Measurements by using an automatic pressure control and predictions of isobaric VLE at 1.5 MPa for binary mixtures of methyl acetate, ethyl acetate, 1–propanol and 1–butanol

Chemical Engineering Research and Design 1 5 2 ( 2 0 1 9 ) 242–253

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Measurements by using an automatic pressure control and predictions of isobaric VLE at 1.5 MPa for binary mixtures of methyl acetate, ethyl acetate, 1–propanol and 1–butanol Pedro Susial ∗ , Diego García Vera, Isabel Montesdeoca, Rodrigo Susial, Silvia Díaz Stevenson, Nayra Pulido Melián Escuela de Ingenierías Industriales y Civiles, Universidad de Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Canary Islands, 35017, Spain

a r t i c l e

i n f o

a b s t r a c t

Article history:

The experimental data of vapor–liquid equilibrium for the binary systems methyl

Received 22 February 2019

acetate + 1–propanol, methyl acetate + 1–butanol and ethyl acetate + 1–propanol at 1.5 MPa

Received in revised form 18

has been obtained, using an ebulliometer made of stainless steel. This equipment works

September 2019

through the Cottrell pump effect, so that the liquid and vapor phases are recirculated.

Accepted 29 September 2019

The isobaric data T–x–y are informed and analyzed with respect to the literature data.

Available online 9 October 2019

The evolution of the azeotropic point with the pressure in the binary system of ethyl

Keywords:

fied by employing the Peng–Robinson equation of state in different forms and using the ϕ–ϕ

VLE isobaric data

approach.

acetate + 1–propanol is included. The thermodynamic consistency of the systems was veri-

Methyl acetate

© 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Ethyl acetate 1–propanol 1–butanol

1.

Introduction

The separation operations of the substances in the different mixtures, which are based on the mass transfer process, are developed when the immiscible phases are in contact. The compositions under the condi-

tal data are essential to develop more robust models (Casimiro et al., 2015) as well as to verify the actual models. On the other hand, some types of mixtures present an azeotrope. This means that the mixture cannot be separated into its pure compounds, so the composition is the same for the liquid and vapor phases

tions of phase equilibrium are function of different properties such as

at constant pressure and temperature. Rectification at different pres-

pressure, temperature and chemical characteristics of the substances. These represent the maximum distribution for constant operating con-

sures is one of the techniques that can be used to separate these type of mixtures. This procedure allows to verify the presence of azeotropes,

ditions of pressure and temperature.

as well as the evolution and behaviour of these when modifying the pressure. Taking into account the above, and as a continuation of previous works (Susial et al., 2012a, a; Susial et al., 2013b, 2014; Susial

The knowledge of the experimental data of the equilibrium between phases is essential to size the unit operations of mass transfer. However, when there are no experimental data available to design and optimize the separation processes, the fundamental information is that which can be obtained by using the interaction parameters of the different models. In addition, the phenomena of association and solvation can be found in the different mixtures, and that is why the experimen-

et al., 2018), the vapor–liquid equilibrium (VLE) of mixtures of esters and alcohol have been determined. In this work, experimental data of VLE at 1.5 MPa are determined for the binary systems: methyl acetate + 1–propanol (MA1P), methyl acetate + 1–butanol (MA1B) and ethyl acetate + 1–propanol (EA1P). The MA1P system has been previously studied at isothermal conditions (Nagata et al., 1976) and in isobaric conditions by Ortega et al.

∗

Corresponding author. (1990) at 101.32 kPa and at 114.66 kPa and 127.99 kPa by Ortega and E-mail address: [email protected] (P. Susial). https://doi.org/10.1016/j.cherd.2019.09.044 0263-8762/© 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Chemical Engineering Research and Design 1 5 2 ( 2 0 1 9 ) 242–253

Susial (1990). In addition, isobarically by Patlasov et al. (see Gmehling et al., 1988) at 101.3 kPa and recently at 0.3 MPa (Susial et al., 2013b) as well as at 0.6 MPa (Susial et al., 2013a). The MA1B system has also been analyzed under isobaric conditions by Susial and Ortega (1995) at 74.66 kPa and 127.99 kPa, while at 101.32 kPa it has been studied by Ortega and Susial (1995) and Patlasov et al. (1977). It has recently been reported at 0.3 MPa by Susial et al. (2013b) and at 0.6 MPa by Susial et al. (2018). On the other hand, EA1P has been studied in isothermal conditions by Nagata et al. (1975), Takamatsu and Ohe (see Gmehling and Onken, 2007) and by Murty et al. (see Gmehling and Onken, 1986). It has also been reported under isobaric conditions by Murty et al. (see Gmehling and Onken, 1986) and Ortega et al. (1986) at 101.3 kPa and more recently at 0.3 MPa by Susial et al. (2012a) and at 0.6 MPa by Susial et al. (2013a). In this paper, the experimental data are verified by applying the ϕ–ϕ approach. The Peng–Robinson (PR) (Peng and Robinson, 1976) and Peng–Robinson–Stryjek–Vera (PRSV) (Stryjek and Vera, 1986) equations of state (EOS) were applied using both quadratic mixing rules, and Wong–Sandler (WS) mixing rules (Wong and Sandler, 1992).

2.

Experimental section

2.1.

Materials and apparatus

Normal boiling point (Tbp ), density (ii ) and refractive index (nD ) at 298.15 K were determined for methyl acetate and ethyl acetate, both from Sigma–Aldrich, with a purity of 99.5%. The same properties were measured for 1–propanol and 1–butanol, both from Panreac Química SLU, with a purity of 99.8% and 99.9%, respectively. The results of these physical properties are not different from previous papers (Susial et al., 2012b, a; Susial et al., 2014 and Susial et al., 2015). The products were used without additional purification treatments. A Mettler Toledo DM40 vibrating tube densimeter with an uncertainty of ±0.1 kg m−3 was used, after calibrating it at 298.15 K using air and distilled water as references, to determine the densities of mixtures and pure compounds, and therefore in the obtaining the VLE data. Furthermore, to determine the refractive index of pure substances, an Atago Co. LTD RX–7000␣ refractometer with an uncertainty of ±0.0001 was used, after calibrating it at 298.15 K using distilled water as reference.

2.2.

VLE equipment

An ebulliometer was used to determine the experimental data of the VLE. This equipment, some of its characteristics have been described in previous works (Susial et al., 2010, 2011; Susial et al., 2013b), was included in an experimental installation (Fig. 1). The equilibrium still [1] was built in stainless steel of 2 mm thick. Its design allows the dynamic recirculation of both liquid and vapor phases as it works under the Cottrell pump effect. To generate this effect, a double-walled inverted vessel with 76 mm (external diameter) and 63 mm (internal diameter) was used. The ebulliometer was built to operate in co-current flow since the equilibrium condition depends on the contact time between the immiscible phases, so this mass transfer process is not just a function of temperature and pressure but also of the residence time. As a result, the statistical value of these properties cannot be taken as an equilibrium criteria, since both temperature and pressure are affected by the Cottrell pump behaviour. The constancy of the composition of both phases must also be verified.

243

The input/output flows of both phases were evaluated with different mixtures and under different operating conditions as in previous works (Susial et al., 2010, 2012a; Susial et al., 2012b). In this paper the residence time of the mixture was also previously evaluated. For this, the equipment was loaded with a 600 mL MA1B mixture of composition x1 = 0.498, the pressure was established at 1.5 MPa by introducing N2 and the electric resistances [4] and [5] were switched on. Every so often a portion of the phases was sampled, and subsequently refills were made in the equipment using the MA1B mixture, whose composition was the same as that of the initial load. The analysis of the compositions as a function of time is summarized as follows: 1.– t = 40 min, x1 = 0.455, y1 = 0.586, Tmean = 461.36 K; 2.– t = 55 min, x1 = 0.443, y1 = 0.579, Tmean = 461.70 K; 3.– t = 70 min, x1 = 0.446, y1 = 0.575, Tmean = 462.08 K; 4.– t = 85 min, x1 = 0.446, y1 = 0.574, Tmean = 462.35 K; 5.– t = 100 min, x1 = 0.439, y1 = 0.572, Tmean = 462.01 K; 6.– t = 115 min, x1 = 0.445, y1 = 0.569, Tmean = 462.20 K; 7.– t = 130 min, x1 = 0.442, y1 = 0.568, Tmean = 462.12 K. It can be seen that after 70 min, the stable state of the compositions can be accepted when operating at temperature (462.35 K) and pressure (1.5 MPa) statistically constant. Also, when the recirculation time is more than 70 min, it is possible to obtain constant composition in each phase with a flow around 25 mL/min. Consequently, the studied mixtures in this work are recirculated under boiling conditions for 90 min to guarantee the stable state (Susial et al., 2010, 2012a). The ebulliometer is equipped with two Pt100 probes [3] from Termocal laboratory (University of Valladolid, Spain) with an uncertainty of 25 mK in the range up to 473 K and of 100 mK for temperatures above 473 K. These probes are hermetically connected to the ebulliometer, and were previously calibrated in the range from 273 K to 500 K by a thermostatic bath and verified by the measurement of distilled water boiling point. The software Dostmann Electronic is used to store and display the measured temperatures [2] in the computer [6A] during experimental work (see Fig. 2A). The experimental installation (Fig. 1) was modified to work at high pressure. A Baumer manometer [11] which operates below the atmospheric pressure (from 0.0 to 0.1 MPa absolute pressure range with an uncertainty of ±0.0005 MPa) is included, whereas in the high–pressure line a control valve IMF from Truflo International [23] (operation range from 0.6 to 2.4 MPa) and a discharge valve from Farichild Ind. Prod. Co. [24] (operation range from 0.035 to 2.8 MPa) were installed to control pressure. Another Baumer manometer [10] (Bourdon-type with a range from 0.0 to 2.5 MPa, uncertainty of ±0.02 MPa) is included in the high–pressure line, in addition to a pressure transducer with digital display from Burket Fluid Control Systems (model 8311) [8] with a range from 0.0 to 5.0 MPa (uncertainty ±0.04 MPa). Consequently, the installation has a pressure transducer from ESI Technology Ltd. Model GS4200–USB [9] (from 0.0 to 2.5 MPa pressure range, uncertainty ±0.001 MPa) whose software is used to perform the pressure control (see Fig. 2B) through a computer [6B]. Another pressure transducer from WIKA Co. [7] (from 0.0 to 4.0 MPa pressure range, uncertainty ±0.02 MPa) is used to send an analogical signal to the PLC (Programmable Logic Controller System Comex of Phywe) [25] where the internal pressure in the ebulliometer, as mA value, compares with a reference value previously assigned. After this, the algorithm of the control regulation channel can send to the control valve [29], by using the Power Interface

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Chemical Engineering Research and Design 1 5 2 ( 2 0 1 9 ) 242–253

Fig. 1 – Schematic diagram of the installation for measuring VLE at high pressure with the ebulliometer, auxiliary apparatus, automatic data monitoring and automatic control–regulation of pressure.

of Phywe [26], the appropriate analogical signal. The proportional valve [29] will open a determined range if the internal pressure in the equipment is too low, allowing the N2 supply. On the other hand, the solenoid valve [28] will discharge gas through the Fairchild Ind. Prod. Co. [24] if the internal pressure in the equipment is too high. In both cases, low or high pressure, the assigned value of reference pressure is taken into account. The control process and pressure regulation depend on the accuracy of the transducer [7] and also on the accuracy allowed by the PLC [25] once the set value (reference value) is assigned, but these limitations are not susceptible to operational actions. However, the manual regulation of the discharge with the back pressure regulator [24] can allow a reduction of the generated disturbances (see Fig. 2B) during the admission of the N2 supplied to compensate the discharges produced by the pulsations generated as a consequence of the Cottrell pump effect. These pulsations cannot be avoided, but their action can be diminished with the inclusion of the damping vessels [13]. In any case, a suitable manual control of the discharge valve [24] and the percentage of admission of the proportional electrovalve [29] can reduce the disturbances up to the range ±0.001 MPa with a small number of peaks in the range of 0.002 MPa (see Fig. 2B). Note that the variation of the equilibrium temperature (see Fig. 2A) between 461.85 and 462.85 K (values read between the perturbation points caused by the loading of the pure product) for the system MA1B operated at 1.5 MPa (mean value 462.35 K) is a consequence of the design of the ebulliometer, which works in co-current flow with continuous recirculation of both phases by the Cottrell pump effect. The mass transfer process developed in the ebulliometer shows that the experimental determination of the VLE data is a function of the residence time. Consequently, the constancy of the compositions, as previously shown, must be verified in addition to the constancy of the pressure and temperature in order to be able to confirm a sufficient stationary state approximation and hence the

thermodynamic condition of the VLE. We can see, there is an evidence in the similitude of data, when comparing the data obtained through the evaluation of residence time (x1 = 0.446, o y1 = 0.574, Tmean = 462.35 K) and the point n 16 in the determination of VLE data (x1 = 0.447, y1 = 0.576, T = 462.47 K) of MA1B system.

2.3.

Experimental procedure

The experimental process starts by cleaning up the equilibrium equipment. First, around 500 mL of ethanol are introduced into the ebulliometer and the heating resistance is switched on. At atmospheric pressure, the ethanol is recirculated for 45 min at its boiling temperature. Then, the ethanol is discharged and the vacuum pump (10 kPa barometric pressure) [12] is connected to the ebulliometer for another 45 min Later, the ebulliometer is filled with around 500 mL of acetone and the heating resistance is connected again. The process with this liquid is the same as the previously mentioned with the ethanol. After another 45 min with the vacuum pump switched on, the ebulliometer is completely closed and dry nitrogen [15] is introduced until reach around 0.15 MPa. Once the ebulliometer is clean and dry, around 0.05 MPa are discharged, thus the equilibrium still has 0.1 MPa of nitrogen inside. Then, around 500 mL of the substance (A) are introduced and the electric resistances [4] and [5] are switched on. After the atmospheric boiling point of the pure substance (A) is reached, the 1.5 MPa pressure is set by introducing nitrogen into the equilibrium area. The equipment works for around 4 h until the temperature is homogenized. After that, around 15 mL of the substance (B) are introduced. This mixture is kept under boiling conditions for about 90 min to ensure stable state. After the recirculation time, samples of liquid and condensed vapor are taken in sealed containers, where they stay up until reaching the room temperature. After that, density

Chemical Engineering Research and Design 1 5 2 ( 2 0 1 9 ) 242–253

245

Fig. 2 – Monitoring temperature (A) and pressure (B) for data point No. 16 of methyl acetate (1) +1–butanol (2) system at 1.5 MPa.

can be measured at 298.15 K. Then, another 15 mL of the substance (B) are added with the aim of modifying the mixture composition without stopping the ebulliometer proper operation. A calibration curve at 298.15 K by densimetry (Susial et al., 2013a, b) is made to determine the phase compositions for

each of the mixtures in this work. Density is calculated for different prepared mixtures by weight. The composition (xi ) vs density (ij ) values for each binary system are verified by the excess volumes. This procedure allows to determine the uncertainty for the molar fraction of the equilibrium phases, giving a result of ±0.002.

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Fig. 3 – Representation of (y1 –x1 ) vs. x1 for the methyl acetate (1) +1–propanol (2) system ( ) at 1.5 MPa. Bibliographic data at 101.32 kPa ( ) (Ortega et al., 1990), at 114.66 kPa ( ) and at 127.99 kPa ( ) (Ortega and Susial, 1990), at 0.3 MPa ( ) (Susial et al., 2013b) and at 0.6 MPa ( ) (Susial et al., 2013a) with fitting curves.

3.

Results

3.1.

VLE data

The experimental results T–x1 –y1 at 1.5 MPa are included in Table 1. The Figs. 3–5 show the isobaric data of this work when compared with literature data. The procedure to obtain the correlation curves in Figs. 3–5, was the same as in previous papers (Susial et al., 2010, 2011; Susial et al., 2014, 2018). When MA1P, MA1B and EA1P data are compared with the lower pressure data, an appropriate evolution of the data at 1.5 MPa is observed. These three systems evolve as a pressure function. On the other hand, the compressive effect of the mixture is verified, higher at higher pressure. However, with high ester compositions in EA1P system, the pressure evolution makes possible a different volumetric behaviour, so the experimental azeotrope of EA1P at 1.5 MPa is positioned as it can see in Fig. 6, in the coordinates x1az,exp = y1az,exp = 0.398; Taz,exp = 461.13 K. To determine the azeotropic point, the experimental data in Table 1 and a FORTRAN program have been used. The FORTRAN program formulates and solves a system of linear equations with a tridiagonal coefficient matrix. The same procedure as in previous papers have been applied (Susial et al., 2013a). In addition, Fig. 6 shows the evolution of the singular point regarding the pressures at which it was determined. All the azeotropic data of the EA1P system in Fig. 6 were correlated using a multiple linear regression procedure as indi-

Fig. 4 – Plot of (y1 −x1 ) vs. x1 for the methyl acetate (1) +1–butanol (2) system ( ) at 1.5 MPa and fitting curves. Bibliographic data at 74.66 kPa ( ) and at 127.99 kPa ( ) (Susial and Ortega, 1995), at 101.32 kPa ( ) (Ortega and Susial, 1995), at 0.3 MPa ( ) (Susial et al., 2013b) and at 0.6 MPa ( ) (Susial et al., 2018).

Fig. 5 – Experimental data of (y1 −x1 ) vs. x1 for the ethyl acetate (1) +1–propanol (2) system ( ) at 1.5 MPa. Bibliographic data at 101.32 kPa ( ) (Ortega et al., 1986), at 0.3 MPa ( ) (Susial et al., 2012a) and at 0.6 MPa ( ) (Susial et al., 2013a) with fitting curves.

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Table 1 – Experimental T–x1 –y1 data for the binary systems at 1.5 MPaa . T K

x1

y1

T

x1

y1

K

T

x1

y1

K

T

x1

y1

K

Methyl acetate (1) + 1–propanol (2) at 1.5 MPa 0 0 458.05 465.87 0.017 0.027 456.36 465.4 0.031 0.048 455.61 464.77 0.044 0.068 455.25 464.19 0.062 0.092 454.53 463.47 0.081 0.119 453.25 462.65 0.098 0.142 452.45 461.86 0.119 0.169 450.12 461.11 0.138 0.195 449.11 460.38 0.155 0.218 447.95 459.61 0.175 0.243 458.79

0.194 0.247 0.27 0.279 0.296 0.332 0.354 0.41 0.453 0.495

0.265 0.33 0.354 0.365 0.385 0.422 0.446 0.508 0.55 0.588

447.11 446.36 445.66 445.06 444.41 443.86 443.21 442.53 441.93 441.35

0.522 0.543 0.57 0.595 0.618 0.645 0.67 0.698 0.727 0.75

0.616 0.64 0.664 0.686 0.708 0.73 0.753 0.776 0.798 0.819

441.05 440.25 439.45 439 438.5 437.8 437.31 436.65 436.47 436.08

0.779 0.811 0.846 0.875 0.899 0.93 0.954 0.981 0.984 1

0.843 0.865 0.889 0.911 0.93 0.952 0.97 0.986 0.989 1

Methyl acetate (1) + 1-butanol (2) at 1.5 MPa 0 0 480.45 495.95 0.006 0.013 478.9 495.35 0.016 494.65 0.028 478.1 493.75 0.028 0.048 475.52 490.65 0.072 0.111 473.2 0.098 0.143 471.93 488.9 0.158 0.22 471.14 484.3 0.172 0.242 483.25

0.208 0.229 0.24 0.273 0.304 0.322 0.33

0.288 0.316 0.33 0.371 0.407 0.434 0.442

467.65 462.47 457.69 452.89 448.7 447.03 445

0.376 0.447 0.516 0.588 0.653 0.687 0.727

0.499 0.576 0.647 0.716 0.773 0.796 0.822

443.82 442.35 440.87 438.87 436.81 436.3 436.08

0.75 0.786 0.831 0.895 0.967 0.997 1

0.842 0.866 0.891 0.93 0.99 0.999 1

0.065 0.09 0.141 0.197 0.213 0.254 0.305 0.325 0.356

0.086 0.116 0.167 0.221 0.235 0.272 0.318 0.336 0.362

461.14 461.13 461.14 461.16 461.19 461.24 461.3 461.47

0.379 0.419 0.448 0.459 0.483 0.516 0.55 0.609

0.382 0.415 0.44 0.452 0.472 0.498 0.528 0.585

461.52 461.78 462.09 462.21 462.4 462.56 462.68 462.75

0.626 0.703 0.787 0.816 0.873 0.938 0.978 1

0.601 0.674 0.762 0.793 0.854 0.928 0.971 1

Ethyl acetate (1) + 1–propanol (2) at 1.5 MPa 0 0 463.83 465.87 0.009 465.39 0.011 463.27 465.28 0.013 0.016 462.54 465.24 0.014 0.018 461.89 0.02 0.024 461.76 465.11 0.028 0.033 461.52 464.92 0.029 0.035 461.29 464.88 0.035 0.05 461.23 464.64 0.041 0.057 461.17 464.46 a

Expanded uncertainties U(k = 2) are: U(T) = 0.2 K, U(P) = 0.001 MPa, U(x1 ) = U(y1 ) = 0.005.

cated in previous works (Susial et al., 2012a). The results after the data correlation for the azeotropes of the EA1P system are 1 = 0.9965 − 0.3178 (Log10 Pr ) Tr x1az exp = −4.7501 + 4.5664

3.2.

1 Tr

(1)

− 0.4339(Log10 Pr )2

(2)

Prediction of VLE data

At high pressure, mixtures with associative effects are difficult to model. Consequently, the prediction by using EOS is considered for vapor pressures of pure substances and for the VLE. In this work Peng–Robinson (1976)equation of state with quadratic mixing rules and with Wong–Sandler (1992) mixing rules are used. The PR–EOS with the attractive parameter of Stryjek–Vera (1986) is also used. The PR–EOS equation takes the expression: Fig. 6 – Plot of azeotropic data at 1.5 MPa ( ) of this work. Bibliographic data at 0.3 MPa ( ) (Susial et al., 2012a) and 0.6 MPa ( ) (Susial et al., 2013a) for the ethyl acetate (1) +1–propanol (2) system. The fitting curves represent the Eqs. (1) and (2). Bidimensional representation of data ( ) and fitting curves are with black color.

P=

a(T) RT − v−b v(v + b) + b(v − b)

(3)

Where the attractive parameter a(T) is a function of temperature by:





a(T) = 1 +  1 − Tr0.5

2

(4)

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Where  is a function of acentric factor (ω) as:



 = 0.37464 + 1.5422ω − 0.26992ω2



(5)

When Stryjek–Vera (1986)equation is used, the PRSV–EOS gives , for Eq. (4), from the expression:  = 0.378893 + 1.4897153ω − 0.17131848ω2 + 0.0196554ω3





+ 1 1 + Tr0.5 (0.7 − Tr )

(6)

Where 1 is an adjustable parameter of each substance that is obtained when vapor pressures correlate to the model. In both PR–EOS and PRSV–EOS the classical mixing rules can be used with the binary parameters k1ij , k2ij , which are determined when experimental data of each system have been correlated. Nevertheless, Wong and Sandler (1992) mixing rules can be used when it refers to non-ideal mixtures. In the WS mixing rules, the excess free energy of Helmholtz can be represented by a low pressure model for excess Gibbs energy. In this paper, the NTRL model (Renon and Prausnitz, 1968) is used. So, the expressions for PRWS–EOS and PRSVWS–EOS are: N 

AE∞ RT

=

N  i

xi

OF =

xj Gji ji

j N 

1986) were applied. The a(T) parameter in Eq. (4), is considered as a function of the temperature in the PR–EOS (Peng and Robinson, 1976) as well as its modification when using PRSV–EOS (Peng and Robinson, 1976; Stryjek and Vera, 1986). In both cases the results for (k1ij , k2ij ) were determined by quadratic mixing rules. Otherwise, when WS mixing rules (Wong–Sandler, 1992) were applied, the parameters (kij ,  ij ,  ji ) were obtained by the PRWS–EOS and PRSVWS–EOS predictive models. The parameters for predictive models were calculated by applying the FORTRAN program mentioned above. This program allows to avoid unnecessary loops since it considers its own FORTRAN functions and subroutines, instead of using the internal Matlab functions as fsolve or fminsearch that generate large time of computer use. The FORTRAN program keeps the aim of the Martín et al. (2011) program but with a significant increase in processing speed. A bubble point P–x1 scheme was applied to perform the data predictions for MA1P, MA1B and EA1P systems at 1.5 MPa. To carry out the minimization, we use the simplex method (Nelder and Mead, 1965) with the objective function (OF) given by the equation:

with

Gij RT



= exp −˛ij ij



1  exp 1  exp T − T calc + y1 − ycalc 1 U (T) U (y1 ) n

n

1

1

(8)

(7)

xi Gri

r

Where ˛ij =˛ji as well as  ij and  ji are adjustable parameters for consistency between experimental data of VLE and those calculated by the models. In this paper, the parameter ˛ij =˛ji was fixed in 0.47 as informed by Renon and Prausnitz (1968). The acentric factor of each substance was determined since PR–EOS, PRWS–EOS, PRVS–EOS and PRSVWS–EOS are extremely dependent of it. Therefore, vapor pressures from literature (Susial et al., 2011, 2012b; Susial et al., 2014, 2015) were used with Daubert and Danner (1989) critical properties. The Nelder and Mead (1965) method was used to correlate experimental vapor pressure data. Standard deviations of vapor pressures [SD(pi 0 )] are employed as a correlation quality parameter; the results are presented in Table 2. Daubert and Danner (1989) acentric factors were used as reference, so the relative errors are obtained were: 1.1%, 0.2%, 1.3% and 1.0% for methyl acetate, ethyl acetate, 1–propanol and 1–butanol, respectively (see Table 2). On the other hand, vapor pressures from literature (Susial et al., 2011, 2012b; Susial et al., 2014, 2015) and the acentric factor previously obtained, were used to determine the Stryjek and Vera (1986) adjustable parameter 1. The Daubert and Danner (1989) critical properties were used and the standard deviation of vapor pressure [SD(pi 0 )], was a statistical parameter used to verify the regression to obtaining the parameter. FORTRAN program was developed from the Matlab program of Martín et al. (2011). The results for methyl acetate, ethyl acetate, 1–propanol and 1–butanol are compared with the Proust and Vera (1989) and Stryjek and Vera (1986) data (see Table 2). The binary parameters for the systems MA1P, MA1B and EA1P of this work were obtained by using the Daubert and Danner (1989) properties as well as the ω and 1 parameters previously calculated when PR–EOS (Peng and Robinson, 1976) and PRSV–EOS (Peng and Robinson, 1976; Stryjek and Vera,

Fig. 7 – Representation of (y1 –x1 ) vs. x1 of methyl acetate (1) +1–propanol (2) (MA1P) ( ), methyl acetate (1) +1–butanol (2) (MA1B) ( ) and ethyl acetate (1) +1–propanol (2) (EA1P) ( ) binary systems at 1.5 MPa and fitting curves of data modeling results of MA1P, MA1B and AE1P respectively for: ), ( ) and ( )] (Peng and PR–EOS [( ), ( ) and ( Robinson, 1976); PRWS–EOS [( )] (Peng and Robinson, 1976; Wong and Sandler, 1992); PRSV–EOS [( ), ( ) and ( )] (Peng and Robinson, 1976; Stryjek and Vera, 1986) and PRSVWS–EOS [( ), ( ) and ( )] (Peng and Robinson, 1976; Stryjek and Vera, 1986; Wong and Sandler, 1992).

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Table 2 – The acentric factor and the Stryjek–Vera parameter of pure compounds results. Substance/Parameters

ωa

SD(pi 0 /kPa)

ωb

ωc

1a

SD(pi 0 /kPa)

1c

1d

Methyl acetate Ethyl acetate 1–propanol 1–butanol

0.3289 0.3619 0.6195 0.6004

0.4 0.7 0.4 0.3

0.3253 0.3611 0.6279 0.5945

0.32027 0.36061 – –

0.0278 0.0686 0.2837 0.4938

3.3 7.3 7.4 4.3

0.05791 0.06464 – –

– – 0.21419 0.33431

a b c d

This work. Daubert and Danner (1989). Proust and Vera (1989). Stryjek and Vera (1986).

Table 3 – Mean absolute deviation and standard deviation results for the VLE data predictions and the parameters obtained with different EOS and objective function. PRa k1

PRSVa,c k2

k1

Methyl acetate (1) +1–propanol (2) at 1.5 MPa −0.0103 −0.0644 0.1205 Parameters 1021 508 OF 0.018 0.015 MAD(y1 ) 0.023 0.019 SD(y1 ) 0.37 0.12 MAD(T/K) 0.53 0.15 SD(T/K) Methyl acetate (1) +1–butanol (2) at 1.5 MPa Parameters 0.2171 0.2487 0.3183 2512 1623 OF 0.081 0.074 MAD(y1 ) 0.094 0.085 SD(y1 ) 1.20 0.56 MAD(T/K) 1.38 0.70 SD(T/K) Ethyl acetate (1) +1–propanol (2) at 1.5 MPa −0.6456 −0.9730 −0.3703 Parameters 768 3343 OF 0.015 0.009 MAD(y1 ) 0.017 0.011 SD(y1 ) 0.36 0.13 MAD(T/K) 0.54 0.18 SD(T/K)

MAD(F) =

1 n−2

n  Fexp − Fcal ;

n SD(F) =

1

PRWSa,b

PRSVWSa,b,c

k2

kij

˛

 ij

 ji

kij

˛

 ij

 ji

0.1289

−0.5059 814 0.014 0.015 0.30 0.44

0.47

1.7423

1.4322

0.1962 559 0.017 0.021 0.13 0.17

0.47

−0.6800

0.5574

0.3974

0.2392 2775 0.078 0.090 1.44 1.75

0.47

−0.5529

0.2102

0.2970 1999 0.070 0.082 0.90 1.19

0.47

−0.9755

0.3511

−0.5429

0.3652 544 0.014 0.017 0.22 0.36

0.47

−1.3265

4.0540

0.0699 163 0.007 0.009 0.04 0.06

0.47

−0.7654

1.9422

2

(Fexp −Fcal ) n−2

F ≡ y1 , T.

1 a b c

Peng and Robinson (1976). Wong and Sandler (1992). Stryjek and Vera (1986).

A similar expression as Eq. (8) is commonly used (see Casimiro et al., 2015) but employing the properties of the SD statistical parameter. However, in this paper the Eq. (8) will be used with the uncertainties U(T) and U(y1 ). This is because SD, a standard parameter, is not sufficient when a VLE data prediction is required. Therefore, by using a greater uncertainty, a better quality can be guaranteed in predictive models. Consequently, P–T–x1 –y1 data from this paper were compared with predictive models PR–EOS (Peng and Robinson, 1976), PRSV–EOS (Peng and Robinson, 1976; Stryjek and Vera, 1986), PRWS–EOS (Peng and Robinson, 1976; Wong and Sandler, 1992) and PRSVWS–EOS (Peng and Robinson, 1976; Stryjek and Vera, 1986; Wong and Sandler, 1992). Mean absolute deviation (MAD) and standard deviation (SD) from vapor composition and temperature data are represented in Table 3. Also, the cal-

culated parameters of each model are included in Table 3. In Figs. 7–10 the correlations of predictive model are represented with the experimental data from Table 1. PRSVWS–EOS (Peng and Robinson, 1976; Stryjek and Vera, 1986; Wong and Sandler, 1992) shows globally the best results for the experimental data of MA1P, MA1B and EA1P systems at 1.5 MPa, which can be seen in Table 3 and Figs. 8–10. PRSV–EOS (Peng and Robinson, 1976; Stryjek and Vera, 1986), also shows a good data reproduction (see Table 3 and Figs. 8 and 10). However, when the prediction of the vapor phase mole fraction is considered, the precision shown by the EOS in this work is deficient, as can be seen in Fig. 7, except for the model PRWS for the MA1P system, as well as with the models PRSV and PRSVWS for the EA1P system. These different predictions from data can be explained considering the reproduction of the vapor phase composi-

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Fig. 8 – Representation of T vs. x1 , y1 of methyl acetate (1) +1–propanol (2) system ( , ) at 1.5 MPa. Fitting curves ( , ) representing data modeling results for: PR–EOS (Peng and Robinson, 1976); PRSV–EOS (Peng and Robinson, 1976; Stryjek and Vera, 1986); PRWS–EOS (Peng and Robinson, 1976; Wong and Sandler, 1992) and PRSVWS–EOS (Peng and Robinson, 1976; Stryjek and Vera, 1986; Wong and Sandler, 1992).

tions, taking into account that they can be a consequence of associative behavior, which occurs between the substances of the systems considered in this work. Also, because the inaccurate reproduction of vapor pressures at high pressures for the polar substances, since SD have been obtained greater than 6, 13, 34 and 55 kPa using PR–EOS and greater than 3, 7, 7 and 4 kPa using PRSV–EOS, respectively, in the prediction of vapor pressures of methyl acetate, ethyl acetate, 1–propanol and 1–butanol. Consequently, it seems evident that PR–EOS is generally inaccurate for phase equilibrium calculations. Otherwise, the way to approximate the attractive term can amplify errors, so that all the improvement in the dependence of  [in Eq. (6)] on temperature can reduce the deviation on vapor pressures predictions.

4.

Conclusions

The isobaric VLE data for binary systems MA1P, MA1B and EA1P were obtained at a pressure of 1.5 MPa. The data were

verified when compared with those previously published by other authors and also with the use of the ϕ–ϕ approach. The Peng–Robinson EOS was employed using different expressions in the attractive parameter and different mixing rules. The results show that by using the Stryjek–Vera equation and the Wong–Sandler mixing rules, good predictions were obtained from the MA1P system. While in the EA1P system significant differences are observed, although the tendency is to adequately reproduce the expansive–compressive behavior. On the other hand, in the MA1B system all the models reproduce the behavior in a similar and inadequate way. The azeotropic point in the EA1P system at 1.5 MPa has been calculated with a precise and stable procedure. The azeotropic data are well correlated with the azeotropic data at different pressures in the literature. The evolution of the singular point regarding the pressure makes possible to predict that the composition of ethyl acetate will decrease at higher pressures than those presented in this work.

Chemical Engineering Research and Design 1 5 2 ( 2 0 1 9 ) 242–253

251

Fig. 9 – Representation of T vs. x1 , y1 of methyl acetate (1) +1–butanol (2) system ( , ) at 1.5 MPa. Fitting curves ( , ) representing data modeling results for: PR–EOS (Peng and Robinson, 1976); PRSV–EOS (Peng and Robinson, 1976; Stryjek and Vera, 1986); PRWS–EOS (Peng and Robinson, 1976; Wong and Sandler, 1992) and PRSVWS–EOS (Peng and Robinson, 1976; Stryjek and Vera, 1986; Wong and Sandler, 1992).

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Fig. 10 – Representation of T vs. x1 , y1 of ethyl acetate (1) +1–propanol (2) system ( , ) at 1.5 MPa. Fitting curves ( , ) representing data modeling results for: PR–EOS (Peng and Robinson, 1976); PRSV–EOS (Peng and Robinson, 1976; Stryjek and Vera, 1986); PRWS–EOS (Peng and Robinson, 1976; Wong and Sandler, 1992) and PRSVWS–EOS (Peng and Robinson, 1976; Stryjek and Vera, 1986; Wong and Sandler, 1992).

Funding This work was supported by the authors. This work has not financial support of the Spanish government.

Conflict of interest The authors declare no competing financial interest.

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