Measurements and Modeling of VLE Data for Butyl Acetate with 2

Article pubs.acs.org/jced

Measurements and Modeling of VLE Data for Butyl Acetate with 2‑Propanol or 2‑Butanol. Binary Systems at 0.15 and 0.6 MPa Pedro Susial Badajoz,* Diego García-Vera, Isabel Montesdeoca, Dunia E. Santiago, and José López-Beltrán Escuela de Ingenierias Industriales y Civiles, Universidad de Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Canary Islands, Spain S Supporting Information *

ABSTRACT: Isobaric vapor−liquid equilibrium is measured at 0.15 and 0.6 MPa for binary mixtures of butyl acetate with 2-propanol and 2-butanol. The experimental data are reported and the thermodynamic consistency is verified by using the point-to-point test. Prediction of these binary systems was obtained by employing the analytical solutions of groups (ASOG) and the different versions of UNIQUAC functional-group activity coefficients (UNIFAC) group contribution models. The perturbed chain-statistical associating fluid theory (PC-SAFT) equation of state has been used to reproduce experimental data.

Gonzalez and Ortega11 at 101.3 kPa, while the BA2B system has been studied at 101.3 kPa by Gonzalez and Ortega12 as well as by Feng et al.13 The quality of experimental data was verified by using the ϕ−ϕ approach. Moreover, considering the γ−ϕ approach, the point-to-point test of Van Ness et al.14 was applied using a modification of the Fredenslund et al. 15 routine. The consistency test results determine that VLE data presented in this work are reliable, as the deviation in the composition of the vapor phase meets the established criteria.15

1. INTRODUCTION There are many interesting mixtures from the industrial point of view, such as oxygenated additives. In this sense, butyl acetate is a renewable biofuel additive which enables improvement of the properties of biodiesel. Biodiesel/alcohol mixtures enable improvement of engine efficiency. 2-Propanol gives better biodiesel that methanol; it is an alternative fuel. 2Butanol has been utilized in several industries in biofuel production. It is an advanced alternative fuel known as a second generation biofuel. For the production of fuels the relative volatility of the mixtures must be known. Accordingly, it is necessary to experimentally determine the phase equilibrium properties. In addition, vapor−liquid equilibrium (VLE) data can be predicted by equations of state and group contribution models. These data are used for the modeling and design of separation operations. However, the reliability of data prediction provided by these applications depends on the operating conditions. Accordingly, verification of these models and equations is necessary to determine whether they need to be modified in order to increase the predictive ability at moderate and high pressure. For this reason, the perturbed chain-statistical associating fluid theory (PC-SAFT)1,2 equation of state (EOS), and the different group contribution models, such as analytical solutions of groups (ASOG)3 and different versions of UNIQUAC functional-group activity coefficients (UNIFAC)4−6 were applied to experimental data of ester/alcohol mixtures, corresponding to the binary systems studied in this work. Following earlier work,7−9 we have experimentally determined the isobaric systems butyl acetate + 2-propanol (BA2P) and butyl acetate + 2-butanol (BA2B) at 0.15 and 0.6 MPa. These systems have been studied previously in different operating conditions. Thus, data for BA2P system have been determined by Gmehling10 at 46.7 and 101.3 kPa and also by © 2017 American Chemical Society

2. EXPERIMENTAL SECTION The physical properties, normal boiling point (Tbp), density (ρii), and refractive index (nD) at 298.15 K were determined for the chemicals (Table 1) used in this work. The substances were employed without further purification. The measured properties were compared with values from literature: such comparison has been published previously.16−18 A Mettler Toledo DM40 vibrating tube density meter (uncertainty of ±0.1 kg·m−3) was used for density determinations of pure substances and mixtures. In addition, for the refractive index determinations of pure components, a Zusi 315RS Abbe refractometer (uncertainty of ±0.0002 units) was used. Binary mixtures were prepared by weighing pure substances to result in compositions from 0 to 1 in ester mole fraction. The uncertainties of the molar fractions are estimated to be around 0.0002. Composition−density (x,ρ) data pairs obtained for each of the binary solutions were used to calculate the excess molar volumes (vE), which were estimated with a combined standard uncertainty lower than 12 × 10−9 m3·mol−1. Received: February 8, 2017 Accepted: June 29, 2017 Published: July 18, 2017 2296

DOI: 10.1021/acs.jced.7b00141 J. Chem. Eng. Data 2017, 62, 2296−2306

Journal of Chemical & Engineering Data

Article

Table 1. Specification of Chemical Samples

a

component

CAS

suppliers

mass fraction

purification method

analysis method

2-butanol 2-propanol butyl acetate

787-92-2 67-63-0 123-86-4

Sigma-Aldrich ́ Panreac Quimica S.A. ́ Panreac Quimica S.A.

>0.995 >0.998 >0.995

none none none

GCa GCa GCa

Gas−liquid chromatography.

Table 2. Densities and Excess Molar Volumes for the Binary Systems BA2P and BA2B at 298.15 K and 101.3 kPaa e = 100|(ρexp − ρlit.)/ ρexp| x1 0 0.0385 0.0995 0.1656 0.2024 0.3568 0.3010 0.3489 0.4058 0.4596 0.5485 0.6017 0.6534 0.7058 0.7462 0.8033 0.8568 0.9003 0.9484 1

ρ/(kg·m−3) 781.3 786.8 794.8 803.2 807.5 824.3 818.5 823.5 829.2 834.3 842.3 846.8 851.0 855.2 858.3 862.6 866.5 869.6 872.9 876.5

109νE/(m3·mol−1)

e = 100|(ρexp − ρlit.)/ρexp|, b

Butyl Acetate (1) + 2-Propanol (2) 0.0 64.7 179.0 252.9 301.5 413.6 383.1 409.4 427.5 440.3 436.4 427.0 411.2 374.2 345.6 289.5 227.4 168.0 101.9 0.0

0.06 0.05 0.01 0.02 0.00 0.00 0.00 0.00 0.00 0.01 0.02 0.02 0.03 0.04 0.04 0.05 0.06 0.06 0.06 0.07

x1 0 0.0512 0.0599 0.0937 0.1434 0.1503 0.2012 0.2506 0.3018 0.3502 0.3539 0.4003 0.4573 0.5028 0.5547 0.6073 0.6607 0.7048 0.7639 0.8074 0.8524 0.8996 0.9453 1

ρ/(kg·m−3)

109νE/(m3·mol−1)

c

Butyl Acetate (1) + 2-Butanol (2) 802.5 0.0 0.00 806.8 119.1 0.01 807.6 128.9 0.02 810.4 196.8 0.03 814.5 280.9 0.04 815.1 287.2 0.04 819.2 361.0 0.04 823.1 422.2 0.03 827.1 470.8 0.03 830.8 508.4 0.04 831.0 521.3 0.04 834.5 545.9 0.04 838.8 554.6 0.04 842.1 562.4 0.05 845.9 549.0 0.06 849.6 537.4 0.06 853.4 500.9 0.08 856.5 462.0 0.08 860.5 412.5 0.10 863.5 354.2 0.11 866.5 296.7 0.04 869.7 215.6 0.02 872.8 124.1 0.03 876.5 0.0 0.07

d 0.10 0.10 0.11 0.12 0.12 0.12 0.12 0.11 0.10 0.11 0.10 0.11 0.10 0.11 0.12 0.12 0.13 0.14 0.16 0.18 0.12 0.11 0.12 0.10

a

Expanded uncertainties U(k=2) of temperature (T), ester mole fraction (x1), liquid density (ρ), and excess molar volumes (vE) are U(T) = 0.01 K, U(p) = 0.0005 MPa, U(x1) = 0.0002, U(ρ) = 0.1 kg·m−3, U(109vE) = 12 m3·mol−1. bReference 11. cReference 12. dReference 20.

which the circulating mixture inside the ebulliometer presents vapor and liquid phase compositions close to that of the equilibrium state, at a given pressure and temperature. The stationary time has been set higher than 75 min and was already evaluated for different mixtures and operating conditions.9 Liquid and vapor samples were taken after 90 min recirculation using external sealed glass bottles. The accuracy for composition data in both liquid and vapor phases is estimated to be better than 0.002 molar fraction units. The vapor pressures of butyl acetate were obtained with the ebulliometer and experimental installation before VLE determinations. Vapor pressures of 2-propanol and 2-butanol have been taken from literature.16,17

A stainless steel dynamic ebulliometer equipped with a Cottrell pump included in an experimental setup described in previous studies7,8 was employed for VLE determinations. The ebulliometer has a double-walled inverted vessel with an electric heater inside to generate the Cottrell pump effect. The equipment and operating procedure have been described in previous works.7−9 The experimental work is carried out in cocurrent flow with continuous circulation of both liquid and vapor phases. Both phases are sampled every 90 min, and then a small amount of one of the substances (approximately 15 cm3) is added to recharge the equipment, modifying the global composition, without stopping the operation of the equipment. As a result of the operation mode, the global composition of the mixture varies every 90 min after sampling. This dynamic behavior of the mixture prevents repeating of the global compositions. Moreover, although the above conditions could be restored, the equipment operates in cocurrent flow, and thus, long contact periods (infinite time or infinite contact lengths) between nonmiscible phases would be needed to reproduce the equilibrium conditions. For this reason, it is necessary to evaluate the stationary time; that is, the time over

3. RESULTS AND DISCUSSION 3.1. Excess Molar Volumes. The experimental data (x,ρ) for BA2P and BA2B mixtures were obtained at 298.15 K and are shown in Table 2. The excess molar volumes (vE; Table 2) were calculated by using the following equation: 2297


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literature11,12,20 and using eq 1 are also included in Figure 1. The densities of the mixtures of this work (Table 2) were verified. A comparison between our data and literature data11,12,20 is shown in Table 2. Considering results shown in Figure 1 and Table 2, deviations appear to result due to the different measurement equipment used and the difference in purities of the chemicals. 3.2. Vapor Pressures. The vapor pressures (pi0) of butyl acetate were obtained by using the stainless steel ebulliometer included in the installation previously detailed.7,8,16,17 The procedure to obtain 2-propanol and 2-butanol vapor pressures has been described in previous works.16,17 The need for these data is mainly due to the inflexibility of the test of Van Ness et al.14 developed in the routine of Fredenslund et al.15 when applied to mixtures of self-association and cross-association substances21 and, next, to the enormous influence that vapor pressures have in the PC-SAFT model when trying to predict VLE of mixtures. T vs pi0 data for butyl acetate (Table 3) were correlated using a nonlinear multiple regression to the Antoine equation;

2

xM v = −∑ ( −1) ∑ ( −1) i i ρij i=1 j=1 i

E

j

(1)

To verify the dispersion of experimental data, the pairs of (vE,x) were correlated as previously mentioned.17 In consequence, data from Table 2 were fitted by applying the Yen and Woods 19 equation to calculate molar volume at atmospheric pressure. Results at 0.1 MPa are as follows: for BA2P, A0 = 1724.2, A1 = −711.3, and A2 = 849.5 with Rn = 1.75 and SD(109vE) = 4 m3·mol−1 (SD being the standard deviation); and for BA2B, A0 = 2327.5, A1 = −448.4, and A2 = 545.3 with Rn = 1.43 and SD(109vE) = 4 m3·mol−1. Figure 1

log(pi 0 /kPa) = A −

B (T /K) − C

(2)

the results for butyl acetate were A = 6.3699, B = 1523.89, C = 49.95, and SD(pi0) < 0.001 MPa. In addition to the statistical procedure, data were verified by calculating the enthalpy of vaporization with the Clapeyron equation as in previous works.17 The critical properties of the bibliography22 were employed to determine vapor and liquid molar volumes of the pure compounds, using the Tsonopoulos23 procedure and Rackett24 equation. A deviation of 1.5% was observed in the enthalpy of vaporization when literature data22 were taken as a reference. The acentric factor was obtained using properties from literature22 and experimental data in Table 3 and using eq 2 with the properties in reduced form. The acentric factor for butyl acetate was 0.410 with a deviation of less than 0.02%; literature data22 were taken for comparison. Figure 2 includes experimental data for butyl acetate and bibliographic data16,17 of 2-propanol and 2-butanol together with the correlation curve of literature vapor pressures22 for comparison. The mean absolute deviation (MAD) and the mean proportional deviation (MPD) of temperature for each vapor

Figure 1. Experimental values for BA2P (blue ●) and BA2B (blue ■) with fitting curves for (vE, x1) pairs. Literature values: for BA2P (red ◀, from ref 11) and BA2B (red ▶, from ref 12) and (green ▲, from ref 20).

shows data obtained in this work and fitting curves. In addition, vE values calculated considering pairs of data (x,ρ) from Table 3. Experimental Vapor Pressuresa

a

T/K

pi0/MPa

T/K

pi0/MPa

T/K

328.98 335.89 346.66 351.77 355.56 362.02 363.70 367.03 369.76 372.26 376.35 379.26 379.96

0.0085 0.0125 0.017 0.021 0.025 0.030 0.034 0.037 0.0415 0.0455 0.0515 0.056 0.0565

383.00 385.97 387.78 389.14 391.24 393.08 393.22 395.97 398.20 407.93 414.72 423.56 427.54

0.0605 0.0665 0.0745 0.0765 0.0795 0.082 0.0865 0.092 0.0975 0.127 0.155 0.195 0.217

428.55 435.40 437.80 440.65 440.81 447.05 451.67 452.25 455.22 456.75 460.69 463.25 464.05

pi0/MPa

T/K

Butyl Acetate 0.220 469.05 0.260 473.70 0.275 475.55 0.297 477.25 0.295 477.55 0.342 479.95 0.377 481.70 0.382 483.15 0.407 485.75 0.420 488.85 0.457 489.95 0.480 492.48 0.492 495.15

pi0/MPa

T/K

pi0/MPa

T/K

pi0/MPa

0.542 0.592 0.615 0.637 0.641 0.670 0.692 0.712 0.747 0.790 0.807 0.842 0.885

496.95 498.95 500.35 501.65 501.95 502.15 502.45 502.85 505.05 507.35 508.25 509.73

0.915 0.947 0.970 0.990 0.997 0.998 1.005 1.012 1.050 1.092 1.107 1.135

512.35 514.25 516.35 518.35 520.65 522.45 524.75 525.85 527.15 528.65 530.35 531.45

1.187 1.225 1.267 1.307 1.357 1.395 1.447 1.472 1.501 1.537 1.577 1.602

Expanded uncertainties U(k=2) of temperature (T) and vapor pressures (pi0) are U(T) = 0.2 K and U(pi0) = 0.002 MPa. 2298



Article

system is the standard state and by considering the isofugacity as the equilibrium condition, can be expressed as follows: γi =

⎡ p exp⎢ (2 ∑ yj Bij − ⎢⎣ RT xipi j yp i

0

∑ ∑ yyi j Bij) − i

j

pi 0 Bii RT

+

(pi 0 − p)viL ⎤ ⎥ ⎥⎦ RT

(3)

Table 4 shows the activity coefficients calculated with eq 3 considering the Tsonopoulos23 procedure, Rackett24 equation, and the pure substances properties of Daubert and Danner.22 Results show positive deviations from ideal behavior; this is due to the hydrogen bonding weakening of secondary alcohols. Deviations are lower for higher chain lengths of alcohol or system pressure. In addition, reference fugacity coefficient (ϕi0), fugacity coefficient (ϕi), vapor pressure of substances (pi0), and pointing factor corrections (POY) were obtained by the mentioned procedure to be applied in eq 3. Results are shown in Table ST2 (see Supporting Information). To verify experimental data, the perturbation scheme indicated by Mathias25 was also employed. For this purpose, the activity coefficients data in Table 4 were correlated with the NRTL26 model using the dimensionless Gibbs function (GE/ RT). For the mixtures studied in this work, 0.47 was taken as the value for the symmetric parameter, in agreement with that published by Renon and Prausnitz.26 For the asymmetric parameter, a simplified version of the equation given by Mathias25 was used:

Figure 2. Experimental vapor pressures for butyl acetate (red □, solid line), 2-propanol (green ○, from ref 16, double dotted−dashed line), and 2-butanol (blue △, from ref 17, short dashed line). Lines represent vapor pressure curves for these chemicals from literature.22

τij = Aij +

pressure was calculated considering the vapor pressure data from this work and literatura data.16,17 Results are 0.57 and 0.13% for butyl acetate, 0.47 and 0.11% for 2-propanol, and 0.46 and 0.11% for 2-butanol, respectively, in MAD and MPD, when literatura data22 were taken for verification. 3.3. Experimental VLE data. Experimental VLE data for the binary systems of butyl acetate (1) + 2-propanol (2) and butyl acetate (1) + 2-butanol (2) obtained at 0.15 and 0.6 MPa are presented in Table 4. The p−T−x1−y1 data were verified with the γ−ϕ approach using the point-to-point test of Van Ness et al.14 developed in the Fortran program of Fredenslund et al.15 In this work the Tsonopoulos23 procedure and Rackett24 equation were included in the subroutines svir and yenwo. The above procedure was applied to isobaric data from this work using the properties of Daubert and Danner22 and the association and solvation parameters of Fredenslund et al.15 It was verified that BA2P and BA2B systems at 0.15 and 0.6 MPa satisfy global consistency criterion.15 Table ST1 (see Supporting Information) shows results obtained from the point-to-point test. It can be verified that 90% of the experimental data satisfy the validation criteria of Fredenslund et al.15 The differences in the vapor phase composition between experimental and calculated values are lower than 10−2. In addition, the original Fortran program of Fredenslund et al.15 was employed using the same literature properties,15,22 and the global consistency criterion was also verified.15 However, it has been found that even if the association capacity of substances is weak, the verification of systems is more restrictive with increasing pressure when using the original procedure. The activity coefficient of liquid phase (γ), by accepting that the fugacity of pure liquid for temperature and pressure of the

Bij 8.314T

(4)

Table ST3 (see Supporting Information) shows the results of correlations. On the other hand, the activity coefficients at infinite dilution were calculated (see Table ST3 in Supporting Information) to apply the perturbation procedure.25 The values of δi (see Table ST3 in Supporting Information) in the phenomenological equation25 were related with the uncertainty in the activity coefficient at infinite dilution. The activity coefficients obtained after applying the perturbation scheme25 were used together with data shown in Table ST2 to calculate the relative volatilities. Table ST4 shows (see Supporting Information) the relative volatilities obtained from experimental data and those obtained by applying the perturbation scheme.25 Figure SF1 (see Supporting Information) represent the relative volatilities and error curves, including systematic errors, which enable one to verify experimental data uncertainties. It is observed (see Table ST3 in Supporting Information) that the perturbation parameter (δi) is very small when the activity coefficient values are close to the ideal condition. For values of the natural logarithm of the activity coefficient at infinite dilution approximately equal to 0.5, as in this work, values of the perturbation parameter are equal to 0.2, indicating global error percentages lower than 10% for the measured p−T−x1− y1 properties. These results that are coincident with a previous analysis found in the literature.25 Figures 3 and 4 show the differences y1 − x1 vs x1 in order to magnify composition errors. Reciprocation is observed between the different isobaric systems of this work. Some differences are seen with that reported in literature,10−13 mainly in the vicinity of the minimum of the curves; this may be due to experimental errors and due to the different purity of the employed substances. Accordingly, these figures show that there is no 2299



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Table 4. Experimental and Calculated Values of VLE Dataa T/K 365.78 366.03 366.30 366.90 367.59 368.26 368.99 369.39 369.94 370.42 370.87 371.48 372.05 372.60 373.02 373.55 374.05 374.79 375.85 376.78 377.94 378.34 379.48 382.83 384.24 387.83 392.22 399.44 403.89 407.86 409.45 413.30 383.84 383.98 384.04 384.27 384.89 385.46 385.93 386.87 387.45 388.20 388.70 389.24 389.82 390.50 390.76 391.19 391.67 392.02 392.35 392.75 392.99 393.84 394.32 394.80 395.70 397.08 398.38

x1

y1

γ1

Butyl Acetate (1) + 2-Propanol (2) at 0.15 MPa 0.000 0.000 0.014 0.004 1.21 0.020 0.009 1.88 0.050 0.024 1.96 0.087 0.037 1.70 0.112 0.046 1.60 0.137 0.057 1.58 0.170 0.066 1.46 0.200 0.077 1.42 0.227 0.084 1.34 0.253 0.093 1.31 0.285 0.100 1.23 0.310 0.110 1.22 0.338 0.119 1.19 0.366 0.128 1.16 0.398 0.143 1.17 0.431 0.158 1.18 0.459 0.168 1.15 0.495 0.188 1.15 0.533 0.202 1.11 0.550 0.213 1.09 0.574 0.227 1.10 0.595 0.240 1.08 0.683 0.293 1.03 0.707 0.314 1.02 0.786 0.378 0.99 0.858 0.461 0.97 0.916 0.614 0.98 0.951 0.724 0.98 0.973 0.837 1.00 0.981 0.883 1.00 1.000 1.000 1.00 Butyl Acetate (1) + 2-Butanol at 0.15 MPa 0.000 0.000 0.005 0.004 1.86 0.024 0.016 1.55 0.041 0.028 1.57 0.087 0.059 1.53 0.122 0.076 1.38 0.149 0.090 1.32 0.201 0.119 1.26 0.229 0.139 1.27 0.267 0.160 1.22 0.296 0.181 1.23 0.327 0.200 1.21 0.358 0.215 1.17 0.399 0.238 1.14 0.422 0.252 1.13 0.440 0.261 1.11 0.478 0.283 1.09 0.510 0.301 1.07 0.531 0.312 1.06 0.543 0.319 1.05 0.556 0.327 1.04 0.591 0.356 1.04 0.610 0.373 1.04 0.628 0.387 1.03 0.657 0.411 1.02 0.699 0.455 1.02 0.730 0.491 1.02

γ2

T/K

x1

y1

γ1

1.00 1.00 0.99 0.99 0.99 0.98 0.97 0.99 0.99 1.00 1.01 1.03 1.03 1.04 1.06 1.08 1.10 1.12 1.13 1.16 1.14 1.17 1.17 1.24 1.25 1.38 1.58 1.55 1.67 1.61 1.57

409.88 410.31 410.79 411.93 413.32 414.77 415.61 416.38 417.35 418.58 419.03 420.23 420.78 422.05 423.12 423.93 427.31 429.04 432.02 436.86 439.62 445.51 449.36 451.89 460.24 468.77 471.24 472.76 474.55

Butyl Acetate (1) + 2-Propanol (2) at 0.6 MPa 0.000 0.000 0.015 0.005 1.42 0.040 0.014 1.47 0.069 0.026 1.53 0.101 0.037 1.44 0.151 0.053 1.33 0.175 0.061 1.29 0.201 0.071 1.28 0.236 0.081 1.21 0.255 0.091 1.22 0.276 0.098 1.20 0.308 0.110 1.17 0.326 0.119 1.18 0.359 0.132 1.15 0.379 0.143 1.15 0.405 0.154 1.14 0.488 0.196 1.10 0.520 0.222 1.13 0.577 0.250 1.06 0.665 0.321 1.06 0.717 0.362 1.04 0.777 0.439 1.02 0.827 0.498 1.00 0.854 0.539 0.99 0.916 0.708 1.02 0.976 0.893 1.02 0.984 0.933 1.00 0.991 0.964 1.00 1.000 1.000 1.00

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.99 1.00 0.99 1.00 1.01 1.02 1.03 1.04 1.07 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.19 1.19

431.73 432.43 433.02 433.88 434.54 435.83 436.58 437.22 438.26 439.28 439.95 440.96 441.95 442.73 443.75 444.97 445.75 446.53 447.56 448.91 449.73 450.63 451.92 452.95 454.25 455.48 456.99

Butyl Acetate (1) + 2-Butanol at 0.6 MPa 0.000 0.000 0.024 0.011 1.11 0.042 0.022 1.26 0.076 0.037 1.14 0.104 0.050 1.11 0.145 0.072 1.11 0.172 0.086 1.10 0.195 0.100 1.11 0.226 0.119 1.12 0.261 0.137 1.09 0.288 0.149 1.06 0.314 0.169 1.07 0.345 0.189 1.07 0.365 0.205 1.08 0.397 0.226 1.07 0.436 0.249 1.04 0.453 0.266 1.05 0.479 0.283 1.04 0.509 0.308 1.04 0.543 0.337 1.04 0.563 0.354 1.03 0.590 0.375 1.02 0.619 0.404 1.02 0.646 0.429 1.02 0.675 0.458 1.01 0.703 0.489 1.01 0.732 0.525 1.01

2300

γ2 1.00 1.00 1.00 0.99 0.98 0.98 0.98 0.98 0.99 0.97 0.98 0.98 0.99 0.99 0.98 0.99 1.01 1.00 1.02 1.05 1.10 1.08 1.15 1.18 1.11 1.21 1.08 1.01

1.00 1.00 0.99 0.99 0.99 0.99 0.98 0.98 0.98 0.98 0.99 0.98 0.97 0.97 0.97 0.98 0.97 0.98 0.98 0.98 0.98 0.99 0.99 1.00 1.00 1.01 1.00



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Table 4. continued T/K 399.56 400.72 402.14 403.99 405.51 407.68 409.36 410.69 413.30

x1

y1

γ1

Butyl Acetate (1) + 2-Butanol at 0.15 MPa 0.765 0.532 1.01 0.795 0.573 1.02 0.833 0.621 1.01 0.869 0.684 1.01 0.898 0.727 1.00 0.924 0.798 1.00 0.948 0.857 1.00 0.967 0.910 1.01 1.000 1.000 1.00

γ2

T/K

1.21 1.22 1.28 1.29 1.36 1.27 1.26 1.20

458.50 459.85 461.61 463.23 464.95 466.33 467.85 469.45 471.55 473.05 474.55

x1

y1

γ1

Butyl Acetate (1) + 2-Butanol at 0.6 MPa 0.763 0.564 1.01 0.790 0.599 1.01 0.824 0.643 1.00 0.854 0.688 1.00 0.878 0.735 1.00 0.900 0.775 1.00 0.923 0.816 1.00 0.944 0.863 1.00 0.970 0.924 1.00 0.988 0.969 1.00 1.000 1.000 1.00

γ2 1.01 1.02 1.05 1.07 1.05 1.06 1.09 1.08 1.07 1.06

a Expanded uncertainties U(k=2) are U(T) = 0.2 K, U(p) = 0.002 MPa, and U(x1)  U(y1) = 0.005. T, x1, y1, γ1, and γ2 represent temperature, liquid phase ester mole fraction, vapor phase ester mole fraction, liquid phase activity coefficient of ester, and liquid phase activity coefficient of alcohol.

Figure 3. Experimental data and fitting curves for BA2P at 0.15 MPa (blue ●) and 0.6 MPa (red ■). Literature data and fitting curves from Gmehling et al.10 at 46.7 kPa (brown ▲) and Gonzalez and Ortega11 at 101.3 kPa (green ▼).

Figure 4. Experimental data and fitting curves for BA2B at 0.15 MPa (blue ●) and 0.6 MPa (red ■). Literature data and fitting curves from Gonzalez and Ortega12 (green ▼) and Feng et al.13 (brown ▲), both at 101.3 kPa.

adequate information for isobaric extrapolations. Figures 5 and 6 include T vs x1,y1 data. The evolution of these surfaces with pressure is seen in the vertical plane, which in turn can be displayed in two dimensions to make it easier to check the compression of systems and the evolution of vapor pressures. 3.4. Group Contribution Models. The group contribution models arise as a usual tool for the prediction of the properties of the substances and their mixtures. They are based on accepting that the functional groups of the molecules always contribute equally to the properties of substances regardless of the substance. To determine the contribution of the groups, the experimental properties of substances or mixtures are correlated to the model equation,

Differences in the models arise from the interpretation given to each one of the contributions. In the ASOG3 model the combinatorial part is obtained by using the Flory−Huggins equation while the residual part is represented by a Wilson-type equation. The UNIFAC4−6 models are generally based in the equations of the UNIQUAC model for the combinatorial part, while the residual part is replaced by the solution of the different groups. The group contributions are evaluated using different expressions. To determine the interaction parameter (mij), the ASOG3 model uses the following equation;

ln γi = ln γicombinatorial + ln γi residual

mij = −a1ij T − a2ij

(5)

(6)

while the UNIFAC−Lyngby4 model indicates the following expression,

whereby it becomes possible to obtain a pair of constants for each group. 2301



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ln aij = −

Figure 6. T vs x1,y1 (blue or red symbol, respectively) for BA2B at 0.15 MPa (blue ●, red ●) and 0.6 MPa (blue ■, red ■). Literature data from Gonzalez and Ortega12 (blue ▼, red ▼) at 101,3 kPa.

⎡ ⎤ T mij = a1ij + a2ij(T − T0) + a3ij ⎢T ln 0 + (T − T0)⎥ ⎣ ⎦ T (7)

and the UNIFAC−Dortmund equation: mij = a1ij + a2ijT + a3ij T 2

T

(9)

It can be seen from eqs 6−8 that all the mentioned group contribution models, except the original UNIFAC5,15 model, use temperature-dependent interaction parameters. Table ST5 shows (see Supporting Information) the constant parameters used in this work for the group contribution models employed. The disadvantages of using group contribution models for predictions arises, on one hand, from the quality of experimental data and, on the other, from the limit of the operating conditions under which they were obtained. Focusing on VLE experimental data, these have been mainly obtained at low pressure; hence the constants given by the groups are limited to be used under such operating conditions. This is why when the group contribution models are used to make predictions at moderate and high pressure, the quality of results is not always satisfactory. In this work data obtained at low and moderate pressure and which have been verified using the test of Van Ness et al.14 are used to check the quality of the predictions made by the ASOG3 and the UNIFAC4−6 models. Tables ST6−ST9 (see Supporting Information) show the results of predictions for each obtained data point by applying the group contribution models. Table 5 shows the overall differences between the experimental data of this work and the predictions of these models. Figure 7 includes the individual differences between experimental data and predictions made using the UNIFAC− Lyngby4 and the UNIFAC−Dortmund6 models. Results for the group contribution model predictions presented in Table 5 indicate that the overall best predictions are obtained with the UNIFAC−Dortmund6 model by considering MAD of temperature. However, the UNIFAC−Lyngby4 model generates good overall predictions when MPD of vapor phase ester mole fraction is considered. This model reproduces with high precision the BA2B system at 0.15 MPa. The ASOG3 model predicts well data at low pressure for both systems at 0.15 MPa, but returns significant errors when data are estimated at moderate pressure, as can be seen from MAD of p results included in Table 5. However, when specific predictions are studied, significant differences are observed (see Figure 7), mainly for temperature of mixtures: this can be observed in the prediction of BA2B at 0.15 MPa with the UNIFAC−Lyngby4 model. Deviatons are also observed for the prediction of composition (Table 5): the most significant deviations can be seen for the prediction made by the UNIFAC−Dortmund6 model for BA2P at 0.15 MPa. 3.5. PC-SAFT Model. As a consequence of the need to specify properties of pure fluids within wide ranges the EOS arise. Its application to mixtures requires the use of appropriate mixing rules. Among the different EOS, Gross−Sadowski1,2 have developed a molecular-based EOS by applying the perturbation theory of Barker and Henderson.27,28 The PCSAFT1,2 equation is written in terms of residual Helmholtz free energy (Ares/NkT):

Figure 5. T vs x1,y1 (blue or red symbol, respectively) for BA2P at 0.15 MPa (blue ●, red ●) and 0.6 MPa (blue ■, red ■). Literature data from Gmehling et al.10 at 46.7 kPa (blue ▲, red ▲) and Gonzalez and Ortega11 at 101.3 kPa (blue ▼, red ▼).

6

mij

model employs the next

Ares Ahc Adisp Aassoc = + + NkT NkT NkT NkT

(8)

(10)

The hard-sphere chain (hc) comprises a number of segments per chain (mi), a segment diameter (σi), and a segment energy parameter (εi). The dispersion contribution (dis) to the

All the mentioned models, including the original UNIFAC5,15 model, calculate the group parameters (aij) as follows: 2302



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Table 5. Results of Predictions Using Group Contribution Modelsa UNIFAC−Lyngby4

a

MAD(y1) MAD(T)/K MAD(p)/MPa MPD(γ1) MPD(γ2)

0.009 1.04 0.006 7.20 5.97


0.013 1.35 0.021 4.49 7.92


0.004 0.55 0.003 1.84 2.41


0.011 0.83 0.011 3.03 5.73

UNIFAC5,15

UNIFAC−Dortmund6

ASOG3

0.014 0.95 0.005 7.15 6.89

0.008 1.38 0.008 10.42 6.01

0.012 0.92 0.014 8.25 5.25

0.014 2.62 0.044 7.84 11.85

0.011 0.63 0.003 5.01 4.16

0.011 1.53 0.008 5.58 8.11

0.007 0.54 0.008 2.27 3.00

0.024 3.44 0.051 9.88 15.49

Butyl Acetate (1) + 2-Propanol (2) At 0.15 MPa 0.015 2.32 0.013 18.29 11.14 At 0.6 MPa 0.028 4.37 0.074 17.80 23.85 Butyl Acetate (1) + 2-Butanol (2) At 0.15 MPa 0.020 2.60 0.013 11.75 14.82 At 0.6 MPa 0.035 4.96 0.075 17.02 24.18

Mean absolute deviation (MAD) and mean proportional deviation (MPD) calculated as follows. MAD(F ) =

1 n−2

n

∑ |Fexp − Fcal|; 1

100 MPD(F ) = n−2

n

∑ 1

|Fexp − Fcal| Fexp

;

F ≡ y1 , T , p , γ1, γ2

method has been used. A multiobjective function such as the sum of the values of individual goals was optimized. Each objective function (OF1, OF2) was multiplied by a coefficient of weight (W1, W2), in order to achieve an equilibrium balance between both properties. Therefore, the resulting multiobjective function (MOF) applied to minimize the correlation of data was

Helmholtz free energy accounts for van der Waals forces, being the sum of the first- and second-order perturbation terms. These can be obtained through power series in the packing fraction which represent a reduced segment density. Both also depend on mi, σi, and εi. If the conventional combining rules are employed for σi and εi, then the binary interaction parameter (kij) is obtained when the mixing data are correlated. The Helmholtz free energy from associating contribution (assoc) is a function of association strength. To describe the molecular association, the association energy parameter (εAiBj) and association volume parameter (κAiBj) are needed. The crossassociation interactions in mixtures can be obtained by using the combining rules suggested by Wolbach and Sandler.29 Model parameters can be obtained by simultaneously correlating the vapor pressures and molar density of substances. For this purpose, the vapor pressures of butyl acetate (Table 2), 2-propanol,16 and 2-butanol,17 along with the constants taken from Daubert and Danner22 to calculate the molar densities of these substances, were used in eq 10. It is the reason why the Fortran program prepared by us following the MatLab program of Martiń et al.30 was implemented for the correlation of data in the way indicated by Gross and Sadowski.1 Accordingly, to fit vapor pressures and molar density data simultaneously with eq 10, the minimizing of both properties is required. We propose to use a modification of the weighted sum method. This is the reason why the goal programming

MOF = OF1 × (W1)2 + OF2 × (W2)2

(11)

being the objective functions and weights of vapor pressures and molar densities, respectively, as follows: ⎡ n |p0 − p0 | ⎤ i ,exp i ,cal ⎥ OF1 = ⎢∑ 0 ⎢ ⎥ p ⎣ 1 ⎦ i ,exp ⎛ 100 W1 = ⎜⎜ n ⎝ −2

n

∑

⎛ 1 /⎜⎜ ⎝n − 2

1

|pi0,exp − pi0,cal | ⎞ ⎟ ⎟ pi0,exp ⎠

n

∑ |pi0,exp 1

(12) n

∑ (pi0,exp − pi0,cal )2 /(n − 2)

⎞ − pi0,cal |⎟⎟ ⎠

⎡ n |ρ L − ρi L,cal | ⎤ i ,D&D ⎥ OF2 = ⎢∑ ⎢⎣ 1 ⎥⎦ ρi L,D&D 2303

1

(13)

(14) DOI: 10.1021/acs.jced.7b00141 J. Chem. Eng. Data 2017, 62, 2296−2306


Article

Figure 7. T vs x1,y1 (blue or red symbols, respectively) as well as y1 − x1 vs x1 (black symbols) for the systems: BA2P at 0.15 MPa (▲), BA2P at 0.6 MPa (▼), BA2B at 0.15 MPa (▶) and BA2B at 0.6 MPa (◀). The predictions are represented by the fitting curves: UNIFAC−Lyngby4 (green), UNIFAC−Dortmund6 (sky blue), and PC-SAFT1,2 (purple) for all these systems. ⎛ 100 W2 = ⎜⎜ ⎝n − 2

n

∑

⎛ 1 /⎜⎜ ⎝n − 2

1

|ρi L,D&D − ρi L,CAL | ⎞ ⎟ ⎟ ρi L,D&D ⎠

n

∑ |ρi L,D&D 1

⎞ − ρi L,cal |⎟⎟ ⎠

normalizing effect because they represent a statistical uncertainty of each property. The relative errors of each property are representative of the independent objectives in the correlation of data. Table 6 contains the results of constant characteristics of each of the substances, by proceeding as previously indicated and using the PC-SAFT1,2 model. We have verified that the obtained constants correlate well with experimental vapor pressures.

n

∑ (ρi L,D&D − ρi L,cal )2 /(n − 2) 1

(15)

The weight coefficients defined by the mean absolute deviation, the standard deviation, and the mean proportional deviation of both properties in eq 11 have a preference and 2304



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Table 6. PC-SAFT Pure Component Parametersa 2-propanol

a

2-butanol

butyl acetate

param

TWa

ref 2

TWa

ref 31

ref 32

TWa

ref 1

mi σi/Å εi/K κAiBj εAiBj/K MAD(p)/kPa MAD(ρ)/(kmol·m−3) MPD(p)/% MPD(ρ)/% SD(p)/kPa SD(ρ)/(kmol·m−3)

3.724015 3.005506 211.9 0.012742 2054.31 0.94 0.01 0.55 0.12 1.25 0.01

3.0929 3.2085 208.42 0.024675 2253.9

3.142169 3.417585 228.53 0.021522 2116.35 1.35 0.05 1.20 0.50 1.73 0.05

2.8460 3.5420 234.61 0.0078 2488.00

3.44 3.313 224.2 0.0104 2067.63

4.014396 3.534224 240.93

3.9808 3.5427 242.52

1.77 0.04 1.04 0.66 2.11 0.05

2.03 1.26

0.7 1.25

0.35 0.78

TW = this work; standard deviation (SD) calculated as follows. n

∑ (Fexp − Fcal)2 /(n − 2) ;

SD(F ) =

F ≡ p, ρ

1

The greatest difference is seen in the BA2B system at 0.6 MPa. However, from the predictions made by the PC-SAFT1,2 model (Figure 7), it can be observed that deviations are only greater than those from the predictions made by the group contribution models in the range of molar fraction close to the minimum of the curves y1 − x1 vs x1. On the other hand, the prediction that PC-SAFT1,2 model makes on temperature for all systems is much more accurate than the one made by the group contribution models: this can be verified in Tables 6 and 7. This aspect is further checked in the Figure 7 to observe the specific deviations in the T vs x1,y1 plots.

Therefore, we have used the PC-SAFT model equation (eq 10) with the constants in Table 6 and have considered the solvation phenomena in ester. Thus, for the prediction of ester/ alcohol mixtures, the association volume parameter corresponding to the alcohol was assigned to the ester. Moreover, for the adjustable interaction parameter of the PC-SAFT1,2 model, the bubble point method was applied and the following objective function (OF3) was used: n

OF3 =

∑ |(Ti)exp − (Ti)cal | 1

1 U (T )

n

+

∑ |(yi )exp − (yi )cal | 1

1 U (y )

4. CONCLUSIONS VLE data for the binary systems butyl acetate + 2-propanol and butyl acetate + 2-butanol were determined at 0.15 and 0.6 MPa. The point-to-point test was applied, and results show a positive global consistency criterion. By applying the group contribution models, it can be clearly seen that UNIFAC−Lyngby and UNIFAC−Dortmund models predict in better agreement with the experimental data of this work, if original UNIFAC is taken for comparison. Data prediction made with the ASOG model was poor. The results for VLE data prediction at higher temperatures show the limits of these models. The PC-SAFT model was employed for VLE data prediction because by using EOS no standard fugacity is required. For this, parameters were obtained for pure substances and VLE data were obtained by applying a bubble point routine; these data were then compared to experimental data. Results show very good correlations between experimental and prediction data considering the T vs x1,y1 diagrams.

(16)

The minimization function (eq 16) has a structure similar to that considered in eq 11. Consequently, a weight normalizing factor has been employed for each separate objective function, which is specified by the sum of the absolute deviations. The use of the uncertainties included in eq 16 as weighting factors provides a higher accuracy for the PC-SAFT1,2 model prediction, since the standard uncertainty (SD) only considers the uncertainty type A, while expanded uncertainty (U) includes the other type B components of the uncertainty. Furthermore, the functional structure of eq 16 is allocated so that it can balance the two simultaneously correlated functions. The overall results of predictions made, as described, by the PC-SAFT1,2 model for the systems studied in this work are shown in Table 7. Table ST10 (see Supporting Information) shows the results of predictions for each data point. It can be seen that the MAD in vapor phase ester mole fraction is slightly higher than that obtained with the group contribution models.

■

Table 7. Binary Interaction Parameters and Prediction Results Using PC-SAFT1,2 BA2P model/binary systems PC-SAFT

MAD(y1) MAD(T)/K kij OF3

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00141. Point-to-point test results, calculated fugacity coefficients, correlation parameters of G E /RT vs x 1 , relative volatilities, group interaction parameters, and various model results (PDF)

BA2B

0.15 MPa

0.6 MPa

0.15 MPa

0.6 MPa

0.016 0.65 0.0138 829.2

0.017 1.06 0.0105 1098.7

0.013 0.29 −0.0062 518.4

0.016 0.28 −0.0145 592.5

ASSOCIATED CONTENT

2305



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(19) Yen, L. C.; Woods, S. S. A generalized equation for computer calculation of liquid densities. AIChE J. 1966, 12, 95−99. (20) Laavi, H.; Pokki, J. P.; Uusi-Kyyny, P.; Massimi, A.; Kim, Y.; Sapei, E.; Alopaeus, V. Vapor-Liquid Equilibrium at 350 K, Excess Molar Enthalpies at 298 K and Excess Molar Volumes at 298 K of Binary Mixtures Containing Ethyl Acetate, Butyl Acetate, and 2Butanol. J. Chem. Eng. Data 2013, 58, 1011−1019. (21) Ortega, J.; Susial, P. Measurements and prediction of VLE of methyl propanoate-ethanol-propan-1-ol at 114.6 and 127.99 kPa. J. Chem. Eng. Jpn. 1990, 23, 349−353. (22) Daubert, T. E.; Danner, R. P. Physical and Thermodynamic Properties of Pure Chemicals: Data Compilation; Hemisphere: New York, 1989. (23) Tsonopoulos, C. An empirical correlation of second virial coefficients. AIChE J. 1974, 20, 263−272. (24) Spencer, C. F.; Danner, R. P. Improved equation for prediction of saturated liquid density. J. Chem. Eng. Data 1972, 17, 236−241. (25) Mathias, P. M. Sensitivity of Process Design to Phase Equilibrium. A New Perturbation Method Based Upon the Margules Equation. J. Chem. Eng. Data 2014, 59, 1006−1015. (26) Renon, H.; Prausnitz, J. M. Local Compositions in Theermodynamic Excss Functions for Liquid Mixtures. AIChE J. 1968, 14, 135−144. (27) Baker, J. A.; Henderson, D. Perturbation theory and equation of state for fluids: The square-well potential. J. Chem. Phys. 1967, 47, 2856−2861. (28) Barker, J. A.; Henderson, D. Perturbation theory and equation of state for fluids: II. A successful theory of liquids. J. Chem. Phys. 1967, 47, 4714−4721. (29) Wolbach, J. P.; Sandler, S. I. Using molecular orbital calculations to describe the phase bahavior of cross-associating mixtures. Ind. Eng. Chem. Res. 1998, 37, 2917−2928. (30) Martín, A.; Bermejo, M. D.; Mato, F. A.; Cocero, M. J. Teaching advanced equations of state in applied thermodynamics courses using open source programs. Educ. Chem. Eng. 2011, 6, e114−e121. (31) Almasi, M. Thermodynamic Properties of Binary Mixtures Containing N,N-Dimethylacetamide + 2-Alkanol: Experimental Data and Modeling. J. Chem. Eng. Data 2014, 59, 275−281. (32) Smith, B. D.; Srivastava, R. Thermodynamic Data for Pure compounds. Part B: Halogenated Hydrocarbons and Alcohols; Elsevier: Amsterdam, 1986.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Gross, J.; Sadowski, G. Perturbed-Chain, SAFT An Equation of State Based on a Perturbation Theory for Chain Molecules. Ind. Eng. Chem. Res. 2001, 40, 1244−1260. (2) Gross, J.; Sadowski, G. Application of the perturbed-chain SAFT equation of state to associating systems. Ind. Eng. Chem. Res. 2002, 41, 5510−5515. (3) Kojima, K.; Tochigi, K. Prediction of Vapor-Liquid Equilibria by the ASOG Method; Kodansha: Tokyo, 1979. (4) Larsen, B. L.; Rasmussen, P.; Fredenslund, Aa A modified UNIFAC Group-Contribution Model for Prediction of Phase Equilibria and Heats of Mixing. Ind. Eng. Chem. Res. 1987, 26, 2274−2286. (5) Hansen, H. K.; Rasmussen, P.; Fredenslund, Aa.; Schiller, M.; Gmehling, J. Vapor-Liquid Equilibria by UNIFAC Group-Contribution. 5. Revision and Extension. Ind. Eng. Chem. Res. 1991, 30, 2352− 2355. (6) Gmehling, J.; Li, J.; Schiller, M. A Modified UNIFAC Model. 2. Present Parameter Matrix and Results for Different Thermodynamic Properties. Ind. Eng. Chem. Res. 1993, 32, 178−193. (7) Susial, P.; Sosa-Rosario, A.; Rios-Santana, R. Vapor-liquid equilibria for ethyl acetate + methanol at (0.1, 0.5, and 0.7) MPa. Measurements with a new ebulliometer. J. Chem. Eng. Data 2010, 55, 5701−5706. (8) Susial, P.; Sosa-Rosario, A.; Rodriguéz-Henriquéz, J. J.; RiosSantana, R. Vapor Pressures and VLE Data Measurements. Ethyl Acetate+Ethanol at 0.1, 0.5 and 0.7 MPa Binary System. J. Chem. Eng. Jpn. 2011, 44, 155−163. (9) Susial, P.; Sosa-Rosario, A.; Rios-Santana, R. Vapour-Liquid Equilibrium with a New Ebulliometer: Ester + Alcohol System at 0.5 MPa. Chin. J. Chem. Eng. 2010, 18, 1000−1007. (10) Gmehling, J.; Onken, U.; Weidlich, U. Vapor-Liquid Equilibrium Data Collection, Chemistry Data Series, Vol. 1; Dechema: Frankfurt, Germany, 1982; Supplement 2, part 2d. (11) Gonzalez, E.; Ortega, J. Vapor−Liquid Equilibria at 101.32 kPa Mixtures of Butyl Esters and Propan-2-ol. J. Chem. Eng. Jpn. 1996, 29, 294−299. (12) Gonzalez, E.; Ortega, J. Vapor−Liquid Equilibria at 101.32 kPa Mixtures Formed by the First Four Butyl Alkanoates and Butan-2-ol. Fluid Phase Equilib. 1996, 124, 162−175. (13) Gmehling, J.; Onken, U. Vapor-Liquid Equilibrium Data Collection, Chemistry Data Series, Vol. 1; Dechema: Frankfurt, Germany, 2009; Supplement 9, part 2k. (14) Van Ness, H. C.; Byer, S. M.; Gibbs, R. E. Vapor-Liquid Equilibrium: I. An Appraisal of Data Reduction Methods. AIChE J. 1973, 19, 238−244. (15) Fredenslund, Aa.; Gmehling, J.; Rasmussen, P. Vapor-liquid Equilibria Using UNIFAC, A Group Contribution Model; Elsevier: Amsterdam, 1977. (16) Susial, P.; Rodríguez-Henríquez, J. J.; Apolinario, J. C.; Castillo, V. D.; Estupiñan, E. J. Vapour pressures and vapour-liquid equilibria of binary systems of n-propyl acetate and isobutyl acetate with ethanol or 2-propanol at 0.15 MPa. J. Serb. Chem. Soc. 2012, 77, 1243−1257. (17) Susial, P.; Rodríguez-Henríquez, J. J.; Castillo, V. D.; Estupiñan, E. J.; Apolinario, J. C.; Susial, R. Isobaric (vapor + liquid) equilibrium for n-propyl acetate with 1-butanol or 2-butanol. Binary mixtures at 0.15 and 0.6 MPa. Fluid Phase Equilib. 2015, 385, 196−204. (18) Susial, P.; García, D.; Susial, R.; Clavijo, Y. C.; Martín, A. Measurement and modelization of VLE of binary mixtures of propyl acetate, butyl acetate or isobutyl acetate with methanol at pressure of 0.6 MPa. Chin. J. Chem. Eng. 2016, 24, 630−637. 2306


Measurements and Modeling of VLE Data for Butyl Acetate with 2

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