Isothermal and Isobaric VaporâLiquid Equilibrium and Excess Molar

Article pubs.acs.org/jced

Isothermal and Isobaric Vapor−Liquid Equilibrium and Excess Molar Enthalpy of the Binary Mixtures of 2‑Methoxy-2-methylpropane + 2‑Methyl-2-butanol or + 2‑Butanol Anna Zaitseva,*,† Helena Laavi,† Leo Ojala,† Jean-Yves Coxam,‡ Karine Ballerat-Busserolles,‡ Juha-Pekka Pokki,† and Ville Alopaeus† †

Department of Biotechnology and Chemical Technology, School of Chemical Technology, Aalto University, Espoo, Finland University Blaise Pascal, Insitute of Chemistry of Clermont-Ferrand, Clermont-Ferrand, France

Downloaded by RUTGERS UNIV on September 1, 2015 | http://pubs.acs.org Publication Date (Web): August 5, 2015 | doi: 10.1021/acs.jced.5b00300

‡

ABSTRACT: Low molecular weight ethers have been used for many years as enhancers for fossil fuels combustion. A gradual replacement of mineral oils by bio-oils requires additional knowledge about the thermodynamic properties of bio-alcohol and ether mixtures. In this work, isothermal vapor−liquid equilibria (VLE) of the binary mixture of methyl tert-butyl ether (MTBE, 2-methoxy-2-methylpropane) with 2-methyl-2-butanol and MTBE with 2-butanol were measured isothermally at 323 K and at constant 90.1 kPa pressure with a recirculation still apparatus. Excess molar enthalpy (hE) was measured for two binary mixtures at 308 K, 323 K, and 363 K by using a SETARAM C80 calorimeter equipped with a flow mixing cell. A comprehensive consistency analysis was performed for the obtained data, and the experimental data were correlated with the nonrandom two liquid and universal quasichemical activity coefficient models. The results were compared with UNIFAC-Dortmund and COSMO-RS predictive models. The investigated mixtures are close to ideal and show small positive deviation from Raoult’s law. Calorimetric measurements show large positive molar excess enthalpy that decreases with the temperature for both investigated binary mixtures.

1. INTRODUCTION

Predictive thermodynamic methods, such as UNIFAC or COSMO-RS, are commonly used for modeling of industrial processes when experimental information for the constituent compounds is not available. Reliability of the predictive models is difficult to assess, because available thermodynamic data are used for development of the models. For evaluation of the models, newly obtained data can be used. In our work vapor−liquid equilibria (VLE) for the binary mixtures of methyl tert-butyl ether with 2-methyl-2-butanol (tert-amyl alcohol) and with 2-butanol are measured at isothermal and at isobaric conditions. Additionally, the enthalpies of mixing at three temperatures were measured for both binary mixtures. Utilization of the obtained mixing enthalpy allows the extension of the thermodynamic models derived in this work to a wider temperature range. Neither VLE, nor heat of mixing data were found in the literature for the investigated binary mixtures.5

Oxygenated compounds have been used as fossil fuel additives for many decades.1 Beside the increase of fuel total volume with oxygenate blending, the oxygenates also improve fuel combustion efficiency and thus reduce the exhaust emissions of CO and hydrocarbons. Ethers, like methyl tert-butyl ether (MTBE), ethyl tert-butyl ether (ETBE) or tert-amyl methyl ether (TAME) are used as blended chemicals because of their high energy density. These ethers are relatively cheap because of their production from fractions of natural gas and crude oils. Recently the alternative chemicals, alcohols, have become more popular blending agents owing to the intensive development of biorefining and the reduction of bioalcohol production cost. The octane number of alcohols is only slightly lower in comparison with ethers,2 but utilization of bioalcohols improves CO2 balance in the atmosphere. The net enthalpy of combustion is more favorable toward ethers: it is −3110 MJ/kmol for MTBE and −2490 MJ/kmol for 2-butanol.3 On the other hand, alcohols are less toxic at inhalation: LD50 (median lethal dose) for 2-butanol is 6.5 g/kg of body weight, whereas for MTBE LD50 is 3.8 g/kg of body weight.4 Inhalation of oxygenates is the most probable route for human exposure to the chemicals, and distribution of ethers and alcohols in the vapor phase is important for the assessment of health hazard effects of blended fuels and biofuels. For the refinery industry, the thermodynamic properties of biofuel blends are of a major importance. © XXXX American Chemical Society

2. MATERIALS AND METHODS The chemicals were ordered from Sigma-Aldrich. The purities and water content of the chemicals are shown in Table 1. Chemicals were used as purchased for the excess molar enthalpy measurements, but for VLE measurements tert-amyl alcohol was distilled in a vacuum. The purity of the used chemicals was Received: March 31, 2015 Accepted: July 23, 2015

A

DOI: 10.1021/acs.jced.5b00300 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Table 1. Supplier and the Purity of the Components


a

chemical name/IUPAC name

CAS number

GC purity, area %a

water content, wt %

nD25 measured

nD25 lit.b

MTBE/2-methoxy-2-methylpropane tert-amyl alcohol/2-methyl-2-butanol 2-butanol

1634-04-4 75-85-4 78-92-2

99.9 99.8 99.5

0.003 to 0.008 0.004 to 0.008 0.02

1.3661 ± 0.0005 1.4022 ± 0.0005 1.3951 ± 0.0005

1.3672 ± 0.0013 1.4037 ± 0.0042 1.3949 ± 0.0095

The chemical GC area in percent, determined as described in Section 3.3. bTaken from ref 3.

checked by gas chromatography (GC) and by refractometery. tert-amyl alcohol purity after the distillation was 99.7 wt % (area %) as determined by GC. The moisture contents were determined using Karl Fischer titrator (Mettler-Toledo DL38, Hydropoint Solvent G and Titrant 2 mgH2O·cm−3) or Karl Fisher Coulometer (Mettler Toledo DL32, sensor Mettler Toledo DM 143-SC, Hydranal Coulomat E). The accuracy of the water content determination was 0.0002 wt %. The measurements were done for several samples of the excess molar enthalpy measurements and for several samples of VLE measurements, and the water content varied slightly for the different samples. Refractive indexes were measured with a digital automatic refractometer Abbemat (Dr. Kernchen, Germany) at 298.15 K. The accuracy of temperature and refractive index measurements were ± 0.03 K and ± 0.0005, correspondingly. The literature value of the refractive index was taken as an average from the DIPPR database experimental values at 298.15 K,3 the standard deviation of the same values was estimated.

The sensitivity of SETARAM C80 was determined as recommended in ref 9 by using water−ethanol binary mixture excess molar enthalpy at 323 K.10 Additionally, the calorimeter was tested by comparing the heat of mixing at 298.15 K for the measured and the reference binary mixtures of cycloxehane− hexane11 and 2-propanol−cyclohexane.12 The average deviation between the measured and literature excess molar enthalpies was 2 % or 4 J·mol−1 for the positive excess molar enthalpies up to 800 J/mol. The accuracy of the temperature measurement in the calorimeter was 0.1 K as referred by the equipment manufacturer. The buffer tank of 0.001 m3 volume was installed at the outlet flow from the calorimeter to reduce the pressure fluctuation in the system and to collect the used chemical components. The back pressure of buffer tank was generated with a nitrogen gas purge. Pressure of the calorimetric measurement was measured with a Rosemount gauge pressure transmitter (0.05 % pressure uncertainty) located between the syringe pump and the calorimeter. The overall accuracy of the pressure measurement was 0.2 bar. At the Institute of Chemistry of Clermont-Ferrand, the heat of mixing was measured with a SETARAM C80 calorimeter equipped with the static flow mixing cell developed at ICCF.13 Two thermostated ISCO 100DM syringe pumps were used to feed the components into the flow mixing cell. Two preheaters, a Chino DB 500 (temperature precision 0.1 K, temperature range 273 to 673 K) and a Fluke Hart Scientific 2200 (temperature precision 0.01 K, temperature range 173 K to 1073 K), were installed inside the calorimeter in series. The pressure in the system was controlled by a pressure regulator Swagelok KPB1L0D412P200B0 (pressure range 0 MPa to 6.89 MPa) and was measured by electronic Druck pressure gauges (overall accuracy 0.25 %) connected to the Druck DPI 280 series pressure indicator.13 A buffer tank of 0.001 m3 volume was installed at the end of the flow line to compensate for the system pressure fluctuations during the measurements. The water−ethanol binary system was used to determine the sensitivity of the calorimeter at several temperatures (308.15 K, 323.15 K, and at 363.15 K) by comparison of the obtained excess molar enthalpies with the literature values.10 The average relative deviation of the excess molar enthalpy for the ethanol−water mixture was 1.8 % at 323.15 K. 3.2. Recirculation Still Measurements. A recirculation still apparatus of Yerazunis type14 was used in the vapor−liquid equilibria (VLE) measurements. The sampling chambers of the apparatuses were modified15,16 to allow withdrawing 1 mL to 2 mL of liquid or condensed vapor samples by syringes. The mixing of both phases was enhanced by magnetic stirrers. Pressure was measured with a pressure transducer Druck PMP 4070 calibrated against a Beamex MC2-PE field calibrator. The calibration of the pressure meter was made by measuring the vapor pressure of water, and the uncertainty of pressure measurements was found to be 0.1 kPa. A stainless steel cylinder of 0.03 m3 was installed in the apparatus vacuum line to stabilize the pressure during the measurements. A Pt-100 temperature probe connected to a Precision Thermometer display F200

3. APPARATUS AND PROCEDURE 3.1. Calorimetric Measurements. Calorimetric measurements were conducted at two research places: at Aalto University (Finland, AU) and at Institute of Chemistry of ClermontFerrand (France, ICCF). The ICCF experiments at 323 K were repeated at AU to validate the performance of the new preheaters installed in the inlet of the AU calorimeter. Additionally, the calorimetric apparatus at ICCF was used for measuring the heat of mixing at other temperatures, namely at 308 K and 363 K. At Aalto University the heat of mixing was measured with the flow mixing cell installed in a SETARAM C80 calorimeter,6 as described in ref 7. The external preheater was installed at the inlet of the calorimeter. Heating element Hotrod T 6.5*60 50 W 230 V was placed in a drilled hole inside a massive block of brass. Additional outside resistors were utilized to reduce the heating power of the heating element to a necessary level. The heat conduction between the heater and the brass block was improved with heat transfer paste. The temperature of the external preheater was controlled by a Fluke 2200 temperature controller, the preset temperature value was 0.1 K lower than the calorimeter preheater temperature. Two 1/16 inch pipes were directed through the heated brass block. The grooves for the pipes were located symmetrically toward the heater. Temperature on the brass block was monitored with Pt100 temperature sensors placed on the block surfaces close to the pipes. The whole preheater system was isolated by insulation foam and styrofoam. The component flow was provided by two thermostated ISCO syringe pumps of volume 260 cm3 and 500 cm3. Accuracy of the pump volumetric flow was 0.5 % as referred by the manufacturer. The preset total flow of 0.5 cm3·min−1 resulted in a constant calorimeter signal after about 20 min from the beginning of the experiment, which was recorded 10 min after stabilization. The heat effect of pure components was taken into account by measuring the calorimeter signals of the pure component flows (baselines).8 B




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(Automatic System Laboratories ASL) was used for temperature recording. The temperature probe was calibrated at the Finnish national standard laboratory, the uncertainty was found to be 0.002 K, but the fluctuation of temperature in the measurements was used as experimental uncertainty of the temperature measurements. The procedure of the VLE measurements using the recirculation still was described previously in refs 16 and 17. About 80 cm3 of the binary mixture was boiled in the apparatus for 30 min to 50 min. When the temperature and the pressure were stable for 10 min, samples of the liquid and condensed vapor phase were taken by Hamilton lock syringes. The samples were analyzed by GC. Owing to the high difference in compound volatility, it was difficult to achieve a uniform heating of the mixtures, and therefore the recorded temperature was slightly fluctuating without stabilization with time. The standard deviation of the temperature within 10 min before the sampling was taken as the uncertainty of the temperature measurements and was always below 0.1 K. 3.3. GC Analysis. For the analysis of the chemical purity and the VLE samples, an Agilent Technology 6890N gas chromatograph and an Agilent liquid injector 7693 were used. The chromatograph inlet flow was divided into two streams. One stream was directed through a DB-WaxETR capillary column (Agilent, 30 m × 0.320 mm × 1 μm) to a flame ionization detector (FID, at 523.15 K), another stream was directed through a HP-5 capillary column (Agilent, 22 m × 0.320 mm × 0.25 μm) to a thermal conductivity detector (TCD, at 523.15 K). The total flow of helium through the columns was 1.6 cm3·min−1; an inlet split ratio of 50:1 was used. Both column temperatures were programmed to increase, at first, from 353.15 K (hold for 2 min) to 378.15 K at the rate of 50 K·min−1, and then to 423.15 K (hold for 5 min) at the rate of 60 K·min−1. Good peak separation in the DB-WaxETR and in the HP-5 columns was observed with both FID and TCD detectors. The detectors were calibrated using gravimetrically prepared binary mixture samples. The GC analysis results from two detectors for experimental samples of VLE measurements were averaged. As the standard deviation of the determined liquid or vapor concentration, we took the larger value of either average deviation of the concentration determined at the calibration of FID detector or the difference between concentrations determined using FID and TCD detectors. 3.4. Vapor Liquid Equilibrium Models. The gamma−phi (γ−ϕ) approach was used for modeling VLE and excess molar enthalpies in the investigated systems, as shown in following equation: ⎧ γixiPi0ϕi0 = yP ϕi exp⎨ i ⎩

∫P

Pi0

⎫ ViL dP ⎬ RT ⎭

Table 2. Pure Component Physical Properties Used in Calculations critical temp, TC (K)a critical pressure, PC (MPa)a ωSRKa Vliq (298.15 K)b Rc Qc Ad B C D E Tmin, K Tmax, K vapor pressure eq ref

MTBE

tert-amyl alcohol

2-butanol

496.4 3.37 0.269 119.8 3.632 4.068 57.13 −5200.7 −5.14 1.65126·10−17 6 164.55 497.1 3 3

545 3.9 0.5007 109.5 4.254 3.446 20.6950 2385.0 −115.27

536.1 4.18 0.5792 92.4 3.598 3.032 22.0892 2980 −90.35

336 375.5 2 23

330 372.7 2 7,23

a

Taken from ref 24. bThe liquid molar volume calculated from density correlation at 298.15 K from ref 3. cThe UNIQUAC model group parameters Ri and Qi are obtained as described in ref 25 from the van der Waals group volume and surface areas Vi and Ai given in ref 3. d Parameters of eq 2 and eq 3

⎛P⎞ ln⎜ ⎟ = A − ⎝ Pa ⎠ ⎛P⎞ ln⎜ ⎟ = A + ⎝ Pa ⎠

B T K

( )+C B T K

()

(2)

+ C ln(T /K) + DT E (3)

For the predictive activity coefficient models, UNIFACDortmund and COSMO-RS, vapor phase composition (yi) or pressure (P), or excess molar enthalpy (hE) was calculated based on the liquid molar fraction (xi) obtained in the experiments using eq 1. 3.5. Predictive Models. Two advanced predictive models, UNIFAC-Dortmand and COSMO-RS were used to predict the VLE of the considered systems. The models were compared with the data measured in this work. UNIFAC-Dortmund model parameters for alcohol−ether group interaction were published in 199826 and were not revised after. The interaction parameters of the UNIFAC-Dortmund model are temperature dependent and the prediction of the temperature dependency of secondary and ternary alcohols is interesting to validate. Another approach to the prediction of the thermodynamic behavior of liquids was proposed by Klamt21 and was based on quantum calculations of a molecule in a conductor medium. The electrostatic interactions between contacting molecule surfaces serve as a basis for the calculation of thermodynamic behavior, and van der Waals and hydrogen bond interactions are parametrized based on the molecule surface charge density. Thus, quantum calculations of MTBE, 2-butanol and tert-amyl alcohol molecules in the conductor medium are required. For the MTBE and tert-amyl alcohol molecules the calculations were performed using the Turbomole program27 with RI-DFT approach and BP-TZVP basis set, as was recommended by the author.28 Three conformers of tert-amyl alcohol and one for MTBE were taken into account.29 The quantum calculation results for 2-butanol were available in COSMOtherm program database.30 The COSMOtherm program was used for further calculations of VLE and hE of the investigated systems.

(1)

where xi and yi are liquid and vapor mole fractions of component i, P is total system pressure, and γi is an activity coefficient of component i described by some of the used activity coefficient models (nonrandom two liquid (NRTL),18 universal quasichemical (UNIQUAC),19 modified UNIFAC-Dortmund,20 COSMORS21). Vapor phase fugacity coefficients (ϕi) and fugacity coefficients of pure components at saturation (ϕi0) are described by the Soave−Redlich−Kwong (SRK)22 equation of state. The Rackett equation is used for calculations of liquid molar volume (ViL). Pi0 is the vapor pressure of pure component i at system temperature T described with the Antoine eq eq 2) or with the modified Antoine eq 3. The empirical parameters A, B, C, D, and E are taken from literature and presented in Table 2. C



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Table 3. Vapor−Liquid Equilibrium Data Measured for Two Binary Mixtures at 90.1 kPa, at Temperature (T), Mole Fraction of MTBE in Liquid Phase (x1) and in Vapor Phase (y1), Activity Coefficients of Both Components (γ1, γ2), and the Variable Standard Uncertainties (u)


(a) MTBE (1) + tert-amyl alcohol (2) a 90.1 kPa

b

γ1

y1b

T/K

u(T)/K

x1

371.85 365.95 363.25 361.95 359.35 356.35 354.15 352.65 351.05 349.25 348.85 347.65 346.35 344.55 342.65 340.95 338.45 332.95 330.45 328.45 326.75 325.05 324.45

0.01 0.04 0.06 0.04 0.05 0.05 0.03 0.05 0.08 0.07 0.10 0.06 0.06 0.07 0.05 0.03 0.06 0.05 0.04 0.04 0.04 0.09 0.03

0 0.064 0.09 0.11 0.143 0.185 0.217 0.238 0.265 0.298 0.3 0.321 0.341 0.372 0.41 0.447 0.512 0.678 0.768 0.846 0.909 0.975 1

T/K

u(T)/K

x1

u(x1)

y1c

γ1

u(γ1)

369.32 364.54 361.93 358.93 356.15 353.25 350.55 348.96 346.2 344.05 341.97 340.69 339.92 338.15 335.97 333.91 331.77 329.8 328.52 326.53 324.6

0.002 0.02 0.04 0.02 0.04 0.05 0.06 0.05 0.06 0.02 0.04 0.04 0.03 0.05 0.04 0.03 0.02 0.02 0.01 0.01 0.03

0 0.046 0.074 0.109 0.138 0.178 0.218 0.242 0.291 0.331 0.38 0.407 0.429 0.476 0.544 0.612 0.695 0.776 0.83 0.917 1

0 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0

0 0.216 0.32 0.418 0.492 0.567 0.632 0.669 0.724 0.761 0.796 0.812 0.826 0.85 0.875 0.9 0.923 0.944 0.958 0.979 1

1.5 1.52 1.45 1.44 1.39 1.35 1.35 1.31 1.28 1.24 1.22 1.21 1.18 1.13 1.1 1.06 1.03 1.02 1.007 1

0.2 0.1 0.07 0.05 0.04 0.03 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0

u(x1)

0 0 0.003 0.248 1.22 0.003 0.347 1.31 0.003 0.389 1.24 0.003 0.472 1.23 0.006 0.544 1.18 0.006 0.597 1.17 0.006 0.63 1.17 0.006 0.669 1.16 0.005 0.701 1.14 0.006 0.703 1.15 0.005 0.725 1.14 0.005 0.748 1.15 0.005 0.775 1.14 0.003 0.81 1.15 0.003 0.836 1.14 0.003 0.868 1.11 0.003 0.928 1.05 0.003 0.95 1.03 0.003 0.968 1.013 0.003 0.981 1.01 0.003 0.995 1.008 0 1 1 (b) MTBE (1) + 2-butanol (2) a 90.1 kPa

u(γ1) 0.07 0.06 0.04 0.04 0.05 0.04 0.04 0.03 0.03 0.03 0.03 0.03 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.009 0.008 0

γ2

u(γ2)

1 1 0.99 0.99 0.99 1.01 1.01 1.02 1.01 1.03 1.04 1.05 1.05 1.07 1.04 1.04 1.06 1.15 1.2 1.3 1.4 1.5

0 0.01 0.01 0.01 0.01 0.02 0.02 0.02 0.02 0.02 0.03 0.03 0.03 0.03 0.03 0.03 0.04 0.07 0.1 0.2 0.3 0.5

γ2

u(γ2)

1 0.99 0.97 0.98 0.99 1 1 0.99 1 1.01 1.02 1.05 1.05 1.07 1.14 1.18 1.28 1.4 1.5 1.7

0 0.01 0.01 0.01 0.02 0.02 0.02 0.02 0.02 0.03 0.03 0.03 0.03 0.04 0.05 0.06 0.09 0.1 0.2 0.4

u(y1) = 0.003. cu(y1) = 0.004.

4. RESULTS AND DISCUSSION

small positive deviation from Raoult’s law and the activity coefficients are close to one for both mixtures (see Figures 1 and 2). No azeotropic behavior was observed for the investigated binary mixtures. The prediction of VLE behavior by UNIFACDortmund is slightly closer to the measured VLE than the prediction with COSMO-RS model (see Figures 1 to 3, Table 5). The UNIFAC-Dortmund model is equally good for mixtures containing tert-amyl alcohol and 2-butanol, whereas COSMO-RS

4.1. VLE. The measured VLE data at 90.1 kPa for the MTBE (1) + tert-amyl alcohol (2) and the MTBE (1) + 2-butanol binary mixture are presented in Table 3a,b together with the estimated uncertainties of the measured values. Isothermal measurements for both binary mixtures are shown in Table 4a for the MTBE (1) + tert-amyl alcohol (2) binary mixture and in Table 4b for the MTBE (1) + 2-butanol binary mixture. Both mixtures show D



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Table 4. Isothermal Vapor−liquid Equilibrium Data at 323.2 K, Composition of MTBE in Liquid (x1) and in Vapor (y1), Mixture Temperature (T), Mixture Pressure, and Activity Coefficients (γ1, γ2) and the Variable Uncertainties (u)


(a) MTBE (1) + tert-amyl alcohol (2)

a

P/kPac

T/K

u(T)/K

x1a

y1b

86 81.1 76.6 71.5 65.3 66.9 59.2 52.8 43.3 39.5 33.6

323.2 323.2 323.16 323.16 322.94 323.15 323.14 323.19 323.16 323.2 323.22

0.1 0.1 0.03 0.03 0.01 0.03 0.03 0.05 0.02 0.1 0.06

P/kPac

T/K

u(T)/K

x1a

y1b

10.8 18.9 22.8 36.9 43.4 47.4 51.2 61.5 69.2 75.1 78.7 85.8

323.1 323.1 323.13 323.1 323.1 323.1 323.0 323.08 323.13 323.11 323.11 323.1

0.2 0.1 0.02 0.1 0.1 0.2 0.1 0.04 0.03 0.01 0.01 0.1

0 0.069 0.106 0.242 0.318 0.37 0.427 0.586 0.722 0.828 0.891 1

0 0.468 0.575 0.775 0.825 0.85 0.87 0.912 0.941 0.958 0.972 1

1 1 0.935 0.988 0.872 0.976 0.797 0.962 0.71 0.945 0.725 0.948 0.607 0.922 0.509 0.895 0.379 0.844 0.332 0.824 0.259 0.764 (b) MTBE (1) + 2-butanol (2)

γ1

u(γ1)

γ2

u(γ2)

1 1 1.006 1.01 1.03 1.03 1.06 1.1 1.15 1.17 1.18

0 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.02 0.02 0.03

1.4 1.4 1.3 1.2 1.21 1.13 1.09 1.06 1.01 1.04

0.4 0.2 0.1 0.08 0.09 0.06 0.05 0.03 0.03 0.03

γ1

u(γ1)

γ2

u(γ2)

1 1.00 0.98 1.00 1.02 1.03 1.07 1.19 1.3 1.6 1.8

0 0.02 0.03 0.03 0.04 0.05 0.05 0.07 0.1 0.2 0.3

1.5 1.58 1.41 1.34 1.3 1.25 1.14 1.06 1.02 1.01 1

0.1 0.08 0.04 0.03 0.03 0.02 0.01 0.01 0.03 0.01 0

u(x1) = 0.003. bu(y1) = 0.003. cu(P) = 0.2 kPa.

Figure 1. Isobaric VLE at 90.1 kPa of (a) MTBE (1) + tert-amyl alcohol (2) mixture; (b) MTBE (1) + 2-butanol (2); tert-amyl alcohol mixture experimental points (squares, ■), 2-butanol experimental points (black circles, ●), solid lines (−) are NRTL model, dash lines (--- ) are UNIFACDortmund models and dash−dot lines (-·-·-·) are COSMO-RS model.

for NRTL and UNIFAC-Dortmund models at 363.15 K (Figure 5). But in this case the UNIFAC-Dortmund error is smaller compared with that of COSMO-RS (see also Table 5). The COSMO-RS model overestimates the excess molar enthalpy for all mixtures except MTBE + 2-butanol at 363.15 K. In Figure 6, the molar excess enthalpies for the MTBE + 2-butanol mixture at 308.15 K, 322.6 K, and at 363.15 K are plotted to demonstrate temperature dependency of the experimentally determined and modeled hE. As can be seen, the excess enthalpy decreases with temperature (Figure 6a). The same change of hE with temperature is observed for the UNIFACDortmund model, but the COSMO-RS model predicts increase of hE with temperature. 4.3. Correlation Models for Activity Coefficients. An in-house software VLEFIT31 was used for fitting NRTL and

is slightly more accurate for the 2-butanol containing mixtures in comparison with the tert-amyl alcohol containing mixtures (see also Table 5). 4.2. Excess Enthalpy. Experimental data on molar excess enthalpy at three different temperatures are given in Table 6 a,b and in Figures 4 to 6. In Figure 4 the excess molar enthalpy for two binary mixtures (MTBE + tert-amyl alcohol and MTBE + 2-butanol) at 322.6 K are compared. The results of ICCF and AU measurements are well in line (Figure 4), even though the measurements were made with a small difference in temperature. The absolute value of hE is higher for the 2-butanol mixture: about 250 J·mol−1 at maximum. For both mixtures the NRTL model described the molar excess enthalpy well. The UNIFACDortmund model shows considerable deviation from the experimental data: it underestimates hE. The same behavior is observed E



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Figure 2. Isothermal VLE at 323.1 K of (a) MTBE (1) + tert-amyl alcohol (2) mixture; (b) MTBE (1) + 2-butanol (2); tert-amyl alcohol mixture experimental points (squares, ■), 2-butanol experimental points (circles, ●), solid lines (−) are NRTL model, dash lines (---) are UNIFAC-Dortmund models and dash−dot lines (-·-·-·) are COSMO-RS model.

Figure 3. Activity coefficients for isobaric VLE at 90.1 kPa for (a) MTBE (1) + tert-amyl alcohol (2) mixture; (b) MTBE (1) + 2-butanol (2) mixture: tert-amyl alcohol mixture experimental points (squares, ■), 2-butanol experimental points (circles, ●), solid lines (−) are NRTL model, dash lines (---) are UNIFAC-Dortmund models and dash−dot lines (-·-·-·) are COSMO-RS model.

Table 5. Absolute Average Pressure Deviation (ΔP), Absolute Average Temperature Deviation (ΔT), Absolute Average Vapor Phase Composition Deviation (Δy) and Absolute Average Molar Excess Enthalpy Deviation (ΔhE) for the Binary Mixture Containing MTBE MTBE (1) + tert-amyl alcohol (2)

ΔP/kPab,c

ΔP =

ΔT/Kd

ΔT =

Δy·100

Δy =

Δγ1·100 Δγ2·100

UNIQUAC

UNIF-Da

0.16

0.24

0.18

0.28

0.30

0.30

0.30

MTBE (1) + 2-butanol (2)

COSMO-RS

NRTL

UNIQUAC

UNIF-D

COSMO-RS

3.24

0.16

0.36

0.83

1.41

0.53

2.35

0.11

0.15

0.70

1.78

0.36

2.08

0.44

0.47

0.34

0.86

N

1 N

∑ |Pkexp − Pkcalc|

1 N

∑ |Tkexp − Tkcalc|

k=1 N k=1 N

100 N

∑ |y1,expk − y1,calck |

100 N

− γicalc | ∑ |γiexp ,k ,k

Δγi =

NRTL

k=1

N k=1

1.47

1.37

1.71

9.40

1.41

1.29

3.69

7.57

2.34

2.09

2.40

14.60

2.99

3.67

3.96

7.04

N

ΔhE/J·mol−1 a

ΔhE =

1 · ∑ |hkE,exp − hkE,calc| N k=1

10.2

18.9

46.8

188.8

16.8

21.0

152.2

120.9

UNIF-D is UNIFAC-Dortmund model. bOnly for isothermal data. ck is an experimental point index and N is total number of measured points. Only for isobaric data.

d

The results of yi, P, or hE predictions were compared with experimentally measured values (see Table 5). As can be seen from Table 5, the NRTL model best describes the experimental data measured at this work, including excess molar enthalpy data. The accuracy of the UNIQUAC model is slightly worse, but the average pressure deviations of both models are comparable with the pressure measurement accuracy. Also the residuals of both models in vapor composition are of the same range with the

UNIQUAC model parameters (Table 7) by minimization of the following objective function (OBJ): NPVLE

OBJ =

∑ i=1

Pcalc, i − Pmeas, i Pmeas, i

NPHE

+

∑ i=1

E E hcalc, i − hmeas, i E hmeas, i

(4)

where NPVLE is the number of measured VLE points and NPHE is the number of measured excess molar enthalpy points. F



Article

Table 6. Experimental Molar Excess Enthalpy (hE) at 322.6, 323.15, and 363.15 Ka, Composition of MTBE (x1) and the Variable Uncertainties (u) (a) MTBE (1) + tert-amyl alcohol (2)


363.15 Kb, 1085 ± 53 kPa

323.15 Kb, 317 ± 17 kPa

322.6 Kc, 204 ± 10 kPa

x1

u(x1)

hE/J·mol−1

u(hE)c

x1

u(x1)

hE/J·mol−1

u(hE)c

x1

u(x1)

hE/J·mol−1

u(hE)c

0.099 0.099 0.2 0.3 0.4 0.4 0.48 0.5 0.6 0.7 0.799 0.892 0.9 0.9 0.916 0.932 0.948

0.004 0.004 0.007 0.009 0.01 0.01 0.01 0.01 0.01 0.009 0.007 0.004 0.004 0.004 0.003 0.003 0.002

108 105 218 311 389 400 449 453 470 451 374 241 223 233 187 144 88

2 2 5 7 10 10 10 10 20 20 10 10 10 10 8 6 4

0.083 0.199 0.3 0.399 0.476 0.476 0.600 0.700 0.800 0.901 0.901 0.927

0.001 0.002 0.003 0.003 0.003 0.003 0.003 0.003 0.002 0.001 0.001 0.001

85 245 380 518 581 585 660 649 550 331 327 227

2 5 8 10 10 10 10 10 10 7 7 6

0.099 0.198 0.3 0.399 0.498 0.599 0.698 0.698 0.799 0.899

0.001 0.001 0.002 0.002 0.002 0.002 0.002 0.002 0.001 0.001

104 240 386 513 609 664 651 650 553 331

3 6 9 10 10 20 20 20 10 8

(b) MTBE (1) + 2-butanol (2) 363.15 K , 1057 ± 110 kPa

322.6 Kc, 205 ± 10 kPa

b

a

x1

u(x1)

0.933 0.92 0.902 0.901 0.901 0.849 0.801 0.699 0.60 0.50 0.40 0.339 0.300 0.277 0.277 0.204 0.200 0.161 0.149 0.100 0.100 0.075 0.049

0.003 0.003 0.004 0.004 0.004 0.006 0.007 0.009 0.01 0.01 0.01 0.01 0.009 0.009 0.009 0.007 0.007 0.006 0.006 0.004 0.004 0.003 0.002

u(T) = 0.1 K.

b

−1

E

h /J·mol 212 265 332 348 348 487 554 675 709 670 603 508 481 451 431 363 337 321 270 177 184 144 105

E c

u(h )

x1

u(x1)

9 12 14 15 15 20 22 24 23 20 16 13 12 11 11 8 8 7 6 4 4 3 2

0.0996 0.0996 0.198 0.3 0.399 0.496 0.598 0.699 0.799 0.9006

0.001 0.001 0.002 0.002 0.003 0.003 0.003 0.002 0.002 0.001

E

h /J·mol 220 219 447 650 796 884 909 858 700 406

−1

308.15 Kb, 580 ± 54 kPa u(h )

x1

u(x1)

hE/J·mol−1

u(hE)c

5 5 11 16 20 22 22 21 17 10

0.9496 0.9401 0.9262 0.904 0.887 0.8626 0.8626 0.825 0.825 0.797 0.759 0.702 0.663 0.611 0.557 0.485 0.402 0.359 0.31 0.282 0.239 0.207 0.164 0.1357 0.0894 0.0728 0.0614 0.0468

0.0004 0.0004 0.0005 0.0006 0.0007 0.0009 0.0009 0.001 0.001 0.001 0.001 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.001 0.001 0.001 0.0009 0.0006 0.0005 0.0004 0.0003

249 292 348 433 499 567 579 673 681 738 807 882 919 930 947 906 834 771 680 649 545 496 393 287 196 156 129 92

5 6 7 9 10 12 12 14 14 15 17 18 19 19 19 19 17 16 14 13 11 11 9 6 5 4 4 3

E c

Measured at ICCF. cMeasured at AU; J·mol−1.

measured composition uncertainties. Both NRTL and UNIQUAC correlation models are superior to the predictive models. 4.4. Uncertainty Calculations. The uncertainty of the activity coefficient values in Tables 3 and 4, and the composition and the excess molar enthalpy uncertainties in the Table 6 were estimated in accordance with the error propagation theory.32

The derivatives of the equations for the recalculated value were taken analytically with respect to the measured variables. For the recirculation still experiment, the derivatives of the activity coefficients were calculated using the reorganized eq 1 with respect to T, P, x, and y. Fugacity coefficient ratio (φ1/φ10) as well as the exponential term in eq 1 (the Poynting correction) G



Article


Figure 4. Excess molar enthalpy (hE) at 322.6 K, −, NRTL model, ---, UNIFAC−Dortmund model, -·-·-, COSMO-RS model. (a) MTBE (1) + tert-amyl alcohol (2) mixture, ●, experimental points measured at AU at 322.6 K; ×, measured at ICCF at 323.15. (b) MTBE (1) + 2-butanol (2) mixture, ■, experimental points measured at AU at 322.6 K.

Figure 5. Excess molar enthalpy (hE) at 363.15 K, , NRTL model, ---, UNIFAC−Dortmund model, -·-·-, COSMO-RS model. (a) MTBE (1) + tert-amyl alcohol (2) mixture, ●, experimental points; (b) MTBE (1) + 2-butanol (2) mixture, ■, experimental points.

Figure 6. Temperature dependence of excess molar enthalpy hE of MTBE (1) + 2-butanol (2) mixture. (a) ●, experimental data at 363.15 K; -·-·-, NRTL at 363.15 K; ▲, experimental data at 322.6 K; ---, NRTL at 322.6 K; ■, experimental data at 308.15 K; , NRTL at 308.15 K. (b) COSMO−RS at -·-·-, 363.15 K; − − −, 322.6 K; and ---, at 308.15 K. UNIFAC−Dortmund at -×-, at 363.15 K; bold , at 322.6 K; and −, at 308.15 K.

where S is a calorimetric signal, Sbaseline is a sum of the pure component signals at the same conditions, K is a calorimetric sensitivity constant. The uncertainty of the volumetric flows were 0.5 % of the flow set point in accordance with the syringe pump manufacturer, the uncertainty of the pure component molar volumes were estimated based on scattering of the data available in literature3 for the measurement temperature. The heat value uncertainty, (S−Sbaseline)/K, was estimated by equipment calibration with the reference ethanol−water system, as it was described in section 3.1.

were both assumed to be 1 for the uncertainty estimation, as their contributions in the derivatives of temperature, pressure, and composition are negligible. For calculation of the excess enthalpy uncertainty, the derivative of eq 5 was calculated with respect to the component volumetric flows (vi), the component molar volumes vi and the measured heat value (S/K). −1 S − S baseline ⎛ v1 v2 ⎞ h = ·⎜ + ⎟ K v2 ⎠ ⎝ v1 E

(5) H



Article

Table 7. Parameters (aijk) of NRTL and UNIQUAC Models a120/Ka NRTLb UNIQUACc

987.9 763.2

NRTL UNIQUAC

1130.2 752.8

a210/Ka

a211

a122/K−1a

a212/K−1a

−5.686 0.051

−0.00086 0.00509

0.0109 −0.00123

−1.106 0.082

0.00455 0.00374

0.0019 −0.00067

a121

MTBE (1) + tert-Amyl Alcohol (2) 641.2 −2.184 −156.5 −2.870 MTBE (1) + 2-Butanol (2) 149.8 −4.245 −153.0 −2.705

a Model parameters aijk. bNRTL parameters are τij = (gij − gjj)/(RT) and Gij = exp(−αijτij),18 in our work τij = ((a0ij + a1ijT + aij2T2)/T) and αij = 0.4, T in K, R = 8.314 J·mol−1 K−1. cUNIQUAC parameters are τij = ((uij − ujj)/(RT)),19 in our work τij = ((a0ij + a1ijT + aij2T2)/T), R and Q component parameters are given in Table 2.


Table 8. Consistency Test Parameters (A, ΔP%, Δy%, δ, Ii) and Data Quality Factor (Q) for the Measured Binary Systems Containing MTBE test:

area, A

pass criteria:

Aisotherm < 5%, Aisobar < 10%

90.1 kPa 323.1 K

4.8 3.0

90.1 kPa 323.2 K

4.9 5.3

Van Ness ΔP%, Δy% ΔP% < 1%

point, δ

Δy% < 1%

δ < 5%

MTBE (1) + 2-Butanol (2) 0.4 0.5 0.3 0.3 MTBE (1) + tert-Amyl Alcohol (2) 0.9 0.4 0.2 0.2

4.5. Consistency Tests. Four consistency tests were performed for the experimental VLE data obtained in this work: the area test,33 the Van Ness test,34 the point test,35 and the infinite dilution test.36 Additionally, the overall data quality factor (Q) was calculated as recommended in ref 37. The quality factor is calculated based on the results of the consistency tests and has the maximum value of 1 for the data that passed all consistency tests (see more details in ref 17). The quality factor varies from 0 to 1 and can serve as a weighting coefficient in model parameter regressions, it is especially useful when incomplete data sets (only xyT data, or xTP data) or low quality data sets are available. Results of the consistency tests and the final data quality factor of the measured data sets are provided in Table 8. The area test was performed also for isobaric data. To do that, the integral J = ∫ 10(hE/(RT2))(∂T/∂x1)P dx1 (see ref 34) was calculated using the NRTL model with parameters optimized in this work. Most of the consistency tests were passed for the investigated binary mixture data (Table 8). A slight scattering of the data is observed in isobaric measurements at high temperature, where MTBE is heated above its boiling temperature. Therefore, the data quality criteria of the infinite dilution test and the point test are not always fulfilled. Similar reduction of the measurement accuracy was observed in the recirculation still equipment earlier,38 and was related to the high difference in a relative volatility of the components. MTBE and the alcohols have more than 40 K difference of the normal boiling point temperature, which means that MTBE is 4 to 8 times more volatile in comparison with tertamyl alcohol or 2-butanol at the experimental conditions. However, the overall quality of the obtained data is high: the quality factor is always larger than 0.8. Good quality of the measured data was also confirmed by visual examination of the slopes of activity coefficients curves at infinite dilution. No activity coefficient extremes were observed for the measured VLE data. The Legendre polynomial description of the activity coefficients for separated sets of our VLE data produces random pressure and composition residuals, which confirms the absence of systematic errors in the measurements.39 There is no criterion for the estimation of the excess molar enthalpy data quality. A scattering of the hE data can be evaluated

infinite dilution, Ii

quality factor

I1 < 30

I2 < 30

Q ∈ [0,1]

7 8

87 7

4 2

0.81 0.91

3.6 2.1

18 27

74 17

0.91 0.88

with average deviation of the data from modeling results. Therefore, the difference between experimental and the NRTL molar excess enthalpy values were calculated (see Table 5). 4.6. Conclusions. VLE data are measured for MTBE + tert-amyl alcohol and MTBE + 2-butanol mixtures with a recirculation still apparatus at constant 90.1 kPa pressure and isothermally at 323.2 K. No azeotropes were found for the investigated binary mixtures. The systems exhibited small positive deviation from Raoult’s law. Molar excess enthalpy was measured for the binary mixtures at 308.2 K, 323 K, and 363.2 K with a static flow calorimeter. The binary mixtures release heat at mixing. Experimental VLE and hE data were used for optimization of the NRTL and UNIQAC model parameters. Also the experimental results were compared with predictive models: UNIFACDortmund and COSMO-RS. UNIFAC-Dortmund was found to be slightly more accurate in the prediction of VLE for the MTBE + alcohol mixtures. Prediction of hE with the considered predictive models is not close to the experimental results, though UNIFAC-Dortmund shows a correct change of the molar excess enthalpy with temperature increase.

■

AUTHOR INFORMATION

Corresponding Author

*Tel. +358 50 361 5082. Fax. +358 9 4702 2694. E-mail: anna.zaytseva@aalto.fi. Funding

The authors would like to acknowledge the Academy of Finland for financial support. Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS The authors would like to acknowledge the IT Center of Science Ltd (CSC) for the provided computing resources. REFERENCES

(1) Hamid, H.; Ali, M. A. In Handbook of MTBE and Other Gasoline Oxygenates; Marcell Dekker: New York, USA, 2004.

I




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