Fluid Phase Equilibria (2001)

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1 Fluid Phase Equilibria (2001) Vapor liquid equilibria for the binary systems decane + 1,1-dimethylethyl methyl ether (MTBE) and decane + 1,1-dimethylpropyl methyl ether (TAME) at , and K Armando del Río a, Baudilio Coto b, Concepción Pando a, Juan A.R. Renuncio a, a Departamento de Química Física I, Universidad Complutense, E Madrid, Spain b ESCET, Universidad Rey Juan Carlos, E Móstoles, Madrid, Spain Received 21 November 2000; accepted 18 May 2001 Abstract Vapor liquid equilibrium (VLE) data are reported for the binary mixtures formed by decane and the branched ethers 1,1-dimethylpropyl methyl ether (tert-amyl methyl ether or TAME) and 1,1-dimethylethyl methyl ether (tert-butyl methyl ether or MTBE). A Gibbs Van Ness type apparatus was used to obtain total vapor pressure measurements for the decane + MTBE and decane + TAME systems as a function of composition at , and K. Both systems show a nearly ideal behavior. VLE data are analyzed together with excess enthalpy (Hm E) data previously obtained at K for these mixtures. The UNIQUAC model is used to correlate VLE and Hm E data and the original UNIFAC group contribution model and the modified UNIFAC (Dortmund model) are used to predict VLE and Hm E data for the binary systems decane + MTBE and decane + TAME Elsevier Science B.V. All rights reserved. Keywords: Binary liquid mixtures; Vapor pressure; Vapor liquid equilibria; Branched ether 1. Introduction Branched ethers have been the subject of numerous investigations in the recent years because of their use as additives in the lead-free gasoline. These ethers are synthesized by the reaction between an isoolefin and an alcohol in excess. The ether purification and the estimation of the phase behavior of the so-called oxi-gasoline requires an accurate knowledge of the phase equilibrium and other thermodynamic properties for the involved mixtures. Both the 1,1-dimethylethyl methyl ether (tert-butyl methyl ether or MTBE) Abbreviations: MTBE, 1,1-dimethylethyl methyl ether (tert-butyl methyl ether); TAME, 1,1-dimethyl-propyl methyl ether (tert-amyl methyl ether); VLE, vapor liquid equilibrium Corresponding author. Fax: address: renuncio@eucmax.sim.ucm.es (J.A.R. Renuncio) /01/$ see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S (01)00543-X

2 300 A. del Río et al. / Fluid Phase Equilibria (2001) and the 1,1-dimethylpropyl methyl ether (tert-amyl methyl ether or TAME) are being widely used as gasoline blending agents and a program is underway at our laboratory to measure the vapor liquid equilibrium (VLE) data of mixtures formed by MTBE or TAME and a hydrocarbon or an alcohol. VLE data (and surface tension data in some cases) have been reported at several temperatures for binary systems formed by methanol, heptane, cyclohexane and MTBE or TAME [1 7]. The purpose of this paper is to report phase equilibria in the binary systems decane + MTBE and decane + TAME for which no data (isobaric or isothermal) have been published in the literature. VLE data taken at , and K will be discussed together with excess enthalpy (Hm E ) data previously obtained at K by Wang et al. [8] and Zhu et al. [9]. 2. Experimental section Decane was purchased from Sigma, with a purity higher than 99%. MTBE was from Fluka with a purity higher than 99.5%. TAME (Fluka 97% purity) was fractionally distilled over 0.3 nm molecular sieves for several hours. The middle distillate used in the present work (approximately 50% of the initial amount) had a purity better than 99.6%, as measured by a gas chromatographic analysis. Chemicals were handled under a dry nitrogen atmosphere and were degassed by reflux distillation for several hours following a procedure described elsewhere [10]. VLE data were measured using a Gibbs Van Ness type static apparatus [11]. Binary liquid solutions of known composition were prepared in a test cell by volumetric injection of degassed liquids using calibrated pistons. The accuracy of the mole fraction is estimated to be about in the dilute regions and about in the middle of the concentration range. Cell and piston-injectors were immersed in a water bath in which temperature was controlled within ±0.002 K. The temperature was measured with a quartz thermometer, Testo 781, with an accuracy of 0.01 K. The total vapor pressure was measured when phase equilibrium was reached using a differential MKS Baratron pressure gauge with a resolution of 0.08% of the reading. Pressure accuracy is estimated to be 0.01 kpa. Table 1 lists values for the molar volumes, isothermal compressibilities and vapor pressures for decane, MTBE and TAME at the temperatures studied. Pure component vapor pressure values obtained in this work are compared to those previously reported. The source for pure component properties is also given Table 1 Pure component properties used in this study T (K) V m (cm 3 mol 1 ) κ T 10 9 (Pa 1 ) p (kpa) Literature values range p (kpa) Decane [12] [14] [12] [14 16] [12] [14 16] MTBE [13] 1.71 [13] [1,5,17 21] [13] 1.89 [13] [1,17 21] [13] 2.07 [13] [1,17 21] TAME [13] 1.53 [13] [2,22,23] [13] 1.80 [13] [2,22,23] [13] 2.07 [13] [2,22,23]

3 A. del Río et al. / Fluid Phase Equilibria (2001) Table 2 Vapor liquid equilibrium data and coefficients and standard deviations for G E m representation by Eq. (1) for decane(1)+mtbe(2) at , and K x 1 p (kpa) p calc (kpa) y 1 G E m (J mol 1 ) lnγ 1 ln γ 2 At temperature T = K a At temperature T = K b

4 302 A. del Río et al. / Fluid Phase Equilibria (2001) Table 2 (Continued ) x 1 p (kpa) p calc (kpa) y 1 G E m (J mol 1 ) lnγ 1 ln γ 2 At temperature T = K c a P 0 = ± ; P 1 = ± ; P 2 = ± 0.003; P 3 = ± 0.005; σ x = ; σ p = 8Pa. b P 0 = ± 0.002; P 1 = ± 0.003; P 2 = ± 0.005; P 3 = ± 0.009; σ x = ; σ p = 38 Pa. c P 0 = ± 0.003; P 1 = ± 0.004; P 2 = ± 0.007; P 3 = ± 0.013; σ x = ; σ p = 90 Pa. in Table 1. The vapor pressures measured in this work are in good agreement with literature values and this is considered an indication of the chemicals purity. 3. Experimental results VLE measurements for decane + MTBE and decane + TAME were carried out at , and K. Results were analyzed using a modified Barker s method and the maximum likelihood principle [24]. The temperature, T, and the amount of substance for components 1 and 2 were considered to be the independent variables in the data reduction. Equations of material balance were included to take into account the amounts of substance present in the vapor phase. The excess Gibbs energy, G E m, of the liquid phase was assumed to be described by an (m/n) Padé approximant and is given by G E m RT = x 1(1 x 1 ) m i=0 P i(2x 1 1) i 1 + n j=1 Q j(2x 1 1) j (1)

5 A. del Río et al. / Fluid Phase Equilibria (2001) Table 3 Vapor liquid equilibrium data and coefficients and standard deviations for G E m representation by Eq. (1) for decane(1)+tame(2) at , and K x 1 p (kpa) p calc (kpa) y 1 G E m (J mol 1 ) lnγ 1 ln γ 2 At temperature T = K a At temperature T = K b

6 304 A. del Río et al. / Fluid Phase Equilibria (2001) Table 3 (Continued ) x 1 p (kpa) p calc (kpa) y 1 G E m (J mol 1 ) lnγ 1 ln γ At temperature T = K c a P 0 = ± 0.004; P 1 = ± 0.007; P 2 = ± 0.010; P 3 = ± 0.018; σ x = ; σ p = 33 Pa. b P 0 = ± 0.004; P 1 = ± 0.005; P 2 = ± 0.010; P 3 = ± 0.017; σ x = ; σ p = 31 Pa. c P 0 = ± 0.004; P 1 = ± 0.008; P 2 = ± 0.016; P 3 = 0.02 ± 0.02; σ x = ; σ p = 62 Pa. where P i and Q j are adjustable parameters, and x 1 is the mole fraction of decane. Data at the three temperatures studied are adequately described by (3/0) Padé approximants. This makes Eq. (1) equivalent to a Redlich Kister equation. The vapor phase is described using the virial equation. Values for the second virial coefficients of the pure component and the cross virial coefficients were calculated by means of the Hayden and O Connell method [25].

7 A. del Río et al. / Fluid Phase Equilibria (2001) Fig. 1. VLE data for the decane(1) + MTBE(2) system: ( ) K; ( ) K; ( ) K; ( ) calculated values using Eq. (1). Table 2 lists values for the decane liquid composition, x 1, and the total pressure, p, at the three temperatures studied, together with the calculated total pressure, p calc, the hydrocarbon vapor composition, y 1, the excess Gibbs energy, G E m, the activity coefficients, ln γ 1 and ln γ 2 for decane(1) + MTBE(2), the Padé coefficients, P i, for G E m representation by Eq. (1), and their uncertainties, and the standard deviations between experimental and calculated values of x 1, σ x, and p, σ p. Table 3 gives similar results for decane(1) + TAME(2). Fig. 1 shows plots of the total pressure against liquid and vapor compositions for the decane + MTBE system at the three temperatures studied. Fig. 2 shows similar plots for the decane + TAME system. Both experimental values and those calculated using Eq. (1) are shown in Figs. 1 and 2. Deviations from Raoult s law are positive and very small in both systems. A similar behavior was reported for the octane + MTBE and octane + TAME systems [26 28]. Values for the excess Gibbs energy of the decane + MTBE and decane + TAME systems are positive. Maximum values are lower than 115 J mol 1 (decane + MTBE) or 75 J mol 1 (decane + TAME). These maxima appear at approximately the same mole fraction (x 1 0.5) for all the temperatures studied.

8 306 A. del Río et al. / Fluid Phase Equilibria (2001) Fig. 2. VLE data for the decane(1) + TAME(2) system: ( ) K; ( ) K; ( ) K; ( ) calculated values using Eq. (1). Table 4 Correlation and prediction of Hm E and VLE data for decane(1) + MTBE(2) and decane(1) + TAME(2) using the UNIQUAC, UNIFAC, and modified UNIFAC (Dortmund) models a K b K K K σ H (J mol 1 ) σ H (%) σ p (kpa) σ p (%) σ p (kpa) σ p (%) σ p (kpa) σ p (%) Decane(1) + MTBE(2) UNIQUAC correlation UNIFAC prediction Modified UNIFAC (Dortmund) prediction Decane(1) + TAME(2) UNIQUAC correlation UNIFAC prediction Modified UNIFAC (Dortmund) prediction a Standard deviations between experimental and calculated H E m, σ H, and percent ratio of σ H and the maximum value of the excess enthalpies, σ H (%), and standard deviations between experimental and calculated vapor pressures, σ p, and percent ratio of σ p and the maximum value of the vapor pressure, σ p (%). b Experimental data taken from Wang et al. [8] for decane + MTBE and from Zhu et al. [9] for decane + TAME.

9 4. Modeling and discussion A. del Río et al. / Fluid Phase Equilibria (2001) The UNIQUAC model [29] was used to correlate the isothermal VLE data together with excess enthalpy data previously obtained at K. Wang et al. [8] reported endothermic Hm E data for the decane + MTBE mixtures with a maximum value of 501 J mol 1 occurring at x 1 = Zhu et al. [9] reported endothermic Hm E data for the decane + TAME mixtures with a maximum value of 382 J mol 1 occurring at x 1 = The interaction parameters of this model, A ji, were considered to vary linearly with temperature according to A ji = A ji,1 + A ji,2 (T ) (2) The resulting values for the interaction parameters are: A 12,1 = K, A 12,2 = , A 21,1 = K, A 21,2 = (decane+mtbe) and A 12,1 = K, A 12,2 = , A 21,1 = K, A 21,2 = (decane + TAME). Values for the standard deviations between experimental and calculated excess enthalpies, σ H, and the percent ratio of σ H and the maximum values of the excess Fig. 3. Comparison of UNIQUAC and modified UNIFAC (Dortmund) calculations of VLE data at K: ( ) decane(1) + MTBE(2) (experimental); ( ) decane(1) + TAME(2) (experimental); ( ) correlated using UNIQUAC; (----) predicted using the modified UNIFAC (Dortmund) model.

10 308 A. del Río et al. / Fluid Phase Equilibria (2001) enthalpy, σ H (%), and values for the standard deviations between experimental and calculated vapor pressures, σ p, and the percent ratio of σ p and the maximum value of vapor pressure, σ p (%), are listed in Table 4. Values for these deviations indicate that the UNIQUAC equation is able to correlate simultaneously the VLE and Hm E data for the decane + MTBE and decane + TAME systems. Fig. 3 shows plots of experimental vapor pressures at K and those calculated from the UNIQUAC equation for the two systems studied in this work. Similar plots are obtained for the other two temperatures studied. Predictions of VLE data from pure components data and the model parameters available in the literature are of great industrial interest and were carried out using the original UNIFAC [30,31], and the modified UNIFAC (Dortmund) [32,33] models. For comparison purposes, Hm E data were also predicted by means of these models. Values for σ H, σ H (%), σ p, and σ p (%), are listed in Table 4. The predicted excess enthalpies cannot be considered accurate. However, the vapor pressures are accurately predicted. The σ p (%) values obtained using the modified UNIFAC (Dortmund) model range from 0.8 to 1.1% for decane + MTBE, and from 1.1 to 1.7 for decane + TAME. The original UNIFAC model leads to higher deviations than those obtained when the modified UNIFAC (Dortmund) model is used. Fig. 3 shows a comparison of UNIQUAC and modified UNIFAC (Dortmund) calculations of VLE data at K. Similar plots are obtained for the other two temperatures studied. The predicted vapor pressures are almost coincident with the experimental data. 5. Conclusion Vapor liquid equilibrium data have been reported for decane + MTBE and decane + TAME at three different temperatures. Both binary systems deviate very slightly from ideal behavior. The UNIQUAC model describes very well the VLE data at , and K and the Hm E data previously reported at K for decane + MTBE and decane + TAME using temperature-dependent interaction parameters. The modified UNIFAC (Dortmund) provides very accurate predictions of isothermal VLE data for those two systems at three temperatures studied. List of symbols A ij UNIQUAC model interaction parameters G Gibbs energy H enthalpy J Joule kpa 10 3 Pa K Kelvin p vapor pressure P i Padé approximant parameter Q j Padé approximant parameter R gas constant T temperature V volume x mole fraction in the liquid phase y mole fraction in the vapor phase

11 A. del Río et al. / Fluid Phase Equilibria (2001) Greek symbols γ activity coefficient κ isothermal compressibility σ standard deviation σ (%) percent ratio of the standard deviation and the maximum value of a magnitude Superscripts E excess property Subscripts calc calculated H excess enthalpy i, j components of binary systems m molar property p vapor pressure x liquid composition of component 1 Acknowledgements This work was funded by the Spanish Ministry of Education, DGICYT PB97-315, A. del Río acknowledges the Comunidad Autonoma de Madrid for its support through a predoctoral grant. References [1] B. Coto, R. Wiesenberg, C. Pando, R.G. Rubio, J.A.R. Renuncio, Ber. Bunsenges. Phys. Chem. 100 (1996) [2] F. Mössner, B. Coto, C. Pando, R.G. Rubio, J.A.R. Renuncio, J. Chem. Eng. Data 41 (1996) [3] F. Mössner, B. Coto, C. Pando, R.G. Rubio, J.A.R. Renuncio, J. Chem. Soc., Faraday Trans. 92 (1996) [4] B. Coto, F. Mössner, C. Pando, R.G. Rubio, J.A.R. Renuncio, Fluid Phase Equilibria 133 (1997) [5] F. Mössner, B. Coto, C. Pando, J.A.R. Renuncio, Ber. Bunsenges. Phys. Chem. 101 (1997) [6] A. del Rio, B. Coto, C. Pando, J.A.R. Renuncio, Phys. Chem. Chem. Phys. 1 (1999) [7] A. del Rio, B. Coto, C. Pando, J.A.R. Renuncio, Ind. Eng. Chem. Res. 40 (2001) [8] L. Wang, G.C. Benson, B.C.-Y. Lu, Thermochimica Acta 213 (1993) [9] S. Zhu, S. Shen, G.C. Benson, B.C.-Y. Lu, J. Chem. Thermodyn. 26 (1994) [10] B. Coto, C. Pando, R.G. Rubio, J.A.R. Renuncio, J. Chem. Soc., Faraday Trans. 91 (1995) [11] R.E. Gibbs, H.C. van Ness, Ind. Eng. Chem. Fundam. 11 (1972) [12] M. Diaz Peña, G. Tardajos, J. Chem. Thermodyn. 10 (1978) [13] U.P. Govender, T.M. Letcher, J. Chem. Eng. Data 41 (1996) [14] J. Gmehling, U. Onken, W. Arlt, Vapor liquid equilibrium data collection, DECHEMA, Chem. Data Ser. I (1980) Part 6b; DECHEMA, Frankfurt Main, Germany. [15] P. Rice, A. El-Nikheli, Fluid Phase Equilibria 107 (1995) [16] A. Dejoz, V. González-Alfaro, P.J. Miguel, M.I. Vázquez, J. Chem. Eng. Data 40 (1995) [17] K. Aim, M. Ciprian, J. Chem. Eng. Data 25 (1980) [18] D. Ambrose, J.H. Ellender, C.H.S. Sprake, R. Townsend, J. Chem. Thermodyn. 8 (1976) [19] M.A. Krähenbühl, J. Gmehling, J. Chem. Eng. Data 39 (1994) [20] H.S. Wu, K.A. Pividal, I. Sandler, J. Chem. Eng. Data 36 (1991) [21] R. Reich, M. Cartes, J. Wisniak, H. Segura, J. Chem. Eng. Data 43 (1998)

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