Measurement and Modelization of VLE for Butyl ... - ACS Publications

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

pubs.acs.org/jced

Measurement and Modelization of VLE for Butyl Acetate with Methanol, Ethanol, 1‑Propanol, and 1‑Butanol. Experimental Data at 0.15 MPa Pedro Susial Badajoz,* Diego García-Vera, José David González-Domínguez, and Patricia Herrera-Vega Escuela de Ingenierias Industriales y Civiles, Universidad de Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Canary Islands, Spain ABSTRACT: Vapor−liquid equilibrium at 0.15 MPa for binary mixtures of butyl acetate with methanol, ethanol, 1-propanol, and 1-butanol has been measured. The thermodynamic consistency was verified with the Redlich−Kister test, the Herington test, the direct Van Ness test, and the point-to-point test. Azeotropic data was found for the butyl acetate + 1-butanol binary system at 0.15 MPa. Modeling of binary systems was obtained by employing the group contribution models (ASOG and different versions of UNIFAC) and the perturbed chainstatistical associating fluid theory equation of state.

isobarically at 101.3 kPa by Beregovikh et al.,8 Patlasov et al.,9 and Resa et al.,7 at 141.3 kPa by A. M. Blanco10 and Espiau et al.,11 and at 0.6 MPa by Susial et al.12 The butyl acetate + ethanol (BAE) system has been studied isothermally8,9,13 and isobarically at 101.3 kPa by Beregovykh et al.,9 Gonzalez and Ortega,13 Polyakova et al.,13 and Shono et al.9 The butyl acetate + 1-propanol (BAP) system has been reported isobarically at 101.3 kPa by Beregovykh et al.,9 Gonzalez and Ortega,14 and Ortega et al.14 The butyl acetate + 1-butanol (BAB) system has been reported isothermally15 and isobarically at 6.67, 19.99, 39.99, 79.99, and 101.3 kPa by Figurski and Von Weber,15 isobarically at 6.67, 22.06, and 101.3 kPa by Sheinker and Peresleni,16 isobarically at 13.33, 26.66, 39.99, 53.33, 66.66, 79.99, 93.33, and 101.3 kPa by Shim et al.,15 and also isobarically at 101.3 kPa by Belousov et al.,15 Brunjes and Furnas,16 Beregovych et al.,17 Gonzalez and Ortega,15 Lladosa et al.,15 Mato and Cepeda,18 and Ortega et al.15 VLE data for the binary systems, BAM, BAE, BAP, and BAB, in this paper were analyzed considering the point-to-point test of Van Ness et al.19 using the Fortran program of Fredenslund et al.20 After this, the thermodynamically consistent data were used to evaluate predictions of the temperature and composition of the vapor phase. For this, the following group contribution models were used: UNIFAC21−23 and ASOG.24 In addition, the PC-SAFT1,2 EOS was also employed.

1. INTRODUCTION The modeling and prediction of the phase behavior of fluids are some of the most important topics in chemical engineering. In spite of the great variety of equations and thermodynamic models that have been developed to represent the behavior of pure substances and mixtures, all of them present certain limitations in their predictions, especially for complex mixtures and for those processes that take place at non-atmospheric pressures. It is the reason why the evaluation of the different models, as well as the thermodynamic−mathematical equations, must be carried out using experimental data obtained at different pressures from the atmospheric one, because in this way the adequate reliability of the predictions done can be considered as well as the utility of modeling. In this context, the study of fluid phase behavior by using many equations of state (EOSs) can be a tool that allows the modeling of pure substances and mixtures. The EOS of perturbed chain-statistical associating fluid theory1,2 (PC-SAFT) is a promising model to predict the vapor−liquid equilibrium (VLE) data for different mixtures. This is the reason why its prediction ability for the ester + alcohol mixtures should be explored. In this sense, VLE data for the ester/alcohol mixtures obtained in this work under isobaric conditions were thermodynamically analyzed considering the γ−ϕ approach and, next, these data were used to verify the modeling generated by the PC-SAFT EOS. Therefore, as a continuation of previous works,3−6 in this paper, T−x−y of VLE measurements were obtained using a dynamic recirculating ebulliometer at 0.15 MPa for the binary mixtures of butyl acetate + methanol, ethanol, 1-propanol, or 1-butanol. These systems have been studied isothermally and isobarically by different authors. The butyl acetate + methanol (BAM) system has been studied isothermally7,8 and also © XXXX American Chemical Society

2. EXPERIMENTAL SECTION The normal boiling point (Tbp), density (ρii), and refractive index (nD) were determined at 298.15 K and atmospheric Received: March 8, 2018 Accepted: May 21, 2018

A

DOI: 10.1021/acs.jced.8b00182 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Specification of Chemicals, Physical Properties, and Literature Values of Pure Substance at 101.3 kPaa ρ (298.15 K) (kg·m−3)

Tbp (K) chemical name

mass fraction

CAS

suppliers

butyl acetate

123-86-4

Panreac Quı ́mica S. A.

>0.995

methanol

67-56-1


ethanol

64-17-5

1-propanol 1-butanol

purification method

analysis method

exptl

none

GC

b

398.98

>0.999

none

GCb

337.85


>0.999

none

GCb

351.45

71-23-8


>0.998

none

GCb

370.35

71-36-3


>0.999

none

GCb

390.83

lit.

exptl c

399.15 399.00d 337.696e 337.85 f 351.443e 351.45 f 370.301e 370.29g 390.88e 390.81c

876.5 786.8 785.2 799.6 805.9

nD (298.15 K)

lit. c

876.6 876.16d 786.64e 786.8 f 784.93e 785.2 f 799.60e 799.75g 805.75e 806.00c

exptl

lit.

1.39201

1.3918c 1.39194d 1.32652e 1.3265 f 1.35941e 1.3594 f 1.38370e 1.38304g 1.39741e 1.3973c

1.32676 1.35933 1.38315 1.39732

a

Expanded uncertainties U(k = 2) of pressure (p), temperature (T), boiling point (Tbp), refractive index (nD), and liquid density (ρii) are U(p) = 0.5 kPa, U(T) = 0.01 K, U(Tbp) = 0.03 K, U(nD) = 0.00005, and U(ρii) = 0.1 kg·m−3. bGas−liquid chromatography. cReference 25. d Reference 26. eReference 27. fReference 28. gReference 29.

109 ·v E (m 3·mol−1) x1(1 − x1) ⎞ ⎛ x1 = ⎜321.52 + 435.80 ⎟ x1 + 2.387(1 − x1) ⎠ ⎝

pressure for pure substances (see Table 1). Substances were employed as received from the manufacturer, and further treatment of purification was not employed. An Atago 7000 Alpha digital refractometer, being temperature controlled with an uncertainty of 0.01 K and an estimated uncertainty in refractive index of ±5 × 10−5 units, was used. For density determinations of pure components and mixtures, a Mettler Toledo DM40 vibrating tube density meter with an uncertainty of ±0.1 kg·m−3 was employed after calibration at 298.15 K using air and distilled water as references. As a previous step to VLE determinations, samples from 0 to 1 mole fraction (xi) were prepared by mass in airtight-stoppered glass bottles using an Sartorius Lab Instruments GmbH&Co. Entris224i-1S balance with an uncertainty of 10−4 g and their densities (ρij) were measured at 298.15 K (Table 2). For boiling points and VLE measurements, a stainless steel ebulliometer, previously described,3 was constructed with a similar configuration to an ebulliometer copper made4 and it was equipped in an experimental setup.5 The PT-100 probes installed in the ebulliometer were verified considering the boiling point of distilled water as a reference. A Dostmann Electronic GmbH model P655 digital recorder and the Windows software of Dostmann Electronic were used for online measurement of temperature. For pressure measurement during the experimental work, a transducer of ESI Technology Ltd. with an operating range from 0.0 to 2.5 MPa (standard uncertainty ±0.001 MPa) and equipped with the ESI Technology, Ltd., software for monitoring and storing pressure data in a computer was installed in the experimental setup.5 The ebulliometer, the experimental installation, and the operation procedure have been described previously.3−6 The stainless steel ebulliometer and the experimental facility were used to determine the normal boiling point at 101.3 kPa when the pure substance is located inside the equilibrium still.

(1)

109 ·v E (m 3·mol−1) x1(1 − x1) ⎡ x1 = ⎢433.88 + 724.08 ⎢⎣ x1 + 1.785(1 − x1) ⎞2 ⎤ ⎛ x1 − 432.66⎜ ⎟⎥ ⎝ x1 + 1.785(1 − x1) ⎠ ⎥⎦

(2)

109 ·v E (m 3·mol−1) x1(1 − x1) ⎡ x1 = ⎢780.16 + 32.34 ⎢⎣ x1 + 1.396(1 − x1) ⎞2 ⎤ ⎛ x1 − 9.22⎜ ⎟⎥ ⎝ x1 + 1.396(1 − x1) ⎠ ⎥⎦

(3)

These correlations were evaluated by the standard deviations (SDs) of fitting curves: SD(109·vE) = 3.9 m3·mol−1 for BAE, SD(109·vE) = 2.0 m3·mol−1 for BAP, and SD(109·vE) = 1.5 m3·mol−1 for BAB. The result obtained for BAM was informed previously.12 Table 2 shows composition−density pairs for mixtures of this work and their comparison with values found in the bibliography.30−33 Figure 1 includes the calculated excess volume points and the fitted curve of BAM, BAE, BAP, and BAB mixtures and compares the results with literature data.11,12,30−33 The moderate differences between our data and literature data are a consequence of differences in the purity of the substances employed in each case and the different equipment used for experimental determinations. However, Figure 1 also represents the calculated xi,max vs vEmax; it can be seen in this case that there is a good similitude between the data of this work and our literature data12 (red line) with literature data11,30,32,33 (blue line).

3. RESULTS AND TREATMENT 3.1. Densities. Different mixtures of (1) ester + (2) alcohol were prepared to consider mass/mass ratios, and their densities were measured at 298.15 K. Mole fraction (xi) vs density (ρij) pairs for mixtures of BAE, BAP, and BAB (Table 2) were verified by the correlation of the excess molar volumes (vE) as follows (see Figure 1): B


C

785.2 793.7 810.2 817.6 824.3 828.8 834.3 843.0 847.2 854.6 858.0 863.9 866.9 869.7 871.7 873.9 876.5

0 12 39 53 71 78 89 112 116 121 119 108 93 71 60 32 0

ρ (kg·m−3) 109·vE (m3·mol−1) e = 0.0002 0.0000 0.0003 0.0004 0.0004 0.0005 0.0005 0.0005 0.0006 0.0006 0.0006 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007

ρexptl

b ρexptl − ρ lit.

e= 0.0003 0.0005 0.0007 0.0007 0.0007 0.0007 0.0007 0.0005 0.0005 0.0004 0.0003 0.0003 0.0003 0.0003 0.0002 0.0003 0.0003

ρexptl

c ρexptl − ρ lit.

0.0000 0.0433 0.1028 0.2026 0.2517 0.2927 0.3500 0.3986 0.4482 0.5540 0.5962 0.6371 0.7071 0.7623 0.8001 0.8413 0.8942 0.9401 1.0000

x1 799.6 805.1 812.1 822.6 827.3 831.0 835.9 839.8 843.6 851.1 853.9 856.5 860.8 864.0 866.1 868.4 871.2 873.5 876.5

0 18 42 84 101 115 131 145 153 163 161 160 144 130 120 95 67 47 0

ρ (kg·m−3) 109·vE (m3·mol−1) e = 0.0000 0.0002 0.0004 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0006 0.0006 0.0006 0.0007 0.0006 0.0007 0.0007 0.0007 0.0007

ρexptl

d ρexptl − ρ lit.

x1 butyl acetate + (1 − x1) 1-propanol

e= 0.0004 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0004 0.0004 0.0003 0.0003 0.0003 0.0002 0.0002 0.0002 0.0003 0.0002 0.0003

ρexptl


0.0000 0.0758 0.1018 0.1458 0.2387 0.3151 0.3468 0.3845 0.3983 0.4316 0.5002 0.5883 0.6709 0.7064 0.7919 0.8673 0.9259 0.9503 1.0000

x1 805.9 812.9 815.2 819.0 826.7 832.7 835.1 837.9 838.9 841.3 846.1 852.0 857.3 859.5 864.7 869.1 872.4 873.8 876.5

0 54 72 100 144 169 178 185 189 193 198 193 176 168 131 91 57 34 0

ρ (kg·m−3) 109·vE (m3·mol−1) e = 0.0003 0.0004 0.0004 0.0003 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0005 0.0005 0.0006 0.0006 0.0007 0.0007 0.0007 0.0007

ρexptl

e ρexptl − ρ lit.

x1 butyl acetate + (1 − x1) 1-butanol

e=

0.0005 0.0004 0.0004 0.0004 0.0004 0.0003 0.0002 0.0002 0.0002 0.0002 0.0001 0.0000 0.0000 0.0000 0.0001 0.0002 0.0002 0.0003 0.0003

ρexptl


Expanded uncertainties U(k = 2) of pressure (p), temperature (T), ester mole fraction (x1), liquid density (ρ), and excess molar volumes (vE) are U(p) = 0.5 kPa, U(T) = 0.01 K, U(x1) = 0.0002, U(ρij) = 0.1 kg·m−3, and U(109·vE) = 12 m3·mol−1. bReference 30. cReference 31. dReference 32. eReference 33.

a

0.0000 0.0443 0.1461 0.2003 0.2554 0.2954 0.3487 0.4451 0.4968 0.5987 0.6505 0.7492 0.8035 0.8567 0.8978 0.9429 1.0000

x1

x1 butyl acetate + (1 − x1) ethanol

Table 2. Densities and Excess Molar Volumes for the Binary Systems BAE, BAP, and BAB at 298.15 K and 101.3 kPaa

Journal of Chemical & Engineering Data Article



Article

VLE data were tested for thermodynamic consistency by using the point-to-point test of Van Ness et al.19 Results (Table 4) indicate that the experimental data for the BAM, BAE, BAP, and BAB binary systems at 0.15 MPa satisfy the criterion of Fredenslund et al.20 In addition, the VLE data of this work were verified by employing the following thermodynamic tests: Redlich−Kister,42 Herington,43 and Van Ness.44 Considering a Redlich−Kister type equation, the integration of the function that results from the plot of ln(γ1/γ2) vs x1 gives the areas above (L) and below (W) the x-axis (see Table 4). The consistency criterion for the Redlich−Kister area test42 has been established for D < 10%, when considering the following equation:

D = 100

Figure 1. Excess molar volumes of BAE (red ●), BAP (green ●), and BAB (dark brown ●) for this work and fitting curves. Literature data of BAM (blue ●, from ref 12; blue ▲, from ref 11), BAE (red ▲, from ref 30; red ★, from ref 31), BAP (green ▲, from ref 32; green ★, from ref 31), and BAB (dark brown ▲, from ref 33; dark brown ★, from ref 31).

The Herrington J = 150

⎡ ⎛ p ⎜ ⎢ exp 2 ∑ yj Bij − γi = ⎢ RT ⎜ xipi0 ⎝ j ⎣ +

(pi0

−

⎞ pi0 Bii ⎟ ∑ ∑ yyi j Bij⎟ − RT i j ⎠

⎤ p)viL ⎥

RT

⎥ ⎦

43

(5)

test proposed the following equation

|Tbp,1 − Tbp,2| Tmin

(6)

with Tbp,1 and Tbp,2 being the boiling point of pure substances and Tmin being the lowest temperature between 0 ≤ x1 ≤ 1 in the mixture. Considering eqs 5 and 6, the Herrington43 test establishes that systems are probably consistent if |D − J| < 10. Data were verified applying the Van Ness44 direct area test; for this purpose, the root-mean-square (RMS) values presented in Table 4 were applied. Previously, the excess Gibbs free energy was correlated to a Redlich−Kister type equation. After this, the consistency index from Van Ness44 was obtained. Results of all tests are presented in Table 4. In addition, the Mathias45 procedure was also employed. The dimensionless Gibbs function (GE/RT) calculated using the activity coefficient data in Table 3 was correlated with the NRTL46 model. For the ester/alcohol mixtures of this work, 0.47 was taken as the value for the symmetric parameter. For the asymmetric parameter, a simplified version of the equation given by Mathias45 was used:

The vE values in the BAM system were negative. Such volumetric contraction suggests the existence of molecular coupling. This is probably a consequence of the significant associative effect due to the relevant polar force of the hydrogen bonding between butyl acetate and methanol. However, the vE values in BAE, BAP, and BAB were all positive, showing an expansive volumetric behavior which increases with the alcohol chain increase, showing the steric effect related to the weakness of the hydrogen bonding in the mixtures. 3.2. VLE Data. The VLE data T−x1−y1 (temperature and the ester mole fraction of the liquid phase and the vapor phase, respectively) for BAE, BAP, and BAB at 0.15 MPa are shown in Table 3. The activity coefficients of the liquid phase (γi) for each system were determined by using the following equation: yp i

L−W L+W

τij =

Δgij RT

= Aij +

Bij 8.314·T

(7)

The perturbation parameter (δi) was calculated from the perturbation approaches [exp(δi) − 1]. Results are in Figure 2 where the relative volatilities (αij) from the different systems are plotted with the uncertainties of the perturbation scheme.45 Considering all of these results, the systems presented in this paper can be considered of acceptable quality. Next, the verified VLE data T−x1−y1 of BAM, BAE, BAP, and BAB at 0.15 MPa were correlated to a polynomial equation as in a previous paper.39 Figures 3 and 4 show data and fitting curves to verify the evolution of the systems with the alcohol chain. It can be observed that there is a uniform evolution in all systems and an evident molar volume reduction in the liquid phase with respect to the vapor phase by increasing the alcohol chain. In addition, as shown in Figure 4, a decrease in the difference x1 − y1 with increasing alcohol chain results in a change from positive to negative values from 1 to 0 ester mole fraction and, therefore, the appearance of the azeotrope of BAB. This azeotrope has been informed at different pressures in the literature.47 In the present work, we have determined an azeotrope at x1,az = 0.167 and Taz = 402.39 K, by using the natural cubic spline method and the Thomas algorithm48 to interpolate in the

(4)

The second virial coefficients (Bii, Bij) were obtained by means of the Tsonopoulos34 procedure by applying the virial state equation truncated at the second term. For mixtures, the mixing second virial coefficients were calculated using the characteristic constant kij = 0.05. The liquid molar volumes of pure compounds (vLi ) were calculated by using the Rackett35 equation. The physical properties of Daubert and Danner36 and the vapor pressures (p0i ) of butyl acetate, methanol, ethanol, 1-propanol, and 1-butanol, obtained previously,37−41 were used in eq 4. In addition, for (Bii, Bij) determinations, the acentric factor (wi) was calculated by using the p0i of the literature.37−41 Table 3 includes the γi values calculated from VLE data and using eq 4, as was previously indicated. Results obtained from γi values indicate a positive deviation from Raul’s law, which is characterized by having a maximum activity coefficient at low alcohol composition and decreasing with increasing number of carbon atoms of alcohol. This behavior is identical to that observed with respect to the Gibbs free energy, since it decreases in each system by increasing the chain length of the alcohol. D



Article

Table 3. Experimental and Calculated Values of VLE Dataa T (K)

x1

y1

γ1

348.27 348.89 349.45 349.94 350.26 351.04 351.61 352.12 352.50 352.96 353.51 354.38 354.59 355.05 355.54 356.36 356.97 357.85 358.89 359.57 360.61 361.71 364.15 365.43 367.45 373.14 379.17 383.15 388.22 395.14 402.36 413.30

Butyl Acetate (1) + Methanol (2) at 0.15 MPa 0.000 0.000 0.031 0.015 3.91 0.066 0.027 3.23 0.086 0.034 3.06 0.112 0.039 2.67 0.143 0.047 2.44 0.176 0.056 2.31 0.202 0.061 2.15 0.234 0.065 1.95 0.268 0.069 1.78 0.300 0.074 1.67 0.364 0.081 1.45 0.381 0.084 1.43 0.405 0.088 1.38 0.440 0.093 1.32 0.490 0.098 1.21 0.521 0.105 1.19 0.555 0.113 1.17 0.594 0.126 1.17 0.621 0.130 1.13 0.659 0.138 1.09 0.695 0.145 1.04 0.734 0.166 1.03 0.757 0.174 1.00 0.791 0.195 1.00 0.837 0.251 1.00 0.867 0.313 0.99 0.885 0.365 0.99 0.905 0.438 0.99 0.931 0.557 1.00 0.955 0.706 1.00 1.000 1.000 1.00

381.24 381.75 381.96 382.16 382.36 382.79 383.96 384.30 384.72 384.99 385.36 386.01 386.12 386.43 387.50 388.03 388.41 388.92 389.65 392.19

Butyl Acetate (1) + 1-Propanol (2) at 0.15 MPa 0.000 0.000 0.033 0.026 2.00 0.052 0.040 1.94 0.073 0.055 1.88 0.100 0.069 1.71 0.133 0.092 1.69 0.221 0.143 1.52 0.259 0.151 1.36 0.276 0.163 1.36 0.304 0.175 1.31 0.323 0.186 1.30 0.375 0.209 1.23 0.388 0.216 1.22 0.431 0.233 1.18 0.478 0.265 1.17 0.498 0.275 1.14 0.527 0.285 1.11 0.545 0.294 1.09 0.593 0.315 1.05 0.683 0.380 1.01

γ2

T (K)

1.00 1.01 1.02 1.01 1.03 1.02 1.03 1.04 1.07 1.10 1.12 1.18 1.20 1.23 1.27 1.35 1.40 1.45 1.51 1.57 1.67 1.79 1.85 1.92 2.04 2.03 1.90 1.80 1.67 1.49 1.25

361.98 362.29 362.33 362.42 362.74 362.99 363.35 363.61 363.90 364.16 364.54 364.82 365.20 365.66 366.06 366.59 367.02 367.38 367.73 368.19 368.60 369.34 369.98 370.84 372.07 373.29 375.12 374.98 375.43 376.21 378.61 380.96 382.83 387.28 393.43 399.96 406.25 409.34 413.30

1.00 0.99 0.98 0.98 0.99 0.99 1.00 1.03 1.02 1.04 1.04 1.08 1.08 1.13 1.14 1.15 1.19 1.20 1.27 1.36

402.59 402.56 402.52 402.50 402.47 402.44 402.41 402.39 402.42 402.45 402.48 402.54 402.60 402.65 402.73 402.82 402.94 403.01 403.09 403.28 E

x1

y1

γ1

Butyl Acetate (1) + Ethanol (2) at 0.15 MPa 0.000 0.000 0.016 0.010 3.07 0.025 0.015 2.94 0.036 0.022 2.98 0.054 0.029 2.59 0.076 0.040 2.52 0.098 0.049 2.36 0.118 0.053 2.10 0.139 0.062 2.06 0.160 0.072 2.06 0.190 0.079 1.88 0.209 0.086 1.84 0.235 0.090 1.69 0.258 0.102 1.72 0.279 0.108 1.66 0.313 0.118 1.58 0.339 0.126 1.54 0.358 0.130 1.48 0.382 0.136 1.44 0.403 0.144 1.42 0.428 0.151 1.38 0.476 0.160 1.28 0.505 0.168 1.24 0.553 0.179 1.17 0.597 0.196 1.14 0.632 0.210 1.11 0.671 0.236 1.10 0.676 0.230 1.07 0.694 0.236 1.05 0.713 0.247 1.05 0.761 0.280 1.03 0.798 0.307 0.99 0.821 0.331 0.98 0.867 0.398 0.97 0.912 0.497 0.95 0.948 0.636 0.97 0.976 0.801 0.99 0.987 0.892 1.01 1.000 1.000 1.00 Butyl Acetate (1) + 1-Butanol (2) at 0.15 MPa 0.000 0.000 0.008 0.011 1.87 0.021 0.026 1.68 0.038 0.044 1.57 0.060 0.068 1.54 0.079 0.087 1.50 0.123 0.129 1.42 0.147 0.150 1.39 0.195 0.190 1.32 0.217 0.207 1.29 0.238 0.225 1.28 0.260 0.243 1.26 0.285 0.264 1.25 0.307 0.281 1.23 0.336 0.303 1.21 0.364 0.322 1.18 0.394 0.342 1.16 0.419 0.361 1.15 0.449 0.386 1.14 0.480 0.408 1.12

γ2 1.00 0.98 0.99 0.99 0.99 0.99 0.99 1.00 1.01 1.01 1.03 1.03 1.05 1.05 1.06 1.08 1.10 1.11 1.13 1.14 1.17 1.23 1.26 1.34 1.40 1.44 1.47 1.51 1.56 1.60 1.70 1.80 1.85 1.95 2.05 2.08 2.08 1.92

1.00 1.01 1.01 1.01 1.01 1.01 1.01 1.02 1.03 1.03 1.03 1.04 1.04 1.05 1.06 1.07 1.09 1.10 1.11 1.13



Article

Table 3. continued T (K) 393.09 394.51 395.75 398.08 402.60 404.22 409.67 413.30

x1

γ1

y1

Butyl Acetate (1) + 1-Propanol (2) at 0.15 MPa 0.708 0.400 1.00 0.741 0.435 1.00 0.778 0.472 0.99 0.818 0.536 1.00 0.893 0.673 1.01 0.906 0.713 1.01 0.967 0.885 1.01 1.000 1.000 1.00

γ2

T (K)

1.39 1.41 1.48 1.48 1.55 1.48 1.44

403.47 403.86 403.90 404.09 404.64 404.88 405.27 405.81 406.24 407.08 407.95 409.11 410.13 410.95 412.05 412.69 413.30

x1

y1

γ1

Butyl Acetate (1) + 1-Butanol (2) at 0.15 MPa 0.509 0.432 1.11 0.570 0.483 1.10 0.578 0.487 1.09 0.599 0.503 1.08 0.663 0.549 1.05 0.689 0.569 1.04 0.713 0.591 1.03 0.749 0.624 1.02 0.775 0.651 1.02 0.807 0.689 1.01 0.841 0.737 1.01 0.882 0.792 1.01 0.915 0.848 1.01 0.943 0.891 1.01 0.972 0.947 1.01 0.989 0.977 1.00 1.000 1.000 1.00

γ2 1.14 1.17 1.18 1.20 1.27 1.31 1.33 1.37 1.40 1.42 1.42 1.46 1.43 1.49 1.43 1.55

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

Table 4. Results of the Thermodynamic Consistency Testa

All azeotropic data for BAB, including the azeotropic data of this paper, were correlated employing a multiple lineal regression, as follows:

0.15 MPa parameter/system W L D J Redlich−Kister test42 Herington test43 RMS direct test of Van Ness index44 103 BIAS(y1) 103 MAD(y1) MPD(y1) BIAS(p) (kPa) MAD(p) (kPa) MPD(p) Van Ness et al. test19,20

BAM

BAE

BAP

BAB

−0.22823 0.29045 12.00 16.01 FAILS FAILS 0.124 5

−0.22437 0.26666 8.61 12.65 PASSES FAILS 0.092 4

−0.14789 0.16867 6.56 6.05 PASSES PASSES 0.098 4

−0.12470 0.11426 4.37 0.38 PASSES PASSES 0.047 2

6.7 6.9 7.34 −0.1 1.8 1.17 PASSES

0.2 5.9 6.40 −0.1 0.6 0.42 PASSES

−2.4 8.1 5.89 0.0 0.6 0.38 PASSES

−4.0 6.6 1.96 0.1 0.4 0.24 PASSES

1 = 0.993 − 0.286 log10 pr Tr xaz = −4.154 + 3.252

The root-mean-square (RMS), average of residuals (BIAS), mean absolute deviation (MAD), and mean proportional deviation (MPD) are calculated as follows: ∑ [d(GERT )/dx1 − ln(γ1/γ2)]2 n−2

∑ (Fexp − Fcal);

1 MAD(F ) = n−2

∑ |Fexp − Fcal|;

MPD(F ) =

100 n−2

;

n

1 n−2

BIAS(F ) =

1 n 1 n

∑ 1

|Fexp − Fcal| Fexp

1 − 0.132(log10 pr )2 Tr

(9)

In addition, the obtained curves of eqs 8 and 9 are also plotted in Figure 5. It can be observed that the azeotrope composition moves to high mole fractions of alcohol with increasing pressure. Therefore, it can be concluded that the azeotrope can be eliminated by increasing pressure in the BAB system. On the other hand, the azeotrope of this work determined for BAB at 0.15 MPa showed a good correlation (see Figure 5) with all literature data.47 Data obtained in this work was plotted against literature data7−18 in Figures 6−12. These plots show some differences when considering the effect of the pressure in the BAM, BAE, and BAP systems (Figures 6−8), even though the uniform evolution of each system is observed. Only data at 101.3 kPa from Beregovykh et al.8,9 verify the symmetric behavior as a function of pressure in all systems. It seems reasonable to observe molar compression with increasing pressure. A similar behavior can be observed from Patlasov et al.9 at 101.3 kPa in the BAE system (see Figure 6). When the BAB system is considered (Figures 9−12), a uniform evolutionary behavior is observed when assessing the effect of the pressure in the system. This can be verified considering data from Figurski and Von Weber15 (see Figure 9), Sheinker and Peresleni16 (see Figure 10), and Shim et al.15 (see Figure 11). However, as previously stated, the compressive effect on the system as a function of pressure is only observed from Shim et al.15 (see Figure 11, curves G and H). This is the reason why the remaining BAB data from the literature15−18 at 101.3 kPa were plotted together with the data from this work at 0.15 MPa (see Figure 12) in order to verify the effect of the pressure.

a

RMS =

(8)

; with F being y , p

experimental data of BAB at 0.15 MPa (see Table 3). Figure 5 includes all literature data47 and the azeotropic data of this work using reduced properties for temperature (Tr) and pressure (pr). The critical properties were taken from the literature.36 F



Article

Figure 2. Relative volatilities (α12) of BAM (blue ▲), BAE (blue ■), BAP (blue ★), and BAB (blue ●) at 0.15 MPa. Comparison of NRTL fit (parameters of eq 7). The solid lines represent the NRTL model in the perturbation scheme,45 and the dashed lines show ±10% deviations from the calculated relative volatilities.

Figure 4. Plot of x1 − y1 vs x1 for BAM (blue ▲), BAE (red ■), BAP (green ★), and BAB (purple ●) binary systems at 0.15 MPa.

Figure 3. VLE data at 0.15 MPa of T−x1−y1 for BAM (blue ▲, red ▲), BAE (blue ■, red ■), BAP (blue ★, red ★), and BAB (blue ●, red ●).

The insets in Figure 12 are presented to verify data of minimum of the plot and the azeotropic data. Therefore, we consider it appropriate to verify the point-topoint evolution of data with pressure. Again, we consider the azeotropic data as a reference. For this reason, the azeotropic point of this work and the one reported by Beregovich et al.17,47 and Shim et al.15,47 were plotted (see Figure 5, insets A and B, respectively) together with the correlation curves (see eqs 8 and 9) for all of

Figure 12 shows that data from Brunjes and Furnas16 and Beregovich et al.17 satisfy the compressive criterion as a function of pressure, although data from Brunjes and Furnas16 do not show a similar trend, as the data are scattered. In addition, the data of several references (see caption in Figure 12) do not satisfy the mentioned behavior probably as a consequence of systematic errors in the experimental determinations. G



Article

Figure 7. Representation points of y1 − x1 vs x1 at 0.15 MPa for BAE (blue ■). Literature data: Beregovykh et al.9 (red ◀), Gonzalez and Ortega13 (green ★), Polyakova et al.13 (purple ▼) and Shono et al.9 (red ▶), both at 101.3 kPa.

Figure 5. Azeotropic data in reduced coordinates for BAB of this work (black ●) and literature data47 (blue ○). Projections of the points in plane are shown in red (○) with black symbols (●) representing the azeotropic points of this work. Equations 8 and 9 are represented by fitting curves. Azeotropic points of this work (black ●), Beregovykh et al.17,47 (black ▼), and Shim et al.15,47 (black ▲) are presented insets A and B with fitting curves.

Figure 8. Plot of VLE points (blue ★) and fitting curve for BAP at 0.15 MPa. Literature data: Beregovykh et al.9 (red ◀), Gonzalez and Ortega14 (green ▼), and Ortega et al.14 (purple ◆) at 101.3 kPa and fitting curves.

Figure 6. Experimental VLE data (blue ▲) and fitting curve for BAM at 0.15 MPa. Literature data: Beregovykh et al.8 (red ◀), Patlasov et al.9 (green ★), and Resa et al.7 (purple ◆) at 101.3 kPa; Espiau et al.11 (red ▼) at 141.3 kPa; Susial et al.12 (dark brown ▶) at 0.6 MPa.

the azeotropic data.47 The correct evolutionary disposition is observed in both cases as a function of pressure. 3.3. Mathematical−Thermodynamic Models. The activity coefficients are related to the thermodynamic function of excess Gibbs free energy as follows Figure 9. Plot of y1 − x1 vs x1 at 0.15 MPa for BAB (blue ●) and fitting curve. Literature data of Figurski and Von Weber15 at 6.67 (red ★), 19.99 (dark brown ▼), 39.99 (green ▶), 79.99 (purple ▲), and 101.3 (red ◀) kPa, respectively, with fitting curves.

GE = x1 ln γ1 + x 2 ln γ2 (10) RT 49 46 and the activity coefficient models of Wilson, NRTL, and UNIQUAC50 can be correlated by using the calculated activity coefficients of Table 3 in eq 10. The excess Gibbs function equation in the Wilson model49 was employed for the determination of the adjustable interaction energy parameter (Δλij). The liquid molar volumes vi and vj were calculated with the Rackett35 equation. For the excess Gibbs function applied by the NRTL model,46 αij = αji is

a non-random parameter of the mixture and 0.47 was used in this work for all mixtures, and the interaction energies Δgij between i−j pairs of molecules are adjustable parameters. In the UNIQUAC model,50 the excess Gibbs function is composed of the combinatorial and residual parts, using Z as the coordination number, Φ as the molecular fraction of segments H



Article

The adjustable parameters in each of these models in J/mol units were obtained using the Nelder and Mead method.51 Deviation in the sum of the squares of the activity coefficient was minimized for both substances during optimization of the parameters. The results shown in Table 5 for BAM using the UNIQUAC model50 yield the lowest mean absolute deviations (MADs) and mean proportional deviation (MPDs) between experimental and calculated values for temperature, vapor composition, and activity coefficient. However, the Wilson model49 yields the best correlation for BAB. All of these mathematical− thermodynamic models reproduce well the azeotropic point of BAB at 0.15 MPa.

4. PREDICTIONS 4.1. Group Contribution Model Prediction. VLE data from this work (see Table 3) were compared with the theoretical predictions generated by the original UNIFAC model20 with Hansen et al. parameters,21 the UNIFAC-Lyngby model proposed by Larsen et al.,22 the UNIFAC-Dortmund model proposed by Gmheling et al.,23 and the ASOG model proposed by Kojima and Tochigi.24 The activity coefficient of the liquid phase in the group contribution models was calculated as a sum of two contributions, the combinatorial part and the residual part, as follows:

Figure 10. Representation points of y1 − x1 vs x1 at 0.15 MPa for BAB (blue ●) and fitting curve. Literature data of Sheinker and Peresleni16 at 6.67 (dark brown ▶), 22.06 (purple ◀), and 101.3 (red ▲) kPa, respectively, and fitting curves.

ln γi = ln γiComb + ln γi Resid

(11)

Differences in the models arise from the interpretation given in each one about the combinatorial and residual contributions. In the ASOG model,24 the combinatorial part is obtained by using the Flory−Huggins equation and the group activity coefficient in the residual part is given by the Wilson equation to obtain the following equation

Figure 11. VLE data of this work at 0.15 MPa for BAB (blue ●) and fitting curve. Fitting curves from literature data of Shim et al.15 at 13.33 (orange, A), 26.66 (black, B), 39.99 (purple, C), 53.33 (black, D), 66.66 (green, E), 79.99 (black, F), 93.33 (dark green, G), and 101.3 (red, H) kPa, respectively.

⎛ ⎞ ϑic ⎟ ϑic ln γi = 1 + ln⎜⎜ − c⎟ c ⎝ ∑j xj ϑj ⎠ ∑j xj ϑj +

∑ ϑki(ln Γk − ln Γik)

(12)

where ϑci is the number of atoms (non-hydrogen atoms) in molecule i, ϑki is the number of atoms (non-hydrogen atoms) in group k in molecule i, Γk is the group activity coefficient of group k, and Γik is the activity coefficient of group k in a standard state (pure component i). The ASOG model24 considers the group activity coefficient as follows ⎛ ⎞ ln Γk = 1 − ln⎜⎜∑ Xlalk ⎟⎟ − ⎝ l ⎠

∑ l

Xlalk ∑m X malm

(13)

where Xl represents the group fraction of group l in the liquid solution. In the above expression (eq 13), the summations extend over all groups and alk and alm are the group interaction parameters. The UNIFAC models20−23 are generally based on the equations of the UNIQUAC model for the combinatorial part, and considering the eq 11 result: For the classical UNIFAC model,20,21

Figure 12. Comparison between y1 − x1 vs x1 points of this work for BAB at 0.15 MPa (blue ●) with fitting curve and literature data at 101.3 kPa from Belousov et al.15 (black ★), Brunjes and Furnas16 (dark green ■), Beregovich et al.17 (red ◆), Gonzalez and Ortega15 (purple ◀), Lladosa et al.15 (black ▲), Mato and Cepeda18 (red solid six-pointed star), and Ortega et al.15 (green ▶) with fitting curves.

⎛Φ ⎞ ⎛Φ ⎞ ⎛Z⎞ ⎛ θ ⎞ ln γi = ln⎜ i ⎟ + qi⎜ ⎟ ln⎜ i ⎟ + li − ⎜ i ⎟ ∑ xjl j ⎝ 2 ⎠ ⎝ Φi ⎠ ⎝ xi ⎠ ⎝ xi ⎠ j

calculated from volume groups of van der Waals, θ as the molecular fraction of surfaces calculated from the area of groups of van der Waals, and Δuij as the adjustable parameters which represent the average interaction energy of molecules.

+ I


(14) DOI: 10.1021/acs.jced.8b00182 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

J

a

Δg12 (J·mol−1) = −270.9 Δg21 (J·mol−1) = 2737.2 0.008 0.65 3.04 1.63 3.53 Δg12 (J·mol−1) = 76.3 Δg21 (J·mol−1) = 1742.8 0.004 0.29 1.21 1.86 1.53

Δλ12 (J·mol−1) = 4491.1 Δλ21 (J·mol−1) = −2044.9 0.008 0.61 2.86 1.78 3.52

Δλ12 (J·mol−1) = 2916.6 Δλ21 (J·mol−1) = −1106.7 0.004 0.28 1.17 1.77 1.50 0.201 402.18

Δg12 (J·mol−1) = 656.7 Δg21 (J·mol−1) = 2892.4 0.007 0.64 3.38 2.67 3.30

Δλ12 (J·mol−1) = 5300.8 Δλ21 (J·mol−1) = −1787.5 0.006 0.61 3.14 2.84 3.16

0.199 402.20

Δg12 (J·mol−1) = −55.6 Δg21 (J·mol−1) = 4620.0 0.015 1.38 7.12 4.00 7.77

Δλ12 (J·mol−1) = 8166.6 Δλ21 (J·mol−1) = −3582.9 0.016 1.48 7.61 4.71 8.84

Predictions using group contribution models and the PC-SAFT EOS.

x1,az = 0.167 Taz = 402.39 K

MAD(y1) MAD(T) (K) MAD(p) (kPa) MPD(γ1) MPD(γ2)

PARAMETERS


PARAMETERS


PARAMETERS


PARAMETERS

NRTL46 (α = 0.47)

Wilson49

Table 5. Results of Mathematical−Thermodynamic Treatmenta UNIFAC22 OH/COOC

Butyl Acetate (1) + Methanol (2) at 0.15 MPa Δu12 (J·mol−1) = 2473.8 Δu21 (J·mol−1) = 65.6 0.013 0.012 1.25 1.09 6.49 0.006 3.09 2.54 6.89 6.38 Butyl Acetate (1) + Ethanol (2) at 0.15 MPa Δu12 (J·mol−1) = 2219.9 Δu21 (J·mol−1) = −483.7 0.006 0.018 0.62 1.10 3.22 0.005 2.59 6.23 3.00 7.08 Butyl Acetate (1) + 1-Propanol (2) at 0.15 MPa Δu12 (J·mol−1) = 804.5 Δu21 (J·mol−1) = −9.2 0.007 0.014 0.62 0.76 2.92 0.003 1.68 3.77 3.38 4.80 Butyl Acetate (1) + 1-Butanol (2) at 0.15 MPa Δu12 (J·mol−1) = 634.8 Δu21 (J·mol−1) = −102.9 0.005 0.013 0.28 1.24 1.17 0.005 1.85 5.49 1.48 6.77 Azeotropic Data 0.202 0.075 402.20 0.075

UNIQUAC50 (Z = 10)

0.284 0.284

0.015 1.23 0.005 8.88 6.11

0.012 2.03 0.010 9.51 9.03

0.005 1.05 0.005 3.29 4.37

0.016 1.17 0.006 4.41 7.95

UNIFAC20,21 OH/CCOO

0.074 0.074

0.011 1.11 0.005 4.98 5.88

0.016 0.86 0.004 6.13 5.20

0.025 1.71 0.008 12.45 8.96

0.016 1.38 0.007 6.23 7.82

UNIFAC23 OH/CCOO

0.201 0.201

0.005 0.34 0.001 2.00 1.81

0.008 0.63 0.003 1.92 3.41

0.019 1.12 0.005 7.99 6.87

0.011 1.19 0.006 2.98 6.31

ASOG24 OH/COO

0.208 402.64

0.016 0.24

kij = −0.011

0.015 0.35

kij = 0.019

0.009 0.38

kij = 0.030

0.025 1.84

kij = 0.013

PC-SAFT1,2

Journal of Chemical & Engineering Data Article



Article

l represents the pure-component lattice parameter which is a function of the van der Waals surface area (q) and the van der Waals volume (r). For the UNIFAC-Larsen model,22 ψi ⎛ψ ⎞ ln γi = ln⎜ i ⎟ + 1 − i + xi ⎝ xi ⎠


the segment energy parameter (εij) and the segment diameter (σij) of the mixture as σij =

Φ⎤ ⎛ Z ⎞⎡ ⎛ Φ ⎞ ln γi = ln δi + 1 − δi − qi⎜ ⎟⎢ln⎜⎜ i ⎟⎟ + 1 − i ⎥ ⎝ 2 ⎠⎢⎣ ⎝ η ⎠ ηi ⎥⎦ i


(16)

where η is the modified molecular surface area fraction and δ is the modified molecular volume fraction. In the UNIFAC models,20−23 ϑki represents the number of groups of type k in molecule i and the following equation is used for the group activity coefficient ⎡ ⎛ ⎞ ln Γk = Q k ⎢1 − ln⎜⎜∑ Θmξmk ⎟⎟ − ⎢⎣ ⎝m ⎠

∑ m

Θmξmk ⎤⎥ ∑n Θnξmn ⎥⎦

ε AiBj = κ AiBj

εiiεjj (1 − kij)

εij =

(19)

1 AiBi (ε + ε AjBj) and 2 ⎛ ⎞3 σiiσjj ⎟⎟ = κ AiBiκ AjBj ⎜⎜ ⎝ 0.5(σii + σjj) ⎠

(20)

By considering what was previously indicated, a PC-SAFT Fortran program developed by us was employed. Since the validation of VLE data is a function of vapor pressures, to obtain the m, σi, and εi of pure fluid parameters, vapor pressures reported in previous papers4,37−41 have been used. To obtain the association parameters εAiBi and κAiBi of methanol, ethanol, 1-propanol, and 1-butanol, a scheme 2B with two number association sites was applied. A multiobjective function such as the sum of the values of individual goals37 was used to minimize the molar densities36 and the vapor pressure data.4,37−41 The standard deviation, the mean absolute deviation, as well as the mean percentual deviations were also calculated for comparison purposes. Results are shown in Table 6, always with the literature parameters.1,2,53 Pure component parameters calculated by us (Table 6) were plotted (see Figure 14) for the molecular consistency test. Results show that the correlation of alcohol parameters obtained by us has an SD of 0.87 and 0.03 and literature parameters2 had an SD of 0.60 and 0.04, respectively (see Figure 14A and B). Therefore, there are obvious similarities in both results. However, it should be noted that data used by us to obtain the parameters have greater dispersion, since direct data T, p0i have been used, while the constants cited in the literature1,2,53 were found using data obtained from the correlations of the vapor pressures. After this, the obtained VLE data were verified by using the ϕ−ϕ approach. A bubble point algorithm was applied to perform VLE predictions by the PC-SAFT model. Binary adjustable interaction parameters kij of the PC-SAFT model1,2 were computed using the pure fluid parameters (Table 6). Two associating sites were considered for alcohols (the 2B model), and one association site was considered for butyl acetate. The self-association of ester was not permitted. Solvation was considered by the cross-association between the site of the ester molecule and the sites of the alcohol molecule. The minimizing objective function (OF) employed was

(17)

where Qk is the van der Waals surface area of group k, Θ represents the group surface area fraction, and ξ is defined by an equation that includes the group contribution parameters. A Fortran computer program of Fredenslund et al.20 was used with modifications to include the different models and interaction parameters of groups. Table 5 shows prediction results from the group contribution models. Figure 13 shows the experimental data and the fitting curves of predictions obtained by using these group contribution models. In general terms, the best prediction for γi was obtained with the ASOG model.24 The UNIFAC-Larsen model22 generates good predictions globally. However, the classical UNIFAC version20,21 generates the best prediction for BAE. The Gmehling et al.23 version also returns a good prediction for BAE and BAP. On the other hand, in general terms, the higher deviations in the MAD of pressure and temperature predictions can be observed in Table 5, except in the BAB prediction of the ASOG model,24 which reproduces VLE data and azeotrope data successfully. 4.2. The PC-SAFT Model. The PC-SAFT EOS is usually given in terms of additive contributions to the Helmholtz free energy (Ares/NkT). Each term represents different qualitative contributions to the total free energy. Neglecting polar interactions, the equation is written as Ares Ahc Adisp Aassoc = + + NkT NkT NkT NkT

and

where kij is the binary interaction parameter. The Helmholtz free energy due to the association (Aassoc/NkT) is dependent on the fraction of molecules i that are not bonded at the association site by measuring the association strength between site A on molecule i and site B on molecule j. This parameter is a function of the radial distribution function which is dependent on the association volume (κAiBi) and the association energy (εAiBi). These last two parameters are required for describing the cross-associating interactions between associating substances. The mixing rules of Wolbach and Sandler52 were employed:

(15)

where ψ represents the modified group volume fraction. For the UNIFAC-Gmehling model,23

+

1 (σii + σjj) 2

(18) hc

The hard-sphere chain reference contribution (A /NkT) is a function of the Helmholtz free energy of the hard-sphere fluid and the radial distribution function of hard-sphere fluid, which are dependent on the number of segments per chain (mi), the segment diameter (σi), and the segment energy parameter (εi). The dispersion contribution to the Helmholtz free energy (Adisp/NkT) accounts for the van der Waals forces, by considering the Helmholtz free energy first-order perturbation term and the Helmholtz free energy second-order perturbation term. These dispersive contribution terms, as indicated by Gross and Sadowski,1 were employed. For a pair of unlike segments, we used conventional Berthelot−Lorentz combining rules, giving

n

OF =

∑ |(Ti)EXP − (Ti)CAL | 1

1 U (T )

n

+

∑ |(y1i )EXP − (y1i )CAL | 1

K

1 U (y )

(21)



Article

Figure 13. Representation of T vs x1, y1 (blue or red symbols, respectively) as well as y1 − x1 vs x1 (black symbols) for the BAM (▲), BAE (■), BAP (★), and BAB (●) binary systems at 0.15 MPa. The predictions are represented by the fitting curves: original UNIFAC20,21 (purple), UNIFACLyngby22 (cyan), UNIFAC-Dortmund23 (green), ASOG24 (dark brown), and PC-SAFT1,2 (magenta) for all of these systems. L



Article

Table 6. PC-SAFT Pure Component Parametersa methanol mi σi (Å) εi/k (K) κAiBi εAiBi/k (K) MAD(p) (kPa) MAD(ρ) (kmol/m3) MPD(p) (%) MPD(ρ) (%) SD(p) (kPa) SD(ρ) (kmol/m3) a

ethanol

1-propanol

1-butanol

butyl acetate

TWa

ref 2

TWa

ref 2

ref 53

TWa

ref 2

TWa

ref 2

ref 53

TWa

ref 1

1.443597 3.301456 190.887 0.046043 2827.504 1.41

1.5255 3.2300 188.90 0.035176 2899.5

2.790863 2.995426 188.229 0.069524 2421.951 3.19

2.3827 3.1771 198.24 0.032384 2653.4

2.547 3.123 208.8 0.04 2392.9

3.567595 3.016381 197.974 0.078938 2139.753 1.97

2.9997 3.2522 233.40 0.015268 2276.8

2.897196 3.52981 247.846 0.010361 2545.323 0.94

2.7515 3.6139 259.59 0.006692 2544.6

3.974 3.140 219.6 0.04 1962.8

4.014396 3.534224 240.930

3.9808 3.5427 242.52

0.02 0.56 0.10 1.78 0.03

0.01 2.36 2.01

0.76 0.09 4.52 0.01

0.02 0.99 0.79

0.22 0.50

1.77

0.02

0.66 0.18 2.61 0.02

0.85 1.71

TW = this work; ref = reference; standard deviation (SD) calculated as follows: SD(F ) =

0.82 0.19 1.17 0.02 ∑1n(Fexp − Fcal)2 n−2

0.04 1.78 1.63

;

1.27 0.52

1.04 0.66 2.11 0.05

2.03 1.26

F ≡ p, ρ

The azeotropic point in the BAB system at 0.15 MPa was found, and the results are well correlated with literature data for azeotropic points at different pressures. The ASOG and different versions of the UNIFAC group contribution models were applied to predict VLE data. The predictions on the molar fraction vapor phase are in general acceptable, but only the ASOG model reproduces the experimental data adequately. However, when the PC-SAFT EOS was applied to the experimental data of BAM, BAE, BAP, and BAB at 0.15 MPa, there were good predictive capabilities and correlation results in the T vs x1, y1 plots. Specifically, the azeotrope of the BAB system at 0.15 MPa was only predicted adequately by the ASOG and PC-SAFT models.

Figure 14. Pure component parameter test of the PC-SAFT EOS. Both insets, from this work (red ●) and from the literature1,2 (blue ▲), for n-alcohols (comparison from C1 to C4) as a molar mass (MM) function.

■

AUTHOR INFORMATION

Corresponding Author

*Phone: 34928451489. Fax: 34928458658. E-mail: psusial@ dip.ulpgc.es.

Equation 21 has a separate objective function for each property, which is specified by the sum of the absolute deviations, respectively, of T and y1. The expanded uncertainties (U) (see Table 3) were used as a weight normalizing factor. OF was minimized by means of the Nelder−Mead simplex method.51 One binary interaction parameter kij (temperature independent) was obtained for each isobaric system (Table 5). Overall results in predictions of T and y1, made by the PCSAFT model,1,2 for the systems BAM, BAE, BAP, and BAB are shown in Table 5. The greatest difference in prediction was obtained from the BAM system (Figure 13). However, the predictions made for temperature for BAE, BAP, and BAB are suitable. The higher differences are in prediction y1 for BAP and BAB. On the other hand, the azeotrope of BAB is successfully indicated by the PC-SAFT model1,2 (see Figure 13).

ORCID

Pedro Susial Badajoz: 0000-0003-0538-4763 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) Susial, P.; Apolinario, J. C.; Rodríguez-Henríquez, J. J.; Castillo, V. D.; Estupiñan, E. J. Isobaric VLE at 0.6 MPa for binary systems isobutyl acetate+ethanol, + 1-propanol or + 2-propanol. Fluid Phase Equilib. 2012, 331, 12−17. (4) 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. (5) Susial, R.; Susial, P. High pressure vapor−liquid equilibria of methyl acetate or ethyl acetate with 2-propanol at 1.5 MPa. Experimental data and predictions. Chem. Eng. Res. Des. 2015, 102, 337−344. (6) Susial, P.; Sosa-Rosario, A.; Rios-Santana, R. Vapor-liquid equilibria for ethyl acetate + methanol at (0.1, 0.5, and 0.7) MPa.

■

CONCLUSIONS Excess molar volumes for BAE, BAP, and BAB at 298.15 K and VLE data for binary systems BAM, BAE, BAP, and BAB at 0.15 MPa were measured, and the results were compared with literature data. VLE data were verified applying the Redlich−Kister area test, the Herington test, the Van Ness direct area test, and the pointto-point test of Van Ness. Results indicated the systems presented in this paper have acceptable quality. M



Article

Measurements with a new ebulliometer. J. Chem. Eng. Data 2010, 55, 5701−5706. (7) Gmehling, J.; Onken, U. Vapor-Liquid Equilibrium Data Collection; Dechema: Frankfurt, Germany, 2005; Vol. 1, part 2g, pp 451−453. (8) Gmehling, J.; Onken, U.; Arlt, W. Vapor-Liquid Equilibrium Data Collection; Dechema: Frankfurt, Germany, 1982; Vol. 1, part 2c, pp 213−216, 424−426. (9) Gmehling, J.; Onken, U.; Rarey-Nies, J. R. Vapor-Liquid Equilibrium Data Collection; Dechema: Frankfurt, Germany, 1988; Vol. 1, part 2e, pp 163, 344, 346, 484. (10) Blanco, A. M. Analysis of the vapor−liquid equilibrium at 141.3 kPa of binary mixtures containing methanol with n-alkanes (C5, C6) and alkyl esters. Doctoral thesis, University of La Laguna, Canary Islands, 1997. (11) Espiau, F.; Ortega, J.; Penco, E.; Wisniak, J. Advances in the correlation of thermodynamic properties of binary systems applied to methanol mixtures with butyl esters. Ind. Eng. Chem. Res. 2010, 49, 9548−9558. (12) 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. (13) Gmehling, J.; Onken, U.; Rarey, J. R. Vapor-Liquid Equilibrium Data Collection; Dechema: Frankfurt, Germany, 2006; Vol. 1, part 2h, pp 367−371. (14) Gmehling, J.; Onken, U. Vapor-Liquid Equilibrium Data Collection; Dechema: Frankfurt, Germany, 2007; Vol. 1, part 2i, pp 253, 254. (15) Gmehling, J.; Onken, U. Vapor-Liquid Equilibrium Data Collection; Dechema: Frankfurt, Germany, 2008; Vol. 1, part 2j, pp 241, 244−255, 257−264. (16) Gmehling, J.; Onken, U.; Arlt, W. Vapor-Liquid Equilibrium Data Collection; Dechema: Frankfurt, Germany, 1990; Vol 1, part 2b, pp 194−197. (17) Gmehling, J.; Onken, U.; Weidlich, U. Vapor-Liquid Equilibrium Data Collection; Dechema: Frankfurt, Germany, 1982; Vol. 1, part 2d, p 197. (18) Gmehling, J.; Onken, U.; Rarey, J. R. Vapor-Liquid Equilibrium Data Collection; Dechema: Frankfurt, Germany, 1990; Vol. 1, part 2f, p 182. (19) 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. (20) Fredenslund, Aa.; Gmehling, J.; Rasmussen, P. Vapor-liquid Equilibria Using UNIFAC, A Group Contribution Model; Elsevier: Amsterdam, The Netherlands, 1977. (21) 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. (22) 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. (23) 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. (24) Kojima, K.; Tochigi, K. Prediction of Vapor-Liquid Equilibria by the ASOG Method; Kodansha Ltd.: Tokyo, 1979. (25) TRC. Thermodynamic Tables Non-Hydrocarbons and Hydrocarbons; Thermodynamic Research Center, Texas A and M University System: College Station, TX, 1996. (26) Acosta, J.; Arce, A.; Rodil, E.; Soto, A. A thermodynamic study on binary and ternary mixtures of acetonitrile, water and butyl acetate. Fluid Phase Equilib. 2002, 203, 83−98. (27) Riddick, J. A.; Bunger, W. B.; Sakano, T. K. Organic Solvents; Wiley-Interscience: New York, 1986.

(28) Nagata, I.; Ohta, T.; Nakagawa, S. Excess Gibss Free Energies and Heats of Mixing for Binary Alcoholic Liquid Mixtures. J. Chem. Eng. Jpn. 1976, 9, 276−281. (29) Resa, J. M.; Gonzalez, C.; Goenaga, J. M. Density, Refractive index, Speed of Sound at 298.15 K, and Vapor−Liquid Equilibria at 101.3 kPa for Binary Mixtures of Propanol + 2-Methyl-1-butanol and Propanol + 3-Methyl-1-butanol. J. Chem. Eng. Data 2006, 51, 73−78. (30) Gonzalez, E.; Ortega, J. Densities and Isobaric VLE of Butyl esters (Methanoate to Butanoate) with Ethanol at 101.32 kPa. J. Chem. Eng. Data 1995, 40, 1178−1183. (31) Hasan, M.; Hiray, A. P.; Kadam, U. B.; Shirude, D. F.; Kurhe, K. J.; Sawant, A. B. Densities, Viscosities, Speeds of Sound, FT-IR and HNMR studies of binary mixtures of n-Butyl Acetate with Ethanol, Propan-1-ol, Butan-1-ol and Pentan-1-ol at 298.15, 303.15, 308.15 and 313.15 K. J. Solution Chem. 2011, 40, 415−429. (32) Gonzalez, E.; Ortega, J. VLE for mixtures of several Butyl Esters (Methanoate to Butanoate) and 1-Propanol at 101.32 kPa. J. Chem. Eng. Jpn. 1995, 28, 765−771. (33) Gonzalez, E.; Ortega, J. Densities and Isobaric VLE for the mixtures formed by four Butyl esters and 1-Butanol. J. Chem. Eng. Data 1996, 41, 53−58. (34) Tsonopoulos, C. An empirical correlation of second virial coefficients. AIChE J. 1974, 20, 263−272. (35) Spencer, C. F.; Danner, R. P. Improved equation for prediction of saturated liquid density. J. Chem. Eng. Data 1972, 17, 236−241. (36) Daubert, T. E.; Danner, R. P. Physical and Thermodynamic Properties of Pure Chemicals: Data Compilation; Hemisphere Publishing Co.: New York, 1989. (37) Susial Badajoz, P.; García-Vera, D.; Montesdeoca, I.; Santiago, D. E.; López-Beltrán, J. Measurements and Modeling of VLE Data for Butyl Acetate with 2-propanol or 2-Butanol. Binary Systems at 0.15 and 0.6 MPa. J. Chem. Eng. Data 2017, 62, 2296−2306. (38) Susial, P.; Rodríguez-Henríquez, J. J.; Apolinario, J. C.; Castillo, V. D.; Estupiñan, E. J. Vapor pressures and vapor−liquid equilibrium of propyl acetate + methanol or + 1-propanol at 0.15 MPa. Binary systems. Rev. Mex. Ing. Quim. 2011, 10, 561−572. (39) Susial, P.; Sosa-Rosario, A.; Rodríguez-Henríquez, 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. (40) Susial, P.; Apolinario, J. C.; Rodríguez-Henríquez, J. J.; Castillo, V. D.; Estupiñan, E. J. Isobaric VLE at 0.6 MPa for binary systems Isobutyl Acetate + Ethanol, + 1-Propanol or + 2-Propanol. Fluid Phase Equilib. 2012, 331, 12−17. (41) 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. (42) Redlich, O.; Kister, A. T. Algebraic Representation of Thermodynamic Properties and Classification of Solutions. Ind. Eng. Chem. 1948, 40, 345−348. (43) Herington, E. F. G. Tests for the Consistency of Experimental Isobaric Vapor−Liquid Equilibrium Data. J. Inst. Petrol. 1951, 37, 457− 470. (44) Van Ness, H. C. Thermodynamics in the Treatment of Vapor/ Liquid Equilibrium (VLE) Data. Pure Appl. Chem. 1995, 67, 859−872. (45) Mathias, P. M. Effect of Phase-Equilibrium Uncertainties on the Separation of Heterogeneous Azeotropes. Application to the Water+1Butanol System. J. Chem. Eng. Data 2016, 61, 4077−4084. (46) Renon, H.; Prausnitz, J. M. Local Compositions in Theermodynamic Excss Functions for Liquid Mixtures. AIChE J. 1968, 14, 135−144. (47) Gmehling, J.; Menke, J.; Krafczyk, J.; Fischer, K. Azeotropic Data, 2nd ed.; Wiley-VCH Verlag: Weinheim, Germany, 2004; Part 1, pp 531−532. (48) Raviart, P. A.; Thomas, J. M. Primal hybrid finite element methods for 2nd order elliptic equations. Math. Comp. 1977, 31, 391− 413. N



Article

(49) Wilson, G. M. Vapor−Liquid Equilibrium. XI. A New Expression for the Excess Free Energy of Mixing. J. Am. Chem. Soc. 1964, 86, 127−130. (50) Abrams, D. S.; Prausnitz, J. M. Statistical Thermodynamics of Liquid Mixtures: A New Expression for the Excess Gibbs Energy of Partly or Completely Miscible Systems. AIChE J. 1975, 21, 116−128. (51) Nelder, J.; Mead, R. A simplex method for function minimization. Comput. J. 1965, 7, 308−313. (52) 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. (53) Fuenzalida, M.; Cuevas-Valenzuela, J.; Pérez-Correa, J. R. Improved estimation of PC-SAFT equation of state parameters using a multi-objective variable-weight cost function. Fluid Phase Equilib. 2016, 427, 308−319.

O


Measurement and Modelization of VLE for Butyl ... - ACS Publications

Recommend Documents