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Vapor−Liquid Equilibrium for Binary Mixtures of Acetates in the Direct Esterification of Fusel Oil Cesar A. Sánchez, Orlando A. Sánchez, Alvaro Orjuela, Iván D. Gil,* and Gerardo Rodríguez Grupo de Procesos Químicos y Bioquímicos, Departamento de Ingeniería Química y Ambiental, Universidad Nacional de Colombia Sede Bogotá, Cra 30 No. 45-03, Ed. 453, Of. 318, Bogotá, Colombia ABSTRACT: In this work, isobaric vapor−liquid equilibrium data for the binary mixtures of the isobutyl acetate + isoamyl acetate and isobutyl acetate + ethyl acetate were measured using an all-glass dynamic-recirculation still equipped with a Cottrell circulation pump (Labodest VLE 602D). For the system of isobutyl acetate + isoamyl acetate the measurements were carried out at 100 and 150 kPa, while for the system isobutyl acetate + ethyl acetate they were performed at 50, 100, and 150 kPa. Vapor pressures of the pure components were also measured to verify the performance and reliability of the equilibrium still, and data were correlated with an Antoinetype expression. The equilibrium data for the pure components were in agreement with literature reports and the data for the binary solutions show a fairly ideal behavior. Binary parameters for nonrandom two liquid (NRTL) and universal quasichemical (UNIQUAC) equations were correlated with experimental data, and both models showed good agreement with experiments and can be used for process design. It was found that, in the absence of experimental data, phase equilibrium in mixtures of acetates formed in the direct esterification of the fusel oil can be confidently predicted using the UNIFAC-DMD model or even the Ideal Model.

1. INTRODUCTION Fusel oil (FO) is a mixture of linear and branched alcohols, ranging from ethylic to isoamylic, obtained as a byproduct of bioethanol industry. Typically, around 1−11 L of FO are generated per each 1000 L of anhydrous ethanol produced.1−3 In countries where the bioethanol plays an important economic role (e.g., USA, Brazil, China, etc.), the valorization of FO is an important issue regarding the sustainability of the whole process, and also an opportunity for creating new value-added products for different market niches. The characteristics of a particular bioethanol process determines the nature of the obtained FO and its composition. This depends on factors such as sugar source (e.g sugar cane, corn, beet, etc.), fermentation conditions (e.g temperature, pH, residence time, etc.) and operating conditions of the distillation train (e.g., the stage where the FO is withdrawn, the number of washes before storing, etc.). In Colombia, sugar cane is the main bioethanol feedstock, and a typical FO composition obtained from cane sugar fermentation is reported in Table 1. In different countries, similar compositions are also reported when using other fermentation feedstock such as corn, grapes, sugar beet molasses, and malt.2−13 As observed, regardless the feedstock, isoamyl alcohol (3-methyl-1-butanol) and optically active amyl alcohol (2-methyl-1-butanol) are the major components of FO, mainly because they are characteristic products of the Ehrlich metabolic pathway during fermentation.14 © XXXX American Chemical Society

An alternative process to upgrade FO into more-valuable byproducts is the conversion into esters, mainly those used in the flavor and fragrance industry. There are two main processing alternatives for the esterification of fusel alcohols:15,16 (1) the indirect process that consists in the separation of the individual FO alcohols followed by their esterification with a carboxylic acid, and (2) the direct process that consists in the simultaneous reaction of the whole FO alcohol mixture with a carboxylic acid. In the first case, only single esterifications (one-acid to one-alcohol at a time) occur and they can be independently studied. However, when directly reacting the fusel mixture, the chemistry of the process is more complex as it is necessary to consider simultaneous esterification and transesterification reactions. Because the isoamyl alcohol is the major component in FO, most literature reports dealing with FO upgrading have focused on the production of iso-amyl esters.17−19 In the case of FO direct esterification, the process is less developed partly because the numerous interactions that must be considered in terms of thermodynamic and kinetic modeling.16 For example, when modeling simultaneous esterification of acetic acid with FO (consisting of a mixture of alcohols as listed in Table 1), a highly nonideal thermodynamic model (e.g., activity-based model) is required for the evaluation of the chemical and phase Received: March 11, 2016 Accepted: October 25, 2016

A

DOI: 10.1021/acs.jced.6b00221 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Typical Composition of Fusel Oil (Water-Free Basis Weight Percentage) Obtained from Different Sources sugar cane Colombia

a

beet

India

Brazil

corn

grape

malt

Turkey

Canada

USAa

USAa

Englanda

alcohol

ref 4

refs 2, 5

refs 3, 6−8

refs 9, 10

ref 11

ref 5

ref 12

ref 13

ethyl n-propyl isopropyl (−)-sec-Butyl n-butyl isobutyl n-pentyl isoamylb

1.8−7.5 0.0−3.8 trace 0.0 0.0−1.9 0.0−16.6 trace 75.6−97.5

1.3−9.8 3.4−22.0 0.6−20.2 0.0 4.8−7.3 0.0−6.7 0.0−3.7 50.0−65.8

10.2−16.2 1.1−1.9 0.0 0.0 0.7−0.8 7.9−11.5 0.0−0.5 69.1−80.0

12.4−34.2 2.1−3.5 0.0 0.0 0.0−0.1 6.4−9.5 0.0 57.2−74.6

1.0 0.0 3.8 0.0 5.9 5.8 0.0 74.6

1.7−20.4 0.0 0.0 0.0 12.2−23.9 0.0 50.9−83.1

4.1 0.0 4.9 1.9 18.3 trace 63.6

1.32 0.00 0.03 0.24 12.30 0.0 80.61

Ethanol-free basis and water-free basis. bIsomers mixture.

2.2. VLE Apparatus and Procedure. Experiments were carried out using a Fischer Labodest VLE 602 isobaric equilibrium cell. Details and technical characteristics of the cell were described elsewhere.23,24 According to the manufacturer, the temperature and pressure sensors were calibrated with an accuracy of 0.01 K and 0.25 kPa, respectively. To carry out equilibrium measurements, initially, the lessvolatile pure component was charged in the cell, while the other was loaded in a side reservoir. Then, different binary mixtures were prepared as needed by the controlled addition of the second component to the equilibrium chamber. For each equilibrium point, the pressure was fixed and the system was maintained under total reflux and agitation. The heating power was adjusted so that the condensate flow was 1−2 drops per second, keeping track of pressure and temperature. The practical equilibrium criteria was defined as the point at which a constant temperature was maintained for 30 min or longer. The fluctuations on the pressure and temperature measurements were continuously calculated using statistical control charts. After reaching the equilibrium condition, samples of liquid and condensed vapor were taken for analysis. For the system iBuAc + EtAc, experiments were carried out at 50, 100, and 150 kPa, while for the system iAmAc + iBuAc, the measures were performed at 100 and 150 kPa. Around 10 to 15 equilibrium points were generated for each pressure. To verify the performance of the apparatus, the vapor pressure of pure components was also measured, and the coefficients of an Antoine-type equation were correlated. Approximately 12−20 equilibrium points for each pure component were obtained. 2.3. Analysis. The compositions of liquid and condensed vapor phases were determined by chromatography using a Shimadzu 2010 GC equipped with an automatic injector, a SGE column (BP20, 30 m−530 μm ID-0.5 μm), and a flame ionization detector (FID) at 543.15 K. The injection port was maintained at 523.15 K using a split injection mode with a split ratio of 50, with an injection volume of 1 μL, and using 2 mL/ min helium as carrier. For each binary mixture, a particular sample preparation method was used, and a slightly different temperature program was developed: 2.3.1. iBuAc + EtAc Mixtures. The initial oven temperature was maintained at 323 K for 4 min, then heated at 0.5 K/min up to 326 K, followed by a second ramp of 40 K/min up to 523 K, and finally the temperature was maintained for 4 min. The vials for chromatography were prepared by dissolving 200 mg of sample in 520 mg of methyl acetate. Around 80 mg of isoamyl butyrate were added at each sample as internal standard.

equilibria, taking into account the 18 components in the mixture (eight alcohols, eight esters, acetic acid, and water). In such a system, several binary and ternary azeotropes and also liquid−liquid behavior are observed.20 Regarding the corresponding acetates of the alcohols listed in Table 1, few binary equilibrium data are available in the literature. Laavi et al.21 measured the binary equilibrium of ethyl acetate + n-butyl acetate, Nishi22 reported data for the ethyl acetate + isopropyl acetate system, and the NIST ThermoData engine (TDE utility, available within Aspen Plus V.8.6) presents experimental reports for the binary mixtures of ethyl acetate + n-pentyl acetate and isoamyl acetate + n-butyl acetate. Taking into account the lack of equilibrium data including acetates of FO alcohols, this work focuses on measuring VLE data for the binary mixtures of the isobutyl acetate (iBuAC) + isoamyl acetate (iAmAc), and isobutyl acetate (iBuAC) + ethyl acetate (EtAc) at different pressures. The obtained experimental data were used to adjust binary parameters for universal quasichemical (UNIQUAC) and nonrandom two liquid (NRTL) activity-based models. Experiments indicated that the binary mixtures under study behave nearly ideally, and also good predictions can be obtained by using the Dortmundmodified universal quasichemical functional group activity coefficients (UNIFAC-DMD) predictive model. The model here obtained can be used for further process development in the simultaneous esterification of fusel alcohols.

2. EXPERIMENTAL SECTION 2.1. Materials. Chemicals used during experiments are listed in Table 2, and the purity reported by the manufacturer was confirmed by gas chromatographic analysis using the area method. Methyl acetate was used as solvent for the chromatographic analyses. For the binary mixtures of iBuAc + iAmAc, ethyl acetate was used as internal standard, while for the mixtures of iBuAc + EtAc, the internal standard was isoamyl butyrate. Table 2. Summary of Components Used in Vapor−Liquid Equilibrium Experiments component

source

purity (%weight)

ethyl acetate isobutyl acetate isoamyl acetate methyl acetate isoamyl butyrate

J.T. Baker Merck KGaA Merck KGaA J.T. Baker Merck KGaA

≥99 ≥98 ≥99 ≥99 ≥98 B



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2.3.2. iBuAc + iAmAc Mixtures. The initial oven temperature was maintained at 323.15 K for 4 min, and then ramped at 1 K/min up to 326.15 K, followed by a second ramp of 40 K/ min up to 493.15 K, and the final temperature was maintained for 1 min. The vials for chromatography were prepared by dissolving 200 mg of sample in 1000 mg of methyl acetate. Around 120 mg of ethyl acetate were added at each sample as internal standard. The uncertainty in the composition measurements was established by previous calibration of the chromatographic techniques, analyzing samples of known composition. A maximum average error of 0.01 in the mole fraction of each component was obtained. The error is defined as the difference between the true value and the value of a particular measure.

Table 4. Adjusted Values of Antoine Coefficients (A, B, C in eq 1) at the Temperature Interval (ΔT), and the Corresponding Standard Deviation σ, for Ethyl Acetate, Isobutyl Acetate, and Isoamyl Acetate parameter component

A (σ)

B (σ)

C (σ)

T range (K)

ethyl acetate

13.270 (0.363) 13.218 (0.640) 13.467 (0.282)

2256.206 (187.259) 2510.842 (364.408) 2792.304 (174.324)

−89.315 (10.693) −97.562 (20.607) −98.797 (9.628)

332−370

isobutyl acetate isoamyl acetate

361−404 365−432

3. RESULTS AND DISCUSSION 3.1. Vapor Pressure Data Regression. To test the performance of the equilibrium apparatus and to verify the reproducibility of the experiments, a portion of the vapor pressure curve for the pure components was measured, and the experimental results are presented in Table 3. A nonlinear data Table 3. Experimental Values of Vapor Pressure P at Temperature T, for Ethyl Acetate, Isobutyl Acetate and Isoamyl Acetatea ethyl acetate

isobutyl acetate

isoamyl acetate

P/kPa

T/K

P/kPa

T/K

P/kPa

T/K

54.99 59.98 70.00 75.00 80.00 84.99 89.91 95.01 101.33 104.99 109.98 119.90 124.98 129.93 134.95 139.96 149.95 154.97 159.96 164.99 174.99 180.00 185.00

332.82 335.16 339.42 340.92 343.18 344.93 346.58 348.20 350.16 351.26 352.67 355.36 356.62 357.86 359.08 360.24 362.48 363.56 364.60 365.64 367.61 368.58 369.50

39.99 49.98 59.99 70.00 80.00 90.00 100.00 110.00 120.00 130.00 140.00 150.00

361.00 367.41 372.89 377.39 381.58 385.54 389.37 392.35 395.26 398.16 400.84 403.64

20.00 29.98 40.01 49.99 60.00 70.00 80.01 90.00 100.01 110.00 119.99 130.00 139.99 149.99 160.01

365.29 376.06 384.31 391.07 396.76 401.72 406.18 410.24 413.90 417.15 420.43 423.46 426.33 429.05 431.61

Figure 1. Vapor pressure temperature dependence for pure esters. ○, experimental data; ■, reported data for EtAc;25 ▲, reported data for iBuAc;26 ●, reported data for iAmAc.27

contrasted with obtained and reported experimental data.25−27 As observed, there is good agreement of the measured data with previous reports, and the Antoine equation fits well with the obtained measurements. The standard deviations of the fitted equations with respect to reports in the literature are 0.355, 0.379, and 0.378 kPa for ethyl acetate, isobutyl acetate, and isoamyl acetate, respectively. 3.2. Experimental Activity Coefficients: Uncertainty and Consistency. The activity coefficient can be calculated from the general equilibrium relation:28 ⎡ 1 yi ϕiP = xiγipisat ϕisat exp⎢ ⎣ RT

⎤ l ⎥ v d p i sat ⎦ i

∫p

p

(2)

Here the Poynting correction can be considered as the unity, because this term is important only at high pressures.28 Furthermore, the low pressures used in this work (50, 100, and 150 kPa) and the similar physicochemical nature of the substances employed (the acetates family), also allow the consideration of the vapor phase as an ideal gas. With these assumptions and using the experimental equilibrium data, the activity coefficient can be calculated as follows:

a

Standard uncertainties u are u(T) = 0.01 K, u(P) = 0.14 kPa for all components.

regression of an Antoine-type equation (see eq 1) was performed by using the “nlinfit” function included in MATLAB R2015a. The results for the regressed parameters and their standard deviation are listed in Table 4 for each component. B ln(psat /kPa) = A − (1) T /K + C

γi =

In Figure 1, vapor pressure predictions calculated with regressed Antoine equation using the parameters in Table 4, are

yP i xipisat

(3)

The experimental uncertainty propagation in the calculation of activity coefficient can be derived from the application of eq 4. C



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Table 5. Experimental Vapor−Liquid Equilibrium Data for the System of Ethyl Acetate (EtAc) + Isobutyl Acetate (iBuAc) at 50 kPaa xEtAc

yEtAc

T/K

0.000 0.061 0.256 0.374 0.459 0.526 0.604 0.630 0.712 0.833 0.949 1.000

0.000 0.192 0.558 0.698 0.773 0.815 0.864 0.873 0.913 0.955 0.987 1.000

367.51 363.08 351.87 346.72 343.46 341.49 338.84 338.22 336.20 333.44 331.06 330.41

γEtAc 1.030 1.015 1.032 1.042 1.027 1.043 1.033 1.030 1.021 1.014 1.000

γiBuAc

ΔγEtAc

ΔγiBuAc

αEtAc

Di (%)

0.995 1.000 1.048 1.043 1.037 1.048 1.032 1.060 1.019 1.028 1.084

0.177 0.044 0.031 0.026 0.023 0.021 0.020 0.018 0.016 0.015

0.016 0.028 0.038 0.050 0.061 0.080 0.088 0.122 0.236 0.860

3.658 3.669 3.869 4.014 3.970 4.165 4.037 4.245 4.255 4.080

2.004 2.525 2.807 2.951 3.159 3.165 3.241 3.394 3.485 3.027

Given are the temperature T, liquid-phase mole fraction x, vapor-phase mole fraction y, calculated results for activity coefficient γ, uncertainty Δγ, relative volatility α, and the consistency parameter Di. Standard uncertainties u are u(T) = 0.01 K, u(P) = 0.14 kPa, and u(x) = u(y) = 0.01. a


yEtAc

T/K

0.000 0.058 0.152 0.260 0.379 0.465 0.549 0.606 0.637 0.708 0.829 0.941 1.000

0.000 0.170 0.374 0.542 0.681 0.757 0.821 0.853 0.866 0.904 0.950 0.985 1.000

389.37 384.96 378.93 372.80 367.40 364.03 360.78 359.32 358.28 356.36 353.11 350.69 349.70

γEtAc 1.043 1.026 1.029 1.035 1.036 1.050 1.034 1.031 1.029 1.025 1.013 1.000

γiBuAc

ΔγEtAc

ΔγiBuAc

αEtAc

Di (%)

0.992 0.997 1.007 1.030 1.026 1.021 1.002 0.993 1.021 0.977 0.983 0.939

0.190 0.086 0.073 0.044 0.031 0.026 0.023 0.020 0.018 0.016 0.015

0.016 0.024 0.012 0.026 0.036 0.046 0.060 0.081 0.107 0.205 0.646

3.327 3.333 3.368 3.498 3.584 3.768 3.773 3.683 3.884 3.919 4.117

2.077 2.302 2.493 2.779 2.957 2.997 3.223 3.223 3.367 3.328 3.184

Given are the temperature T, liquid-phase mole fraction x, vapor-phase mole fraction y, calculated results for activity coefficient γ, uncertainty Δγ, relative volatility α, and the consistency parameter Di. Standard uncertainties u are u(T) = 0.01 K, u(P) = 0.14 kPa and u(x) = u(y) = 0.01. a


yEtAc

T/K

γEtAc

0.000 0.053 0.148 0.312 0.461 0.554 0.599 0.631 0.700 0.817 0.929 1.000

0.000 0.149 0.354 0.603 0.743 0.808 0.838 0.854 0.892 0.943 0.980 1.000

403.64 399.57 393.26 383.99 377.44 374.17 372.52 371.75 369.77 366.19 363.89 362.48

1.047 1.036 1.058 1.050 1.039 1.044 1.032 1.028 1.033 1.011 1.000

γiBuAc

ΔγEtAc

ΔγiBuAc

αEtAc

Di (%)

0.996 1.000 1.007 1.009 1.023 1.027 1.018 1.023 0.995 0.973 0.954

0.210 0.076 0.038 0.027 0.023 0.021 0.020 0.019 0.017 0.015

0.016 0.020 0.029 0.044 0.058 0.068 0.075 0.098 0.179 0.496

3.128 3.155 3.349 3.380 3.388 3.463 3.421 3.540 3.706 3.745

2.001 2.239 2.525 2.790 2.986 2.998 3.141 3.282 3.083 3.334

a Given are the temperature T, liquid-phase mole fraction x, vapor-phase mole fraction y, calculated results for activity coefficient γ, uncertainty Δγ, relative volatility α, and the consistency parameter Di. Standard uncertainties u are u(T) = 0.01 K, u(P) = 0.14 kPa and u(x) = u(y) = 0.01.

(Δf )2 =

∑ i

∂f (Δzi)2 ∂zi

(Δγi)2 =

(4)

This equation allows the calculation of the combined uncertainty in the function f that depends on the variables z.29,30 The substitution of γ from eq 3 into eq 4 results in eq 5.

yP yi P i 2 2 x ( Δ ) + (ΔP)2 i sat (Δyi ) − xipisat xipi xi2pisat −

D

yP d ln(pisat ) i xipisat

dT

(ΔT )2 (5) DOI: 10.1021/acs.jced.6b00221 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Table 8. Experimental Vapor−Liquid Equilibrium Data for the System Isobutyl Acetate (iBuAc) + Isoamyl Acetate (iAmAc) at 100 kPaa xiBuAc

yiBuAc

T/K

0 0.045 0.194 0.264 0.290 0.371 0.428 0.474 0.571 0.642 0.695 0.806 1

0 0.085 0.339 0.435 0.466 0.560 0.624 0.664 0.747 0.799 0.836 0.902 1

413.99 412.52 407.37 405.05 404.44 401.97 400.40 399.33 397.13 395.47 394.16 392.31 388.93

γiBuAc 0.999 1.049 1.056 1.044 1.049 1.057 1.045 1.037 1.035 1.038 1.018 1.005

γiAmAc

ΔγiBuAc

ΔγiAmAc

αiBuAc

Di (%)

0.997 0.996 0.989 0.991 0.990 0.991 0.976 0.981 0.971 0.975 0.974 0.968

0.252 0.062 0.047 0.042 0.034 0.030 0.027 0.023 0.021 0.019 0.017

0.015 0.019 0.022 0.023 0.027 0.031 0.034 0.045 0.055 0.067 0.111

1.980 2.126 2.152 2.135 2.159 2.221 2.193 2.215 2.212 2.232 2.219

3.622 2.198 2.061 2.215 2.119 2.123 2.216 2.343 2.285 2.144 2.433


Table 9. Experimental Vapor−Liquid Equilibrium Data for the System Isobutyl Acetate (iBuAc) + Isoamyl Acetate (iAmAc) at 150 kPaa xiBuAc

yiBuAc

T/K

γiBuAc

γiAmAc

ΔγiBuAc

ΔγiAmAc

αiBuAc

Di (%)

0.087 0.179 0.272 0.355 0.410 0.449 0.522 0.569 0.635 0.688 0.746 0.801 0.846 1

0.158 0.305 0.430 0.534 0.595 0.631 0.690 0.732 0.784 0.820 0.860 0.894 0.921 1

426.36 423.25 420.38 417.62 416.17 415.28 413.34 412.06 410.60 409.17 407.88 406.84 405.82 403.22

1.021 1.033 1.030 1.047 1.046 1.036 1.024 1.029 1.024 1.027 1.026 1.022 1.023 1.007

0.988 0.984 0.982 0.977 0.967 0.966 0.987 0.983 0.976 0.988 0.985 0.974 0.968

0.133 0.067 0.045 0.035 0.031 0.028 0.025 0.023 0.021 0.019 0.018 0.017 0.016

0.016 0.018 0.022 0.026 0.029 0.031 0.038 0.043 0.052 0.063 0.080 0.104 0.138

1.959 2.007 2.022 2.081 2.110 2.098 2.043 2.069 2.081 2.073 2.085 2.107 2.130

4.136 2.792 2.658 2.311 2.394 2.542 2.493 2.386 2.494 2.247 2.192 2.214 1.987


This equation provides a way to calculate the combined uncertainty for the activity coefficient of component i. The uncertainties of the independent variables (x, y, T, and P) were established as follows: for the mole fraction, the uncertainty was considered as the error associated with the chromatography (Δx = Δy = 0.01); for the temperature and pressure, the uncertainty was assumed as the maximum allowable variation in the equilibrium conditions (ΔT = 0.01 K; ΔP = 0.01 kPa). The results of application of eqs 3 and 5 for the EtAc + iBuAc system are listed in Tables 5, 6, and 7, and in Tables 8 and 9 for the system iBuAc + iAmAc. In both systems, the activity coefficient of the lighter component is nearly constant and very close to unity. The activity coefficient for the second component presents a greater variation; however, taking into account the uncertainties, it can also be considered nearly constant. This behavior is characteristic of ideal solutions and to verify it, the relative volatility for the lighter component was calculated according to eq 6 and listed within Tables 5−9. As observed, for all practical purposes, the obtained relative volatility values are nearly constant.

αi =

(yi /xi) (1 − yi )/(1 − xi)

(6)

With regard to the calculated uncertainties, and as expected, the maximum values occurred at low concentrations (mole fraction less than 0.1). This behavior is a direct consequence of the dependency on the mole fraction of the activity coefficient in eq 3. The relative uncertainties in the activity coefficients (Δγi/γi) in the diluted region are greater than 0.5 (50%), making it difficult to estimate the activity coefficient at infinite dilution. The thermodynamic consistency of experimental data was evaluated by using the Wisniak point method.31,32 This method was selected considering the nearly ideal behavior of the systems under study. In the Wisniak method, consistency is expressed by eq 7 and the practical criteria is provided by the variable Di in eq 8. The test is approved when values of Di are less than 5%. Li = E

1 Δs

∑ xiΔsi ,vapTisat − T = i

gE RTw − = Wi Δs Δs

(7)


Journal of Chemical & Engineering Data Di = 100

|Li − Wi | ≤5 Li + Wi

Article

⎛ bi , j ⎞ τi , j = exp⎜ai , j + ⎟ T⎠ ⎝

(8)

The different terms in eq 7 are calculated as follows: eq 9 provides the relation between activity coefficients and the excess Gibbs free energy, and eq 10 is the entropy of vaporization for the i component. Equations 11 and 12 are convenient grouping variables. gE = RT

∑ xi ln(γi) i

Δsi ,vap =

Δs =

The evaluated objective function (maximum likelihood function) was based upon the summation of differences between all measured and predicted variables.39 The convergence algorithm used was the Britt−Luecke40 with a tolerance of 1 × 10−8. Tables 10 and 11 present the regressed parameters for the pressure ranges analyzed, with their corresponding standard deviation.

(9)

Table 10. Regressed NRTL and UNIQUAC Parameters in the Range of Pressure of 50 to 150 kPa for the System Ethyl Acetate (1) + Isobutyl Acetate (2)

Δhi ,vap Tisat

∑ xiΔsi,vap i

⎛y⎞ w = ∑ xi ln⎜ i ⎟ ⎝ xi ⎠ i

(10)

(11)

UNIQUAC

NRTL

−0.5287 (0.0775) 0.3784 (0.0493)

1.1970 (0.1292) −0.7812(0.0723) 0.30 0.028 0.007 0.013

0.027 0.007 0.013

Table 11. Regressed NRTL and UNIQUAC Parameters in the Range of Pressures of 100 to 150 kPa for the System Isobutyl Acetate (3) + Isoamyl Acetate (4) parameter

UNIQUAC

NRTL

a3,4 (σ) a4,3 (σ) α3,4= α4,3 ΔTmax (K) Δxmax Δymax

−0.8535 (0.0591) 0.4931 (0.0295)

1.5528 (0.0989) −1.0075 (0.0443) 0.3 0.021 0.006 0.006

0.029 0.008 0.006

Figures 2 and 3 present the T−x−y diagrams obtained for the systems under study. From these figures, it is possible to observe the good agreement between the experimental data and the regressed models. A contrast with the predictions of the UNIFAC-DMD model41−43 was also included in the figures. These predictions correspond very well with the experimental data. This result might indicate that, in absence of experimental

Figure 2. T−x−y diagram for the system isobutyl acetate (iBuAc) + ethyl acetate (EtAc) at the pressures under study (●, 50 kPa, ▲, 100 kPa, ■, 150 kPa, , fitted with NRTL, ---, calculated with UNIFACDMD).

bi , j T

parameter a1,2 (σ) a2,1 (σ) α1,2= α2,1 ΔTmax (K) Δxmax Δymax

(12)

According to Wisniak,31 the values of Di are more realistic when data of the heat of vaporization from calorimetric experiments are available. However, except for the ethyl acetate for which there is a considerable amount of data,33,34 there is little available for the other two acetates at the experimental conditions under study. For the isoamyl acetate there is only one data point reported at 416.73 K,35 and for isobutyl acetate there are only two available data points at 389.13 and 388.6 K.35,36 Taking into account the aforementioned, it is clear that it was not possible to obtain Di using data from literature reports only. For this reason, the heat of vaporization (Δhi,vap) used in the calculations was obtained from the Clausius− Clapeyron equation28 using the Antoine correlation (eq 1) with the adjusted parameters of Table 4. In this case, the use of the Clausius−Clapeyron equation was considered a good approximation to estimate the enthalpy of vaporization. Otherwise, interpolation and extrapolation procedures that introduce additional uncertainties would be required. The values of the variable Di in eq 8 are listed in Tables 5, 6 and 7 for the EtAc + iBuAc system, and in the Tables 8 and 9 for the iBuAc + iAmAc system. As observed, and according with criterion of eq 8, all reported experimental points fulfill with the Wisniak’s test. 3.3. NRTL and UNIQUAC Parameters Regression. Parameters for the NRTL37 and UNIQUAC38 activity-based models were adjusted by using Aspen Plus V.8.6 regression tool. Taking into account that the systems under study offer small deviations from ideality it is suitable consider parameters independent of temperature. The parameters were modeled with the default equations in the simulator. For the NRTL model, the relation is provided for the eq 13, and for the UNIQUAC model, the correlation is described with eq 14. In both cases bi,j = 0. The choice of these activity models is based on the need to unify information for the design of processes for the direct esterification of fusel oil because the available information is fitted with NRTL and UNIQUAC models.16 τi , j = ai , j +

(14)

(13) F



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Therefore, in this aspect, the predictions of all models are considered good. However, in the predictions of the temperature, there are a significant differences between NRTL (μy ≈ 0.02 K) and the other models (μy > 0.50 K). Thus, taking into count the two aspects (temperature and vapor-phase mole fraction), the best correlation is obtained using the NRTL model. 3.3.2. For the Isobutyl Acetate (iBuAc) + Isoamyl Acetate (iAmAc) System. The predictions of the vapor-phase molar fraction calculated with the NRTL (μy ≈ 0.004) and UNIQUAC (μy ≈ 0.003) models are very similar to each other and are different of the predictions calculated with UNIFAC-DMD and Ideal models (μy ≈ 0.009). Therefore, in this aspect, the NRTL and UNIQUAC models are preferred. On the other side, in the predictions of the temperature, there are significant differences between NRTL (μT ≈ 0.05 K) and the other models (μT > 0.40 K). Thus, taking into count the two aspects (temperature and vapor-phase mole fraction), the best correlation is obtained using the NRTL model. For a comparison on the same basis of all the experimental data, Figure 4was prepared to show the vapor−liquid

Figure 3. T−x−y diagram for the system isobutyl acetate (iBuAc) + isoamyl acetate (iAmAc) at the pressures under study (■, 100 kPa, ●, 150 kPa, , fitted with NRTL, ---, calculated with UNIFAC-DMD).

data, phase equilibrium in mixtures of acetates formed in the direct esterification of the fusel oil, can be confidently predicted with UNIFAC-DMD model. The predicted curves using the UNIQUAC equation model were not included in Figures 2 and 3 because it is not possible distinguish these from those generated with the NRTL model. This implies that in a practical sense, for the systems under consideration, both models offer the same prediction capacity. According to the results, the regressed models can be confidently integrated in a more complex thermodynamic model to study the direct esterification of the fusel oil. To exemplify which model presents the best predictions, the bubble points (temperature and vapor-phase mole fraction) for all experimental data were calculated with four models (NRTL, UNIQUAC, UNIFAC-DMD, and Ideal), the results were compared using the metrics of the average error and the standard deviation in relation to the experimental vapor-phase mole fraction and temperature. A summary of these calculations is presented in Table 12. According to the results in Table 12, the following statements can be established: 3.3.1. For the Ethyl Acetate (EtAc) + Isobutyl Acetate (iBuAc) System. The predictions of the vapor-phase molar fraction with the four models (NRTL, UNIQUAC, UNIFACDMD, and Ideal) result in an average error of μy ≈ 0.002.

Figure 4. Vapor−liquid equilibrium ratio temperature dependence for the most volatile compound in the systems isobutyl acetate (iBuAc) + isoamyl acetate (iAmAc) and ethyl acetate (EtAc) + isobutyl acetate (iBuAc). ■, EtAc at 50 kPa; ●, EtAc at 100 kPa; ○, EtAc at 150 kPa; ◀, iBuAc at 100 kPa; □, iBuAc at 150 kPa; ---, calculated with UNIFAC-DMD model; ···, calculated with Ideal model.

equilibrium ratio (also clled the K-value and defined as the ratio yi/xi) as a function of the inverse of temperature. The main advantages of this representation are (a) it is possible to visualize all data in the same plane, and (b) a system is approximately ideal if in this plane (logarithm of K against the inverse of temperature) the equilibrium curve is a straight line. The inherent disadvantage is the associated uncertainty with the calculation of the K-value. Figure 4 shows that the experimental data can be considered approximately linear and can be predicted reasonably with the UNIFAC-DMD model or even the Ideal model.

Table 12. Average Errors (μy and μT) and Standard Deviations of the Error (σy and σT) in the Vapor-Phase Mole Fraction and in the Bubble Point Temperature for the Predictions with NRTL, UNIQUAC, UNIFAC-DMD, and Ideal Models, for the Systems Isobutyl Acetate (iBuAc) + Isoamyl Acetate (iAmAc) and Ethyl Acetate (EtAc) + Isobutyl Acetate EtAc + iBuAc model NRTL UNIQUAC UNIFAC-DMD Ideal

iBuAc + iAmAc

μy (σy)

μT (σT)

μy (σy)

μT (σT)

0.0018 (0.0066) 0.0019 (0.0063) −0.0016 (0.0036) −0.0024 (0.0035)

−0.0164 (0.1776) 0.5010 (0.3820) 0.5010 (0.3820) 0.6772 (0.4782)

−0.0042 (0.0034) −0.0032 (0.0037) −0.0091 (0.0062) −0.0092 (0.0062)

0.0473 (0.2082) 0.4283 (0.3222) 0.4283 (0.3222) 0.4441 (0.3268)

4. CONCLUSION Isobaric vapor liquid equilibria of isoamyl acetate + isobutyl acetate at two different pressures (100 and 150 kPa) and ethyl acetate + isobutyl acetate at three different pressures (50, 100, and 150 kPa) have been studied. Vapor pressure of ethyl acetate, isobutyl acetate, and isoamyl acetate were measured within the temperature range of equilibrium experiments to G



Article

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verify the reliability of the equilibrium apparatus, and obtained data were correlated with an Antoine-type equation. After verifying the reliability of the equipment, isobaric equilibrium experiments were carried out. Obtained VLE data were successfully regressed using the NRTL and UNIQUAC models, obtaining good agreement with experimental observations. Generated binary parameters for NRTL and UNIQUAC equations can be integrated in a more complex thermodynamic model to study the direct esterification of the fusel oil. Results also indicate that missing equilibrium data for mixtures of other fusel oil acetates could be reasonably predicted with the UNIFAC-DMD model or even the Ideal model.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +5713165000 ext 14100. Funding

This work has been supported by Colciencias, Ecopetrol S.A. and Universidad Nacional de Colombia (Project No. 201010023545-DIB 2015 and Project No. 1101-490-26038). Notes

The authors declare no competing financial interest.

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