triangle, Weng and Lee.37 (b) T = 333.15 K: blue asterisk, this work; purple square, Byun and Kwak.29 E



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5−10 bar between the critical data reported by Scheidgen30 and those of Ke et al.28 are acceptable. The calculations by GEOS are illustrated with lines. In Figure 3a, the dashed green lines represent the calculations with the average optimized binary interaction parameters shown in Table 8 (k12 = 0.066; l12 = −0.008). It can be noticed that the minimum of the critical curve is about 100 bar higher than the experimental one and the slope of the LL critical curve is negative. Therefore, we adjusted this set of binary interaction parameters by a trial and error procedure such that the minimum of the critical curve was better reproduced (purple tick full line). In Figure 3b, this area is highly enlarged and it can be observed that the predicted pressure is less than 10 bar off, although the predicted minimum temperature is lower than the experimental one. Also, the shape of the predicted LL critical curve is similar to the experimental one and the maximum of the LV critical curve is well reproduced. It must also be pointed out that type III phase diagrams are known to represent challenging systems for equations of state in general and more particularly for cubic EoS. Slight deviations in the reproduction of the vertical part of the liquid−liquid critical line induce high deviations in the reproductions of the corresponding isothermal phase diagrams. In the lower part of Figure 3b, one can notice the LLV equilibrium curve, the second LV critical curve, the critical point of CO2 and its vapor pressure curve. The UCEP predicted by GEOS is located at slightly higher temperature and pressure than the experimental ones measured by Lam et al.,32 but the LLV equilibrium curve is reasonably well predicted by GEOS with the modified parameters (Table 8). The same parameters were then used to calculate the five isotherms measured in this study and all literature data. Figure 4 shows the experimental data acquired in this work (symbols) and the calculations (dashed and full lines) by GEOS. Dashed lines represent the correlations by GEOS at each temperature (303.15 K, below UCEP temperature; 310.15, 315.15, 323.15, and 333.15 K, all above UCEP temperature), while the full lines illustrate the predictions with the modified

Table 8. Optimized Binary Interaction Parameters (k12, l12) Using Experimental Data Measured in This Work model

GEOS/2PCMR

PR/2PCMR

T/K

k12

l12

k12

l12

303.15 310.15 315.15 323.15 333.15 average parameters modified parametersa

0.0662 0.0567 0.0785 0.0679 0.0620 0.066 0.055

−0.0008 −0.0134 −0.0040 −0.0078 −0.0133 −0.008 −0.030

0.0621 0.0943 0.1291 0.1157 0.1059 0.101 0.090

−0.0043 −0.0255 −0.0003 −0.0066 −0.0180 −0.011 −0.030

a

Modified binary interaction parameters obtained by a trial and error procedure.

parameters were then used to calculate all available data, such as the critical curves, the three-phase equilibrium line, the isotherms, and isobars. Thus, in Figure 3 the available literature critical data and the results of GEOS calculations are compared. The symbols represent experimental data from the literature. It can be observed that the experimental phase diagram is almost complete. Scheidgen30 measured the LL critical curve up to almost 1000 bar, Ziegler et al.31 determined several LV critical points to very high temperatures on the LV critical curve starting from 1-octanol (LV1), as well as one point on the second LV critical curve, originating from carbon dioxide (LV2), Byun and Kwak29 reported a few critical points on the second LV critical curve, and Lam et al.32 measured the UCEP, several LLV equilibrium points, and the Q-point. It must also be noted that Ke et al.28 investigated the minimum of the critical curve, a few points being measured on the LV critical curve and several points on the LL critical curve. Moreover, they also reported one critical point on the second LV critical curve and several points on the three-phase equilibrium line. As experiments at high pressures are difficult, the noted differences of

Figure 3. P−T fluid phase diagram of the carbon dioxide (1) + 1-octanol system. (a) Experimental values: orange diamond, this work; blue open diamond, Ziegler et al.;31 blue open circle, Scheidgen;30 pink open square, Byun and Kwak;29 orange asterisk, Ke et al.;28 green square, green triangle, green diamond, Lam et al.;32 Calculations with GEOS/2PCMR: green dashed line, critical curves and LLV line calculated with the average of the binary interaction parameters from Table 8; purple line, critical curves and LLV line calculated with modified average of the binary interaction parameters from Table 8. (b) Enlargement of the minimum part of the critical curve and the LLV three-phase line. F



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Figure 4. Comparison of new experimental data and calculations (green dashed line, correlations; purple line, predictions) by GEOS for the carbon dioxide (1) + 1-octanol (2).

critical curve with the average set (k12 = 0.066; l12 = −0.008). On the other hand, the calculations by GEOS (k12 = 0.055; l12 = −0.030) lead to critical points in good agreement with the

parameters. As expected, the critical points from the correlations of the five isotherms are situated at false very high pressures, this overestimation being anticipated by the shape of the calculated G



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Figure 5. P−T fluid phase diagram of the carbon dioxide (1) + 1-octanol system. (a) Experimental values: orange diamond, this work; blue open diamond, Ziegler et al.;31 blue open circle, Scheidgen;30 pink open square, Byun and Kwak;29 orange asterisk, Ke et al.;28 green square, green triangle, green diamond, Lam et al.;32 Calculations with PR/2PCMR: ---, critical curves and LLV line calculated with the average of the binary interaction parameters from Table 8; red line, critical curves and LLV line calculated with modified average of the binary interaction parameters from Table 8. (b) Enlargement of the minimum part of the critical curve and three-phase line. (c) The three-phase line, CO2 vapor pressures, and LV critical curve. (d) Enlargement of the intersection of the three-phase line and LV critical curve.

the minimum of the critical curve is overestimated in the case of the averaged set (about 40 bar). In Figure 5b, the minimum part of the critical curve is also enlarged and it can be seen that the difference between experimental and predicted pressure is less than 2 bar, whereas the difference between experimental and predicted temperature is about 6°. The maximum temperature of the LV curve is very well predicted by PR, but the maximum pressure is overestimated by about 30 bar. In Figure 5c, the LLV equilibrium curve and the second LV critical curve are depicted, comparing experimental data with the calculations by PR using both the averaged and the modified set of parameters, while in Figure 5d the intersection of LV critical curve with the LLV equilibrium curve is significantly enlarged. It can be seen that both the

experimental one, even though they overestimate the vapor− liquid curves. The same procedure was used for the second model chosen to reproduce the phase behavior of the carbon dioxide + 1-octanol binary system, PR EoS. Figure 5 shows the phase diagram of the system calculated with PR EoS. Symbols represent experimental data from the literature, as detailed previously, the dash line represents calculations of the critical and equilibrium curves by PR (averaged parameters from Table 8 are k12 = 0.101; l12 = −0.011), and the full line represents the predictions by PR (modified parameters from Table 8 are k12 = 0.90; l12 = −0.030). The slopes of the LL critical curves are positive both for the averaged and modified set of parameters by PR (Figure 5a), but H



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Figure 6. continued

I



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Figure 6. P−T fluid phase diagram of the carbon dioxide (1) + 1-octanol system and comparison of new experimental data and calculations by PR EoS. (a−e) Experimental values: orange diamond, this work; blue open diamond, Ziegler et al.;31 blue open circle, Scheidgen;30 pink open square, Byun and Kwak;29 orange asterisk, Ke et al.;28 green square, green triangle, green diamond, Lam et al..32 Calculations with PR/2PCMR: blue dotted line, critical curves calculated with the optimized binary interaction parameters corresponding to each temperature measured in this study (Table 8); ---, critical curves and LLV line calculated with the average of the binary interaction parameters (Table 8); red line, critical curves and LLV line calculated with modified average of the binary interaction parameters (Table 8). (f−j) Experimental data of this study: symbols. PR calculations: blue dotted line, correlations at the corresponding temperature; ---, predictions with the average of optimized parameters; red line, predictions with the modified average of binary interaction parameters.

drawn in the P−T diagrams on the left. If we analyze for instance Figure 6a,f, it can easily be noticed that the 303.15 K isotherm is located on the left side of the LL critical curve calculated by PR with the optimized parameters from correlation at 303.15 K (Figure 6a), resulting in an open curve in the pressure−composition diagram (Figure 6f). The same observation holds true for the 315.15 K isotherm in Figure 6c,h. As in the case of GEOS, the correlations lead to overestimation of critical points, while the predictions are closer to the experimental critical data, especially at the temperatures measured in this work. Because the 310.15 K isotherm is located under the calculated UCEP temperature, false three-phase lines can be observed in Figure 6g. Finally, the PR modified set of binary interaction parameters (k12 = 0.090; l12 = −0.030) was used to model all available

calculated UCEP (T = 310.86 K, P = 81.67 bar) with the averaged set of parameters and the predicted UCEP (T = 312.72 K, P = 84.07 bar) by PR (k12 = 0.090; l12 = −0.030) are very close to the experimental one32 (T = 309.12 K, P = 79.72 bar). In addition to the critical curves calculated with the two sets of parameters (Table 8), Figure 6a −d also shows as dotted lines the critical curves obtained with the optimized binary interaction parameters at each temperature, while Figure 6f−j illustrates the five isotherms (303.15, 310.15, 315.15, 323.15, and 333.15 K) measured in this work compared against PR results: correlations at each temperature (dotted lines), calculations with the average set of parameters (dotted lines), and predictions with the modified set of parameters (full lines). The isotherms, for which pressure−compositions diagrams are given on the right, are also J



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Figure 7. Comparison of literature data and predictions by PR EoS for carbon dioxide (1) + 1-octanol (2).

literature data. In Figures 7 and 8, we compared all available literature data with the predictions by PR EoS. Isotherms between 293.15 and 453.15 K are shown in Figure 7, whereas two

isobars (101 and 150 bar) are shown in Figure 8. In Figure 9, the pressure−composition diagram along the three-phase equilibrium line is depicted. The scatter of literature data is particularly K



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Figure 8. Temperature−composition diagram for carbon dioxide (1) + 1-octanol (2): experimental data and PR predictions.

well predicted, taking into account the relatively simple models and the semipredictive procedures used.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (C.S.). *E-mail: [email protected] (V.F). ORCID

Catinca Secuianu: 0000-0001-5779-6415 Dan Geană: 0000-0003-2532-1575 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by a grant of Ministry of Research and Innovation, CNCS - UEFISCDI, project number PN-III-P4-IDPCE-2016-0629, within PNCDI III.

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REFERENCES

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Figure 9. Pressure−composition diagram along the LLV line for carbon dioxide (1) + 1-octanol (2): experimental data and PR predictions.

noticeable, especially at 313 and 348 K. The predictions by PR are reasonably good for most isotherms with an overestimation of the critical points toward temperatures closer to the maximum critical temperature.

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CONCLUSIONS New isothermal vapor−liquid equilibrium data for the carbon dioxide + 1-octanol system were measured using a visual highpressure static-analytic setup. Five isotherms at 303.15, 310.15, 315.15, 323.15, and 333.15 K and pressures up to 145 bar are reported. The cubic GEOS and PR equations coupled with classical van der Waals mixing rules were used to model the phase behavior of the mixture by a semipredictive method. The calculation results from the two models were compared with our experimental data and the available literature data for carbon dioxide + 1-octanol binary system. The phase behavior of the system is reasonably L



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High-Pressure Phase Equilibria of Carbon Dioxide + 1-Octanol Binary

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