Experimental VaporâLiquid Equilibria Data of Methyl Acetate or Ethyl

Article pubs.acs.org/jced

Experimental Vapor−Liquid Equilibria Data of Methyl Acetate or Ethyl Acetate with 2‑Butanol at 0.3 MPa and 0.6 MPa. Quality Assessment and Predictions Pedro Susial,* Rodrigo Susial, Victor D. Castillo, Esteban J. Estupiñan, José J. Rodríguez-Henríquez, and José C. Apolinario Escuela de Ingenierias Industriales y Civiles. Universidad de Las Palmas de Gran Canaria, 35017-Campus de Tafira. Las Palmas de Gran Canaria, Canary Islands, Spain ABSTRACT: Isobaric vapor−liquid equilibria for the binary system methyl acetate + 2-butanol at 0.3 MPa and 0.6 MPa and ethyl acetate + 2-butanol at 0.3 MPa and 0.6 MPa have been determined. Thermodynamic consistency was checked. The Redlich−Kister and Herington area tests were employed. The Point test, Area test and Infinite dilution test (PAI) of Kojima et al. and the point-to-point test of Van Ness et al. were also applied. The different criteria for validation were considered, and all systems showed an acceptable quality. The results of global and individual deviations on experimental data calculated by using the Fredenslund et al. routine are shown. The different versions of the unique functional group activity coefficient (UNIFAC) and analytical solution of groups (ASOG) predictive group contribution models were applied. The experimental data were also correlated with the Peng−Robinson equation applying quadratic mixing rules.

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INTRODUCTION The study of ester + alcohol mixtures allows advancement in the knowledge of molecular interactions because of the breaking and formation of new bonds by hydrogen bonding.1 Furthermore, there is special interest in these studies to increase the utilization of these solvents in different industrial processes. Alcohols, among them 2-butanol, are used as additives in the reformulation of gasoline. This alcohol is also used as a flotation agent in the production of pesticides and in the fabrication of perfumes. Alternately, alkyl esters are used in a wide range of industrial processes. Thus, methyl acetate is used in organic synthesis and is also an excellent solvent for resin and paints, while ethyl acetate is used in the food, photographic, textile, and paper industries. For these reasons and as a continuation of previous works,2−4 the experimental values of the vapor−liquid equilibria (VLE) of the binary mixtures methyl acetate + 2butanol (MA2B) and ethyl acetate + 2-butanol (EA2B) have been determined at 0.3 MPa and 0.6 MPa. The system MA2B has been studied under isobaric conditions at 74.66 kPa and 127.99 kPa.5 Also, VLE data for MA2B at 101.32 kPa have been obtained.5,6 The EA2B system has been reported in the literature at 101.32 kPa7 and isotermically8 at 350 K only. To verify the quality of the experimental data, the consistency test point-to-point from Van Ness et al.9 has been applied in the way proposed by Fredenslund et al.10 Afterward, consistent data were used to verify the predictions of the group contribution models used: the analytical solution of groups (ASOG)11 and different versions of the unique functional group activity coefficient (UNIFAC).12−14 Finally, © 2014 American Chemical Society

the experimental data were correlated with the Peng− Robinson15 (PR) equation of state (EOS) using quadratic mixing rules.

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EXPERIMENTAL SECTION Chemicals and Apparatus. Methyl acetate with a purity of > 99.0 % and ethyl acetate with a purity of > 99.9 % have been employed, both from Panreac Quimica S.A., with properties not different from that previously published.2,4 The normal boiling point (Tbp), density (ρii) and refractive index (nD) at 298.15 K of 2-butanol, from Sigma-Aldrich (purity higher than 99.5 %), and their comparison with literature data are presented in Table 1. These substances were used without further purification. The normal boiling point at 0.1 MPa was determined using a stainless steel ebulliometer.3 The density was determined with a Kyoto Electronics DA-300 vibration density meter with an uncertainty of ± 0.1 kg m−3. The refractometer Zusi 315 RS Abbe with an uncertainty of ± 0.0002 units was employed for the determination of the refractive index. Equipment and Procedure. An ebulliometer of continuous operation, in which both the liquid and vapor phases are recirculated, as well as the experimental installation used in this work has been previously described.3,4 A Pt100 probe with digital display P655 from Dostmann Electronic GmbH was used. The calibration of the probe-display unit was performed Received: April 9, 2014 Accepted: July 28, 2014 Published: August 4, 2014 2763

dx.doi.org/10.1021/je5003225 | J. Chem. Eng. Data 2014, 59, 2763−2772

Journal of Chemical & Engineering Data

Article

Table 1. Physical Properties with Literature Values of Pure Substance at Atmospheric Pressurea

a

Tbp

ρii (298.15K)

K

kg·m−3

nD (298.15 K)

compound

purity

exptl

lit.

exptl

lit.

exptl

lit.

2-butanol

puriss. w > 99.5

372.76

372.47b 372.70c

802.5

802.41b 802.60c

1.3949

1.39503b 1.3949c

Uncertainties u are u(T) = 0.01 K, u(Tbp) = 0.03 K, u(p) = 0.0005 MPa, u(nD) = 0.0002 and u(ρii) = 0.1 kg·m−3. bReference16. cReference17.

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RESULTS AND ASSESMENT Excess Molar Volumes. Table 2 shows vE at 298.15 K for mixtures MA2B and EA2B, calculated for every density− composition pair of values using the molecular mass (Mi) and densities (ρi) of the pure components and with the following equation:

by Dostmann Electronic GmbH and the standard procedure NPL and NIST was followed (uncertainty of ± 0.03 K). A digital transducer model 8311 from Burket Fluid Control Systems was employed as pressure controller; its operational range is from 0.0 MPa to 4.0 MPa (uncertainty of ± 0.004 MPa). The pressure in the system was obtained using dry nitrogen, which was circulated through a silica gel vessel. As a consequence of the moderate work pressure, and to regulate the dry nitrogen flow, a control valve Binks MFG Co. with 1.0 MPa operation limit was used. Redistribution of the substances inside the ebulliometer takes place due to a concurrent flow between both phases for 90 min. The mass transfer process during this time allows acquisition of a steady state near to the equilibrium condition. After that, samples from both the liquid and vapor phases were extracted. These were analyzed as in previous works.2−4 A calibration curve density vs composition previously prepared allowed the calculation of the composition of both phases. Table 2 shows the data corresponding to the ester molar fraction (xi) vs density (ρij) for the mixtures MA2B and EA2B. These pairs of values were verified when the molar excess volumes (vE) were correlated. The composition of both phases for the equilibrium data were estimated with an uncertainty less than 0.002 units.

2 i=1

x1 0.0000 0.0580 0.1719 0.2756 0.3391 0.4544 0.4714 0.5051 0.0000 0.0415 0.0917 0.1482 0.2080 0.2570 0.2963 0.3488 0.3914 0.4397 0.4905

109·vE −3

kg m

3

−3

m mol

ρij x1

kg m

Methyl Acetate (1) + 2-Butanol (2) 802.5 0.0 0.5458 858.5 807.2 182.8 0.5930 864.5 817.3 463.2 0.6822 876.6 827.5 633.9 0.7990 893.7 834.2 703.6 0.8576 902.9 847.3 762.9 0.8788 906.3 849.3 768.2 0.9586 919.9 853.4 767.8 1.0000 927.3 Ethyl Acetate (1) + 2-Butanol (2) 802.5 0.0 0.5313 847.3 805.6 110.4 0.6000 853.8 809.5 222.9 0.6539 859.0 813.9 343.6 0.7031 863.8 818.7 449.3 0.7410 867.5 822.8 512.7 0.7953 873.0 826.2 548.2 0.8528 878.9 830.7 596.8 0.8891 882.6 834.5 616.3 0.9484 889.0 838.9 624.9 1.0000 894.5 843.5 633.7

j=1

xiMi ρij

(1)

To verify the data dispersion, the v vs x1 pairs were correlated to the expression: m

ν E = x1(1 − x1) ∑ A kZTk

(2)

k=0 18

where the active fraction (ZT) of Ocón is modified to systematize the correlation of data using the pure properties of substances at any pressure as follows: x1 ZT = x1 + R νx 2 (3) where Rn is the ratio of molar volumes of the pure substances (vi0) as Rn = v01/v02. Consequently, data from Table 2 were correlated to eq 2 by applying eq 3 and using the Yen and Woods19 equation to calculate molar volumes at atmospheric pressure. Results at 0.1 MPa are A0 = 3455.8; A1 = −1405.3; and A2 = 1284.2 with Rn = 1.03 and σ(109·vE) = 2 m3·mol−1 as standard deviation for the MA2B system. Results for system EA2B are A0 = 2853.3; A1 = −1059.5; and A2 = 730.1.0 with Rn = 1.30 and σ(109·vE) = 4 m3·mol−1. Figure 1 shows the data from this work with their respective fitting curves, as well as vE values from literature.5−8,16,20 Figure 1 shows an agreement correlation between data obtained in this work and that found in the literature.5−8,16,20 A comparison of both systems shows an expansion volumetric effect on system MA2B as compared to that of the system EA2B. This may be a consequence of a lower polar force of ethyl acetate as compared to that of methyl acetate. Experimental VLE Data. T−x1−y1 data from VLE for the MA2B and EA2B systems at 0.3 MPa and 0.6 MPa are presented in Table 3. For the activity coefficient calculation of the liquid phase (γi) the following equation was used.

109·vE −3

∑ (−1) j

E

Table 2. Densities and Excess Molar Volumes for Binary Systems at 298.15 K and Atmospheric Pressurea ρij

2

ν E = −∑ ( −1)i

m3 mol−3 757.7 745.3 670.8 505.2 388.9 344.6 128.0 0.0 626.2 597.3 559.1 515.2 479.2 402.3 309.1 251.1 114.2 0.0

⎡ (po − p)v L ⎤ i ⎢ i ⎥ γi = o o exp ⎢⎣ ⎥⎦ xiφi pi RT φiyp i

(4)

The fugacity coefficient (ϕi) was calculated truncating the second term of the virial equation of state. ⎡ 2 p (2 ∑ yj Bij − φi = φi exp⎢ ⎢⎣ RT j=1 o

a

Uncertainties u are u(T) = 0.01 K, u(p) = 0.0005 MPa, u(x1) = 0.0002, u(ρij) = 0.1 kg·m−3, u(109·vE) = 12 m3·mol−1.

pio Bii ⎤ ⎥ ∑ ∑ yyi j Bij) − ⎥⎦ RT i=1 j=1 2

2

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the zero line (see Figure 2), as confirmed also by the small numerical value of the bias of the vapor phase composition (see Table 4). Thus, the system MA2B at 0.3 MPa considering the numerical values of δp and δy1, could be declared consistent. In Figure 3, it is observed than the numerical values for δy1 showed an important bias (see Table 4) and failed in the random distribution about the zero line, but the tendency is not marked enough as to be correlated. Thus, the analysis of the numerical results for δp and for δy1 in the system MA2B at 0.6 MPa is not determinant about its consistency. For the numerical values of δy1 for the system EA2B at 0.3 MPa, a moderate random dispersion from the zero line was observed (see Figure 4), which is confirmed by the bias value shown in Table 4 for the composition of the vapor phase. Thus, considering the numerical values of δp and δy1, the system could be declared consistent. The δy1 values for the system EA2B at 0.6 MPa shown in Figure 5, allow verification that the random distribution from the zero line is very small and the bias is moderate (see Table 4). However, the numerical value for MPD (y1) is low. It may be verified in Figure 5 that most of the residual values are lower than 0.005 units, and therefore considering the δp and δy1 values, the system could be considered as consistent. Alternately, Wisniak et al.22 suggest that another different test must be applied to verify the quality of the data. This is the reason why the area consistency test23,24 was applied, using eq 6:

Figure 1. Experimental values at 298.15 K of vE vs x1 and fitting curves of (●) MA2B and (◆) EA2B. Comparison with literature data of MA2B by (green ★) Ortega and Hernandez;5 (blue ▼) Ortega and Susial;6 (red ◀) Canosa et al.20 Comparison with literature data of EA2B by (blue ×) Hernandez and Ortega;7 (green ▶) Laavi et al.;8 (red ▲) Resa et al.16

∫0

1

ln

γ1

dx1 =

γ2

∫0

HE ⎞⎛ ∂T ⎞ ⎜ 2 ⎟⎜ ⎟ dx1 ⎝ RT ⎠⎝ ∂x1 ⎠ p

1⎛

(6)

E

When the excess enthalpy (H ) is considered to be small, then the right term of eq 6 can be neglected, and the Redlich− Kister23 test can be expressed using eq 7, after resolving the integral:

For the calculation of the virial coefficient (Bii, Bij) the Hayden and O’Connell method21 was employed. The molar volume of the liquid in the pure component (viL) was estimate using the Yen and Woods equation.19 The experimental data presented in this work have been evaluated considering the test of Van Ness et al.9 using the routine of Fredenslund et al.10 According to the Fredenslund et al.10 criterion, the experimental data are consistent if the mean absolute deviation between the calculated and measured mole fraction vapor phase is less than 10−2. In the present study, the values obtained are presented in Table 4. It is observed that all the systems meet the Fredenslund et al.10 criterion. However, the bibliography22 suggests that a detailed analysis of the deviation of vapor phase and pressure values should be done after checking the data with the point-to-point test. Consequently, residual values (δy1 = y1,exp − y1,calc) of the molar fraction of the vapor phase, as well as residual values (δp = pexp − pcalc) of the pressure were determined (see Figures 2 to 5). The average residuals (BIAS), the mean absolute deviations (MAD), and the mean percent deviations (MPD) of the F properties (F being y1 or p) are also included in Table 4. It was observed that globally only 3 % of the data do not meet the criterion of Fredenslund et al.10 When the residual values of the pressure were checked (see Figures 2 to 5), a marked bias was not observed. The numerical values are small (see Table 4), which can mean that the systematic error in the bubble-point pressure is not very important. Moreover, all the systems have shown that the numerical values for δp are totally random without any remarkable tendency. The vapor phase mole fraction residual values for the system MA2B at 0.3 MPa showed a random scatter distribution about

D = 100

L−W L+W

(7)

Equation 7 resolves the integral of the left side of eq 6 considering the areas above (L) and below (W) the x-axis in the plot ln(γ1/γ2) vs x1. The consistency criterion for the Redlich−Kister23 test has been established for the condition D < 10%. The obtained results when the Redlich−Kister23 area test was applied to the data of this paper are presented in Table 4. It was observed that only the system EA2B at 0.3 MPa met the consistency criterion. To resolve the term in the right part of eq 6, Herrington24 proposed the following solution: J = 150

|Tbp,1 − Tbp,2| Tmin

(8)

When eqs 7 and 8 are considered together with the relation | D−J| < 10, Herrington24 establishes the criterion for which the systems are probably consistent. The obtained results when the Herrington24 area test was applied with the system of this work are presented in Table 4. It was observed that both systems at 0.3 MPa were consistent. The Kojima25 method (PAI test) was also employed to verify the VLE data corresponding to the systems MA2B and EA2B at 0.3 MPa and 0.6 MPa. Equation 6 is employed to apply the area test from Kojima et al.25 The consistency criterion (A*) in the area test of Kojima et al.25 is as follows: 2765



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Table 3. Experimental Data T−x1−y1 and Calculated Values for the Activity Coefficients of the Liquid Phasea T/K

x1

y1

γ1

γ2

T/K

Methyl Acetate (1) + 2-Butanol (2) at 0.3 MPa 405.81 405.49 404.12 400.37 397.22 395.28 393.43 388.94 386.31 384.92 383.72 382.48 380.95 379.81 379.02 377.93 376.85 376.14 375.53 374.91 374.05 373.40 371.33 370.79 369.74 368.78 367.91 367.01 366.43 366.19 365.55 405.81 405.19 404.57 403.56 402.01 401.18 400.47 399.63 398.65 398.17 396.93 396.6 396.06 395.4 394.32 393.60 393.13 392.05 391.37 391.04 390.97 390.63 390.16 389.81 389.51 389.10 388.91

0.000 0.000 0.005 0.018 1.38 0.022 0.074 1.33 0.061 0.206 1.45 0.100 0.303 1.39 0.121 0.363 1.44 0.146 0.417 1.43 0.227 0.539 1.32 0.289 0.605 1.24 0.326 0.638 1.20 0.358 0.666 1.17 0.396 0.692 1.14 0.441 0.725 1.11 0.467 0.748 1.11 0.494 0.764 1.10 0.544 0.785 1.05 0.575 0.806 1.05 0.606 0.818 1.03 0.623 0.831 1.03 0.645 0.843 1.03 0.678 0.858 1.02 0.709 0.870 1.00 0.782 0.907 1.00 0.810 0.916 0.99 0.849 0.933 0.99 0.884 0.947 0.99 0.909 0.964 1.00 0.947 0.979 1.00 0.977 0.989 1.00 0.989 0.994 0.99 1.000 1.000 1.00 Ethyl Acetate (1) + 2-Butanol (2) at 0.3 MPa 0.000 0.000 0.017 0.039 1.51 0.028 0.067 1.60 0.052 0.115 1.51 0.097 0.186 1.36 0.121 0.230 1.38 0.144 0.263 1.35 0.181 0.308 1.28 0.223 0.353 1.22 0.243 0.376 1.21 0.306 0.442 1.16 0.323 0.460 1.15 0.352 0.489 1.14 0.393 0.528 1.12 0.457 0.586 1.10 0.505 0.629 1.08 0.545 0.657 1.06 0.634 0.725 1.04 0.688 0.771 1.03 0.718 0.793 1.03 0.736 0.802 1.01 0.764 0.822 1.01 0.803 0.850 1.00 0.833 0.872 1.00 0.859 0.891 1.00 0.892 0.915 1.00 0.921 0.933 0.99

x1

y1

γ1

γ2

Methyl Acetate (1) + 2-Butanol (2) at 0.6 MPa 1.00 1.00 1.00 1.00 1.01 1.00 1.00 1.01 1.03 1.04 1.05 1.07 1.09 1.09 1.11 1.17 1.17 1.22 1.21 1.22 1.26 1.30 1.34 1.42 1.49 1.59 1.42 1.48 1.82 2.10

431.73 429.62 428.08 422.35 420.53 418.52 416.51 415.44 412.92 411.28 410.61 409.73 408.68 407.71 406.80 406.03 405.19 404.54 403.82 403.11 402.47 401.42 400.86 399.48 397.34 396.61 395.43 394.16 393.70 393.01

1.00 1.00 1.00 1.00 1.02 1.01 1.02 1.02 1.04 1.04 1.06 1.06 1.06 1.07 1.09 1.09 1.11 1.15 1.15 1.16 1.19 1.21 1.24 1.26 1.28 1.32 1.43

431.73 430.48 429.78 429.06 428.00 427.75 427.48 426.68 426.46 425.54 424.22 423.47 422.82 422.53 421.99 421.84 421.35 421.14 420.72 420.35 419.96 419.69 419.25 418.93 418.60 418.22 417.48

2766

0.000 0.038 0.063 0.148 0.181 0.225 0.269 0.297 0.365 0.410 0.429 0.456 0.484 0.512 0.538 0.562 0.592 0.610 0.631 0.657 0.678 0.716 0.740 0.786 0.856 0.880 0.922 0.964 0.979 1.000

0.000 0.092 0.148 0.332 0.384 0.443 0.499 0.528 0.593 0.633 0.650 0.671 0.696 0.718 0.738 0.756 0.774 0.788 0.803 0.818 0.831 0.852 0.863 0.889 0.927 0.942 0.962 0.981 0.988 1.000

1.13 1.13 1.20 1.18 1.14 1.12 1.09 1.05 1.04 1.03 1.02 1.02 1.01 1.01 1.01 1.00 1.00 1.00 0.99 0.99 0.99 0.98 0.98 0.98 0.99 0.99 0.99 1.00 1.00

Ethyl Acetate (1) + 2-Butanol (2) at 0.6 MPa 0.000 0.000 0.062 0.097 1.18 0.094 0.143 1.16 0.129 0.187 1.12 0.186 0.252 1.07 0.198 0.266 1.07 0.210 0.280 1.07 0.257 0.336 1.06 0.266 0.347 1.07 0.319 0.406 1.06 0.397 0.487 1.05 0.449 0.538 1.04 0.495 0.582 1.04 0.520 0.604 1.03 0.559 0.639 1.03 0.572 0.651 1.03 0.613 0.685 1.02 0.631 0.700 1.02 0.667 0.728 1.01 0.699 0.753 1.00 0.732 0.780 1.00 0.765 0.806 1.00 0.798 0.834 1.00 0.833 0.862 0.99 0.863 0.886 0.99 0.894 0.914 1.00 0.962 0.970 1.00

1.00 1.00 1.00 1.00 1.00 1.01 1.02 1.03 1.05 1.06 1.07 1.08 1.08 1.09 1.10 1.11 1.13 1.13 1.13 1.15 1.16 1.19 1.22 1.25 1.31 1.27 1.33 1.50 1.65

1.00 1.00 1.00 1.01 1.02 1.02 1.02 1.02 1.02 1.02 1.03 1.04 1.04 1.04 1.05 1.05 1.06 1.07 1.08 1.10 1.11 1.12 1.13 1.15 1.17 1.15 1.14



Article

Table 3. continued T/K

x1

γ1

y1

γ2

T/K

Methyl Acetate (1) + 2-Butanol (2) at 0.3 MPa Ethyl Acetate (1) + 2-Butanol (2) at 0.3 MPa 0.969 0.974 1.00 1.000 1.000 1.00

388.31 387.85 a

x1

y1

γ1

γ2

Methyl Acetate (1) + 2-Butanol (2) at 0.6 MPa 1.45

417.29 417.02

Ethyl Acetate (1) + 2-Butanol (2) at 0.6 MPa 0.980 0.982 1.00 1.000 1.000 1.00

1.30

Uncertainties u are u(T) = 0.03 K, u(p) = 0.004 MPa, u(x1) = u(y1) = 0.002.

Table 4. Results of Thermodynamic Consistency Test MA2B parameter\system

EA2B

0.3 MPa

0.6 MPa

0.1005 0.1494 19.57 16.42 fails passes 0.047 0.6 passes 6.3 fails 23.1 29.0 passes

0.0382 0.1155 50.29 14.85 fails fails 0.047 2.6 passes 4.8 passes 4.0 52.8 fails

0.0944 0.0954 0.53 6.94 passes passes 0.027 2.4 passes 4.2 passes 25.7 13.1 passes

0.0326 0.0536 24.36 5.36 fails fails 0.027 0.6 passes 2.4 passes 3.7 44.8 fails

0.110

0.109

0.046

0.039

5 4.7 0.98 −1.2 0.9 0.30 −0.1 passes

5 6.5 1.1 −6.4 0.9 0.15 0.1 passes

2 3.9 1.13 1.8 0.3 0.11 0.0 passes

2 2.8 0.74 −2.2 0.4 0.07 0.0 passes

L W D J Redlich−Kister23 test Herington24 test ε 100|A*| < 3 Kojima et al.25 area test (100/n)∑i n= 1|δ*| < 5 Kojima et al.25 point test 100|I1*| < 30 100|I*2 | < 30 Kojima et al.25 infinite dilution test RMS = ((∑[d(GERT)/dx1 − ln(γ1/γ2)]2)/(n − 2))1/2 direct test of Van Ness26 index 103 MAD(y1)a MPD(y1)a 103 BIAS(y1)a MAD(p/kPa)a MPD(p)a BIAS(p/kPa)a Van Ness et al.9 test

0.3 MPa 0.6 MPa

Figure 2. Results of (blue ●) δy1 and (red ▲) δp from thermodynamic consistency test for MA2B system at 0.3 MPa using the Fredenslund et al.10 routine.

a BIAS(F) = (1/(n − 2))∑n1(Fexp − Fcal); MAD(F) = (1/(n − 2))∑n1| Fexp − Fcal|; MPD(F) = (100/(n − 2))∑n1((|Fexp − Fcal|)/(Fexp)).

A* =

∫0

1

ln

γ1 γ2

dx1 +

∫0

1

ε dx1

(9)

In eq 9, the parameter ε, is related to the heat of mixing in the isobaric experiment. The obtained results when the area test of Kojima et al.25 was applied to the data of this work are shown in Table 4. It was observed that when different values for the energetic parameter in MA2B and EA2B were used, all the systems met the consistency criterion. In the Kojima et al.25 point test, the deviation of the experimental data (δ*) is calculated by eq 10: δ* = d(GERT )/dx1 − ln(γ1/γ2) − ε

(10) Figure 3. Consistency analysis results of (blue ●) δy1 and (red ▲) δp for the MA2B system at 0.6 MPa using the Fredenslund et al.10 routine.

The global results for (δ*) are presented in Table 4. It was concluded that only the system MA2B at 0.3 MPa did not meet the consistency criterion. Kojima et al.25 also proposed an infinite dilution test. The following equations are employed to calculate this condition: ‐1 ⎡⎛ E ⎛ γ ⎞⎤ ⎡ ⎛ γ ⎞⎤ G /RT ⎞ 1 ⎥ ⎢ 1 ⎥ * ⎢ ⎜ ⎟ ⎜ ⎟ I1 = ⎜ ⎟ − ln⎜ ⎟ · ln⎜ ⎟ ⎢⎣⎝ x1x 2 ⎠ ⎝ γ2 ⎠⎥⎦ ⎢⎣ ⎝ γ2 ⎠⎥⎦

x1= 0

‐1 ⎡⎛ E ⎛ γ ⎞⎤ ⎡ ⎛ γ ⎞⎤ ⎞ G / RT 2 2 I2* = ⎢⎜ ⎟ − ln⎜⎜ ⎟⎟⎥ ·⎢ln⎜⎜ ⎟⎟⎥ ⎢⎣⎝ x1x 2 ⎠ ⎝ γ1 ⎠⎥⎦ ⎢⎣ ⎝ γ1 ⎠⎥⎦

x2 = 0

(12)

The results for the infinite dilution condition for both substances, using in eqs 11 and 12 the excess Gibbs free energy

(11) 2767



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To verify the study of data tests using the PAI25 test, we proceeded using the extended equation of Redlich−Kister (see eqs 13 and 14) and considered the energetic parameter as an adjustable parameter equal to 0.047 in MA2B systems and 0.027 in EA2B systems. We employed eq 13 using two or three parameters for the correlations of the excess Gibbs free energy, and for eq 14, always three or four parameters were used for the correlation of activity coefficients. Table 4 shows that the systems do not present a uniform behavior when the different area tests23−25 are considered. However, as Van Ness26 suggested, the area test is a global test of the data and it could be a necessary condition, but not sufficient, of the consistency of the data. For this reason, after the point-to-point area test from Kojima et al.25 was applied, the data were verified with the direct area test from Van Ness.26 The results obtained when eq 13 was applied to obtain the root-mean-square (RMS) are presented in Table 4. The consistency index from Van Ness26 is shown for comparison purposes in Table 4. Therefore, considering the obtained results when the different consistency tests were applied it may be indicated that the data from this work are of acceptable quality.

Figure 4. Results of (blue ●) δy1 and (red ▲) δp from the thermodynamic consistency test for EA2B system at 0.3 MPa using the Fredenslund et al.10 routine.

■

TREATMENT OF VLE DATA Subsequently to the reduction data process and its validation with the different consistency tests, the analytic verification of the systems MA2B and EA2B at 0.3 MPa and 0.6 MPa was performed considering its adequacy to the literature data.5−7 Figure 6 shows the data for the system MA2B at 0.3 MPa and 0.6 MPa and its correlations, as well as the literature data,5,6

Figure 5. Consistency analysis results of (blue ●) δy1 and (red ▲) δp for EA2B system at 0.6 MPa using the Fredenslund et al.10 routine.

(GE/RT), as well as the activity coefficients calculated from eqs 4 and 5, are presented in Table 4. It can be checked that the systems MA2B and EA2B at 0.3 MPa met the consistency criterion while the systems MA2B and EA2B at 0.6 MPa did not. To apply eqs 6 and 9 to 12, the data from this study were correlated using the following relationships: GE = x1x 2[B + C(x1 − x 2) + D(x1 − x 2)2 + ...] RT

(13)

⎛γ ⎞ ln⎜⎜ 2 ⎟⎟ = a + b(x 2 − x1) + c(6x1x 2 − 1) + .... ⎝ γ1 ⎠

(14)

Figure 6. Experimental points (blue ◆) and (red ●) of (y1 − x1) vs x1 representation and fitting curves for the MA2B system at 0.3 MPa and 0.6 MPa, respectively. Fitting curves and bibliographic data at (red ▲) 74.66 kPa, (blue ▶) 101.32 kPa, and (red ◀) 127.99 kPa from Ortega and Hernandez;5 also with data at (green ★)101.32 kPa from Ortega and Susial.6 2768



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applied, and the minimization of the objective function (OF) was employed to ensure the ponderation of the results as follows:28

while Figure 7 presents the data for the system EA2B at 0.3 MPa and 0.6 MPa and its correlations together with the

n

OF =

n

∑ (γ1exp − γ1calc)i2 + ∑ (γ2exp − γ2calc)i2 1

1

(15)

Good correlations were obtained with the thermodynamic models (see Table 5), and except in the MA2B system at 0.6 MPa, acceptable deviations were observed for MAD(F) and s(F) (F being y1, γi, T or GE/RT) in the prediction of the temperature and vapor phase mole fraction. Group Contribution Models. A preliminary requirement for the design of a separation process is the reliable knowledge of the phase equilibrium behavior of the systems to that of the separated material. When no experimental data are available, group contribution methods can be applied. This is the reason why VLE data for the binary systems MA2B and EA2B at 0.3 MPa and 0.6 MPa were predicted using the following group contribution methods to calculate the liquid-phase activity coefficients: the ASOG11 method; the original UNIFAC10 method; with the structural and group-interaction parameters recommended by Hansen et al.;13 the UNIFAC−Lyngby12 method; and the UNIFAC−Dortmund14 method. Table 6 lists the MAD(F) (F being y1, T, or p) between the experimental VLE data and those predicted by using the different group contribution models. It is observed that the UNIFAC−Lyngby12 model generated the best predictions for all the systems of this work when the following properties, pressure, temperature, vapor phase composition, and liquid phase activity coefficient, were considered. The UNIFAC− Dortmund14 model returned acceptable predictions except for the system MA2B at 0.6 MPa. Figures 8 and 9 show the VLE data of the binary systems MA2B and EA2B at 0.3 MPa and 0.6 MPa, comparing the correlation results with the UNIFAC− Lyngby12 method. In the y1−x1 vs x1 plot (see Figure 9) the good prediction that UNIFAC−Lingby12 model achieved for the data of this work could be observed. Modeling with PR-EOS. Mixtures containing associating and/or polar components are of interest to chemical industries. Traditional thermodynamic models such as cubic EOS perform

Figure 7. Fitting curves with experimental data (blue filled star) and (red ■) of (y1 − x1) vs x1 plot for EA2B at 0.3 MPa and 0.6 MPa, respectively; also with data at (red ▼) 101.32 kPa from Hernandez and Ortega7 and fitting curve.

literature data.7 In general, it is verified that the evolution of the systems presented an apparent symmetric behavior, and volumetric compression when pressure is increased is observed. Moreover, to represent the phase equilibrium behavior, the activity coefficient models such as Wilson, NRTL, and UNIQUAC are usually employed in the chemical industry. This is the reason why the calculated activity coefficient data (Table 3) were correlated to the previous models, to obtain their interactions parameters. The simplex method27 was

Table 5. Correlation Parameters for GE/RT with Average and Standard Deviations in Predictionsa model Wilson NRTL (α = 0.47) UNIQUAC (Z = 10) Wilson NRTL (α = 0.47) UNIQUAC (Z = 10) Wilson NRTL (α = 0.47) UNIQUAC (Z = 10) Wilson NRTL (α = 0.47) UNIQUAC (Z = 10) a

parameters

MAD(y1)

Methyl Acetate (1) + 2-Butanol (2) at 0.3 MPa Δλ21/(J·mol−1) = 2720.4 0.008 g21/(J·mol−1) = −504.3 0.009 Δu21/(J·mol−1) = −202.8 0.008 Methyl Acetate (1) + 2-Butanol (2) at 0.6 MPa Δλ12/(J·mol−1) = −1188.5 Δλ21/(J·mol−1) = 2576.8 0.013 −1 g12/(J·mol ) = 2888.7 g21/(J·mol−1) = −1251.1 0.014 Δu12/(J·mol−1) = 1090.4 Δu21/(J·mol−1) = −616.8 0.013 Ethyl Acetate (1) + 2-Butanol (2) at 0.3 MPa Δλ12/(J·mol−1) = 2014.5 Δλ21/(J·mol−1) = −480.1 0.004 −1 g12/(J·mol ) = −421.9 g21/(J·mol−1) = 1948.0 0.005 Δu12/(J·mol−1) = −729.5 Δu21/(J·mol−1) = 1292.0 0.004 Ethyl Acetate (1) + 2-Butanol (2) at 0.6 MPa Δλ12/(J·mol−1) = −321.2 Δλ21/(J·mol−1) = 999.0 0.005 −1 g12/(J·mol ) = 1193.5 g21/(J·mol−1) = −482.5 0.005 Δu12/(J·mol−1) = 787.6 Δu21/(J·mol−1) = −532.2 0.005 Δλ12/(J·mol−1) = −915.2 g12/(J·mol−1) = 2449.2 Δu12/(J·mol−1) = 802.5

MAD(T)/K

σ(γ1)

σ(γ2)

σ(GE/RT)

0.96 1.08 0.96

0.06 0.06 0.05

0.08 0.08 0.08

0.016 0.018 0.017

1.34 1.46 1.33

0.06 0.07 0.06

0.06 0.05 0.06

0.018 0.020 0.018

0.23 0.26 0.23

0.02 0.03 0.03

0.04 0.04 0.04

0.007 0.008 0.007

0.22 0.24 0.22

0.02 0.02 0.02

0.03 0.02 0.03

0.005 0.005 0.005

σ(F) = ((∑n1(Fexp − Fcal)2)/(n −2))1/2. 2769



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Table 6. Mean errors and average deviations in the prediction of VLE data using ASOG and UNIFAC models UNIFAC-198712 OH/COOC MAD(y1) MAD(T)/K MAD(p)/MPa

0.011 0.76 0.005

MAD(y1) 0.011 MAD(T)/K 0.69 MAD(p)/MPa 0.009 Ethyl Acetate (1) + 2-Butanol (2) at 0.3 MPa MAD(y1) 0.005 MAD(T)/K 0.46 MAD(p)/MPa 0.003 Ethyl Acetate (1) + 2-Butanol (2) at 0.6 MPa MAD(y1) 0.003 MAD(T)/K 0.23 MAD(p)/MPa 0.003

UNIFAC-199113 OH/COOC

Methyl Acetate (1) + 2-Butanol (2) at 0.3 MPa 0.011 0.012 2.03 0.98 0.016 0.007 Methyl Acetate (1) + 2-Butanol (2) at 0.6 MPa 0.021 0.016 3.88 2.03 0.054 0.028

a(T ) = 0.457235

0.014 0.74 0.006

0.032 5.57 0.078

0.007 0.70 0.010 0.007 0.51 0.004

0.030 3.68 0.050

0.007 0.73 0.010

0.032 3.79 0.052

0.003 0.38 0.005

Figure 9. Experimental points of y1−x1 vs x1 for MA2B at (blue ◆) 0.3 MPa or (red ●) 0.6 MPa and EA2B at (blue ★) 0.3 MPa or (red ■) 0.6 MPa. Fitting curves from UNIFAC-Lingby12 model (―) and from PR-EOS15 model (− − −).

b = 0.077796

RTc pc

(18)

where Tc and pc are the critical temperature and pressure of each pure compound, respectively. The correlation for the α(T) function is

(16)

α(T ) = [1 + (0.37464 + 1.54226ω − 0.26992ω 2) × (1 − Tr0.5)]2

2

R Tc α (T ) Pc

0.017 2.85 0.023

0.020 1.80 0.014

where p is pressure, T is temperature, R is the universal gas constant, and v is the molar volume. Through parameters b and a free volume effects and intermolecular attractive interactions are taken into account. For a pure component the energy and size parameters are calculated, respectively, as follows: 2

PR-EOS15

0.008 0.69 0.005

well using VLE data. The PR-EOS15 was used in this work; this EOS has the following form: a(T ) RT v − b v(v + b) + b(v − b)

ASOG11 OH/COO

0.023 2.01 0.016

Figure 8. Equilibrium diagram T−x1−y1 of MA2B at (blue and red ◆) 0.3 MPa or (blue and red ●) 0.6 MPa and EA2B at (blue and red ★) 0.3 MPa or (blue and red ■) 0.6 MPa. Curves represent the prediction with UNIFAC−Lingby12 model.

p=

UNIFAC-199314 OH/COOC

(19)

where ω and Tr are, respectively, the acentric factor and the reduced temperature.

(17) 2770



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the PR-EOS15 predictions. Although simple mixture rules have been used, it is observed that the modelization is acceptable: it showed (see Figure 9) the higher difference at lower ester composition, fundamentally in the system MA2B at 0.3 MPa. In addition, the MAD of data predicted by PR-EOS15 in Table 6 and the composition−composition diagram in Figure 9 show fitting curves for all data predicted by UNIFAC−Lyngby12 and PR-EOS15 with comparison purposes. It is observed that the predictions using a low pressure model are somewhat better in the MA2B system.

The two parameters of PR with quadratic mixing rules are given by N

am =

bm =

N

∑ ∑ xixj(aiaj)0.5 (1 − k1ij ) i

j

N

N

(20)

⎛ bi + bj ⎞ ⎟(1 − k 2ij) ⎝ 2 ⎠

∑ ∑ xixj⎜ i

j

(21)

■

where k1ij and k2ij are the binary interaction parameters of the components in the mixture. The binary interaction parameters for the binary systems were treated as fitting parameters. The physical properties of ref 17 were used. The k1ij and k2ij were obtained using a modification of the Matlab program of Martin et al.29 applying the simplex method27 in a similar way to eq 15. The minimum OF was as follows: n

OF =

n

∑ (pexp − pcalc )i2 + ∑ (y1exp − y1calc )i2 1

CONCLUSIONS Phase equilibria for MA2B and EA2B systems were measured and new data were obtained at the 0.3 MPa and 0.6 MPa. Validation of experimental data was performed with five tests of thermodynamic consistency. Results indicate that the reliability of the data of this paper is high. In this work, the ASOG and three different versions of UNIFAC group contribution models were analyzed regarding their capability to represent the phase equilibrium at moderated pressures. Results showed that the UNIFAC−Lingby model returns satisfactory predictions on temperature and composition of both phases. The experimental data were correlated with the PR-EOS using the conventional mixing rules. Calculated results with these equations have given good agreement by comparison with the experimental data.

1

(22)

VLE data of this work were used with the PR-EOS15 equations previously presented using the computer program of Martin et al.29 Results obtained were MA2B at 0.3 MPa (k1ij = 0.0314 and k2ij = −0.0043); MA2B at 0.6 MPa (k1ij = 0.0223 and k2ij = −0.0051); EA2B at 0.3 MPa (k1ij = 0.0258 and k2ij = 0.0092) and EA2B at 0.6 MPa (k1ij = 0.0181 and k2ij = 0.0056). An apparent decrease of the binary interaction parameters could be observed at each system with pressure increase. Figures 9 and 10 provide a comparison in the composition− composition and temperature−composition diagrams between experimental data obtained in this work for the binary systems at 0.3 MPa and 0.6 MPa of MA2B and EA2B, respectively, and

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: 34-928-451489. Fax: 34-928-458658. E-mail: psusial@ dip.ulpgc.es. Funding

This work was supported by the authors and by the ULPGC. This work was not financially supported by Spanish government. Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Oswal, S. L.; Putta, S. S. R. Excess Molar Volumes of Binary Mixtures of Alkanols with Ethyl Acetate from 298.15 to 323.15 K. Thermochim. Acta 2001, 373, 141−152. (2) Susial, P.; Rios-Santana, R.; Sosa-Rosario, A. Vapor−Liquid Equilibrium Measurements for the Binary System Methyl Acetate +Ethanol at 0.3 and 0.7 MPa. Braz. J. Chem. Eng. 2011, 28, 325−332. (3) 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. (4) Susial, P.; García-Vera, D.; Susial, R.; Castillo, V. D.; Estupiñan, E. J.; Apolinario, J. C.; Rodríguez-Henríquez, J. J. Experimental Determination of Vapor−Liquid Equilibria. Binary Systems of Methyl Acetate, Ethyl Acetate, and Propyl Acetate with 1-Propanol at 0.6 MPa. J. Chem. Eng. Data 2013, 58, 2861−2867. (5) Ortega, J.; Hernandez, P. Isobaric Vapor−Liquid Equilibria for Methyl Esters+Butan-2-Ol at Different Pressures. Fluid Phase Equilib. 1996, 118, 249−270. (6) Ortega, J.; Susial, P. Vapor−Liquid Equilibria of Binary Mixtures of Methyl Alkanoates + Isomeric Butanols. ELDATA: Int. Electron. J. Phys.-Chem. Data 1995, 1, 1−12. (7) Hernández, P.; Ortega, J. Vapor−Liquid Equilibria and Densities for Ethyl Esters (Ethanoate to Butanoate) and Alkan-2-ol (C3−C4) at 101.32 kPa. J. Chem. Eng. Data 1997, 42, 1090−1100.

Figure 10. Experimental data T−x1−y1 of MA2B at (blue and red ◆) 0.3 MPa or (blue and red ●) 0.6 MPa and EA2B at (blue and red ★) 0.3 MPa or (blue and red ■) 0.6 MPa with fitting curves from PREOS15 modeling. 2771



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(8) 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. (9) Van Ness, H. C.; Byer, S. M.; Gibbs, R. E. Vapor−Liquid Equilibrium: Part I. An Appraisal of Data Reduction Methods. AIChE J. 1973, 19, 238−244. (10) Fredenslund, A.; Gmehling, J.; Rasmussen, P. Vapor−Liquid Equilibria Using UNIFAC. A Group Contribution Model; Elsevier: Amsterdam, 1977. (11) Kojima, K.; Tochigi, K. Prediction of Vapor-Liquid Equilibria by the ASOG Method; Kodansha Ltd.: Tokyo, 1979. (12) Larsen, B. L.; Rasmussen, P.; Fredenslund, A. A modified UNIFAC Group-Contribution Model for Prediction of Phase Equilibria and Heats of Mixing. Ind. Eng. Chem. Res. 1987, 26, 2274−2286. (13) Hansen, H. K.; Rasmussen, P.; Fredenslund, A.; Schiller, M.; Gmehling, J. Vapor−Liquid Equilibria by UNIFAC Group-Contribution. 5. Revision and Extension. Ind. Eng. Chem. Res. 1991, 30, 2355− 2358. (14) Gmehling, J.; Li, J.; Schiller, M. A Modified UNIFAC Model. 2. Present Parameter Matrix and Results for Different Thermodynamic Properties. Ind. Chem. Eng. Res. 1993, 32, 178−193. (15) Peng, D. Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 1976, 15, 59−64. (16) Resa, J. M.; González, C.; Juez, M.; Ortiz de Landaluce, S. Density, Refractive Index and Speed of Sound for Mixtures of Ethyl Acetate with 2-Butanol and 3-Methyl-1-Butanol, Vapor−Liquid Equilibrium of the Ethyl Acetate + 3-Methyl-1-Butanol System. Fluid Phase Equilib. 2004, 217, 175−180. (17) TRC Thermodynamic Tables Non-hydrocarbons and Hydrocarbons; Thermodynamic Research Center, Texas A&M University System: College Station, TX, 1996. (18) Ocón, J. Binary Mixtures Rectification. A New Method of Fitting and Equilibrium Data Correlation (in Spanish). Anales R. Soc. Esp. Fis. Quim. 1953, 49, 295−300. (19) Yen, L. C.; Woods, S. S. A Generalized Equation for Computer Calculation of Liquid Densities. AIChE J. 1966, 12, 95−99. (20) Canosa, J.; Rodríguez, A.; Orge, B.; Iglesias, M.; Tojo, J. Densities, Refractive Indices and Derived Excess Properties of the System Methyl Acetate + Methanol, + 2-Butanol at 298.15 K. J. Chem. Eng. Data 1997, 42, 1121−1125. (21) Hayden, J. G.; O’Connell, J. P. A Generalised Method for Predicting Second Virial Coefficients. Ind. Eng. Chem. Process Des. Dev. 1975, 14, 209−216. (22) Wisniak, J.; Apelblat, A.; Segura, H. An Assessment of Thermodynamic Consistency Tests for Vapor−Liquid Equilibrium Data. Phys. Chem. Liq. 1997, 35, 1−58. (23) Redlich, O.; Kister, A. T. Algebraic Representation of Thermodynamic Properties and Classification of Solutions. Ind. Eng. Chem. 1948, 40, 345−348. (24) Herington, E. F. G. Tests for the Consistency of Experimental Isobaric Vapor−Liquid Equilibrium Data. J. Inst. Petrol 1951, 37, 457− 470. (25) Kojima, K.; Moon, H. M.; Ochi, K. Thermodynamic Consistency Test of Vapor−Liquid Equilibrium Data. Fluid Phase Equilib. 1990, 56, 269−284. (26) Van Ness, H. C. Thermodynamics in the Treatment of Vapor/ Liquid Equilibrium (VLE) Data. Pure Appl. Chem. 1995, 67, 859−872. (27) Nelder, J.; Mead, R. A Simplex Method for Function Minimization. Comput. J. 1965, 7, 308−313. (28) Holmes, M. J.; Vanwinkle, M. Prediction of Ternary Vapor− Liquid. Equilibria from Binary Data. Ind. Eng. Chem. 1970, 62, 21−31. (29) 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.

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Experimental VaporâLiquid Equilibria Data of Methyl Acetate or Ethyl

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