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Viscosities of dimethyl carbonate with alcohols at several temperatures
Fluid Phase Equilibria 216 (2004) 167–174
Viscosities of dimethyl carbonate with alcohols at several temperatures UNIFAC-VISCO interaction parameters (–OCOO–/alcohol) A. Rodr´ıguez, J. Canosa, A. Dom´ınguez, J. Tojo∗ Chemical Engineering Department, Vigo University, P.O. Box 36200 Vigo, Spain Received 28 March 2003; received in revised form 4 July 2003; accepted 29 October 2003
Abstract Viscosities have been determined for the binary mixtures dimethyl carbonate (DMC) + methanol, + ethanol, + 1-propanol, + 2-propanol, + 1-butanol, + 2-butanol, and + 1-pentanol at 293.15, 298.15, 303.15 and 313.15 K and atmospheric pressure. Viscosity deviations for the binary systems were fitted to the Redlich–Kister equation. From the experimental data (DMC or diethyl carbonate with above mentioned alcohols at the same temperatures) the interaction parameters (CH3 OH–OCOO) and (OH–OCOO) have been determined for their application in the UNIFAC-VISCO method, based on contribution groups, to predict the dynamic viscosities of the binary mixtures. Root-mean-square deviations are also gathered. The group contribution thermodynamic viscosity model GC-UNIMOD has been used to predict the dynamic viscosity of the binary mixtures at 298.15 K and their deviations have been shown. © 2003 Elsevier B.V. All rights reserved. Keywords: Viscosities; Dimethyl carbonate; Interaction parameters; UNIFAC-VISCO; Carbonate group
1. Introduction Organic carbonates have been suggested as fuel additives because their use may reduce the vapour pressure of fuels and in turn reduce their emissions to the atmosphere by evaporation [1]. DMC has about three times the oxygen content that MTBE this fact focus it as a strong contender to help the refining industry. DMC has a good blending octane, it does not phase separate in a water stream like some alcohols do, and it is both low toxicity and quickly biodegradable [2]. In this work, we continue our work [3–5] on the determination of interaction parameters of thermodynamic and transport properties of dialkyl carbonates with alkanes and alcohols. We present viscosity data for the binary systems DMC + methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol and 1-pentanol at 293.15, 298.15, 303.15 and 313.15 K. Viscosity deviations for the binary mixtures dimethyl carbonate with alcohols were correlated using the Redlich–Kister [6] equation. Comparison with literature has been made for the binary mixtures dimethyl
∗
Corresponding author. Tel.: +34-986-812287; fax: +34-986-812382. E-mail address: [email protected] (J. Tojo).
0378-3812/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2003.10.014
carbonate + methanol [7] at 298.15 and 303.15 K, dimethyl carbonate + ethanol, dimethyl carbonate + 1-propanol and dimethyl carbonate + 1-pentanol [8] at 293.15, 303.15 and 313.15 K. The predictive UNIFAC-VISCO method [9] can be used to predict viscosities using pure component data and group interaction parameters. As the interaction parameters (CH3 OH–COOO) and (OH–COOO) had not been determined, we have used our experimental data [10] to calculate them and incorporate them into the interaction parameter matrix. In a previous paper, we have determined the interaction parameters OCOO–alkanes [5]. The group contribution thermodynamic viscosity model GC-UNIMOD [11] has been used to predict the dynamic viscosities of the binary mixtures at 298.15 K and the root-mean-square deviations are shown.
2. Experimental 2.1. Chemicals Methanol (99.8 mass%), ethanol (99.9 mass%), 1-propanol (99.8 mass%), 2-propanol (99.9 mass%), 1-butanol (99.8 mass%), 2-butanol (99.5 mass%), and 1-pentanol (99.0
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Table 1a Comparison of physical properties at 298.15 K of pure components with literature data Component
ρ (g cm−3 )
η (mPa s)
Experimental
Literature
Experimental
Literature
Dimethyl carbonate
1.0635
1.0635a
0.585
0.589b
Methanol
0.7866
1.0632b 0.78664c,d
0.553
0.545c 0.5513d 1.0826d 1.9430d 1.968f 2.0436d
Ethanol 1-Propanol
0.7850 0.7995
2-Propanol
0.7809
1-Butanol
0.8059
2-Butanol
0.8024
1-Pentanol
0.8109
a b c d e f g h i
0.78509d 0.79950e
1.105 1.970
0.78126c 0.78090g 0.80575c
2.098
0.8026c 0.80250h 0.81080c
3.115
2.620
3.347
2.571c 2.600f 2.998c 3.084i 3.548c
From [16]. From [17]. From [18]. From [12]. From [19]. From [20]. From [21]. From [22]. From [23].
mass%) were supplied by Merck. DMC (99 mass%) by Fluka. They were degassed by ultrasound and dried over molecular sieves (Aldrich) Type 4 Å, in the case of methanol where Type 3 Å is used. The chemicals were kept in an inert argon atmosphere with a maximum water content of 2×10−6 in mass fraction. The maximum water content of the liquids was determined using a Metrohm 737 KF coulometer. The obtained values showed negligible quantities for the liquids (<0.1 mass%). The solvents were compared with recent published density and dynamic viscosity values at 298.15 K (Table 1a). In Table 1b dynamic viscosities of dimethyl Table 1b Comparison of dynamic viscosities at several temperatures of dimethyl carbonate with literature data Temperature (K)
η (mPa s) Experimental
Literature
293.15
0.626
298.15
0.585
303.15
0.536
313.15
0.494
0.623a 0.630b 0.579a 0.534c 0.548a 0.550b 0.503c 0.486a 0.495b
a b c
From [8]. From [24]. From [7].
carbonate have been compared with literature data at several temperatures. Analysing these experimental values, we consider that the discrepancies in the binary mixtures of the literature data [7] and our experimental data are due to the differences with the pure components. The densities were measured using an Anton Paar DSA-48 digital vibrating tube densimeter with an uncertainty of ±0.0001 g cm−3 . 2.2. Apparatus and procedure The mixtures were prepared by adding known masses of the pure liquids into stoppered bottles with a syringe to prevent preferential evaporation and to reduce possible errors in mole fraction calculations, using a Mettler AT-261 Delta Range balance with a precision of ±10−5 g. Viscosities were measured with an automated AMV 200 Anton Paar microviscometer. This apparatus is based on the rolling ball principle. A gold-covered steel ball rolls down the inside of inclined, sample-filled glass capillary. The apparatus is equipped with an automatic timer (±0.01 s) so the time taken for the ball to roll a fixed distance between two magnetic sensors allows one to evaluate the viscosity of the fluid mixture. The time measuring range is from (12–250 s), the accuracy and the precision in the time measurement is ±0.01 and ±0.1 s, respectively. The capillary was placed in a block, thermostated with a PolyScience controller bath model 9010 with a temperature stability of ±10−2 K. The calibration of the apparatus was done periodically, using three fluids of known viscosity, Millipore quality water and degassed and dried Fluka quality octane and 1-pentanol as reference liquids [12]. These reference fluids have mass fraction purities of 99.5 mass%. The uncertainty in the viscosity and the mole fraction were estimated as better than 2 × 10−3 mPa s and 5 × 10−5 , respectively.
3. Results and discussion The experimental viscosities of the binary mixtures DMC + methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol, 1-pentanol at 293.15, 298.15, 303.15 and 313.15 K, and atmospheric pressure are given in Table 2. Fig. 1 shows the experimental viscosity values at these temperatures and the comparison with the literature data. The experimental densities of these binary mixtures at these temperatures have been published previously [13]. The viscosity deviations are calculated from experimental viscosities of the pure components and the mixture by the equation η (mPa s) = η −
k i=1
(ηoi · xi )
(1)
where η and ηoi are the viscosity of the mixture and the pure component, respectively; xi represents the mole fraction of
A. Rodr´ıguez et al. / Fluid Phase Equilibria 216 (2004) 167–174 Table 2 Viscosity (η) and viscosity deviations (η) of the binary mixtures DMC with alcohols at several temperatures x
η (mPa s)
η (mPa s)
x
η (mPa s)
η (mPa s)
0.553 0.531 0.518 0.502 0.498 0.498 0.504 0.509 0.517 0.53 0.548 0.566 0.585
0 −0.024 −0.038 −0.058 −0.065 −0.068 −0.065 −0.063 −0.058 −0.049 −0.034 −0.018 0
0.450 0.437 0.434 0.428 0.426 0.428 0.429 0.437 0.444 0.451 0.471 0.476 0.494
0 −0.016 −0.020 −0.031 −0.037 −0.039 −0.042 −0.038 −0.037 −0.033 −0.019 −0.015 0
1.105 0.966 0.897 0.786 0.685 0.625 0.594 0.573 0.561 0.555 0.556 0.565 0.585
0 −0.108 −0.159 −0.231 −0.278 −0.280 −0.263 −0.236 −0.192 −0.138 −0.093 −0.053 0
0.826 0.731 0.662 0.535 0.472 0.450 0.440 0.438 0.440 0.445 0.463 0.475 0.494
0 −0.078 −0.133 −0.222 −0.252 −0.246 −0.219 −0.188 −0.152 −0.116 −0.062 −0.035 0
x DMC + (1−x) methanol 293.15 K 0 0.591 0 0.0537 0.567 −0.026 0.0996 0.551 −0.043 0.2058 0.536 −0.062 0.3135 0.533 −0.069 0.4100 0.535 −0.070 0.5086 0.540 −0.069 0.6104 0.545 −0.067 0.7229 0.554 −0.062 0.8338 0.570 −0.050 0.9067 0.586 −0.037 0.9509 0.600 −0.024 1 0.626 0 303.15 K 0 0.514 0 0.0260 0.503 −0.012 0.0707 0.489 −0.027 0.1832 0.469 −0.049 0.2839 0.467 −0.053 0.3823 0.468 −0.054 0.4869 0.472 −0.053 0.5847 0.475 −0.052 0.6832 0.480 −0.049 0.8119 0.496 −0.036 0.8969 0.512 −0.022 0.9581 0.525 −0.010 1 0.536 0
298.15 K 0 0.0506 0.1042 0.2079 0.3011 0.3963 0.4931 0.5890 0.6927 0.8137 0.8997 0.9575 1 313.15 K 0 0.0648 0.1008 0.1978 0.3027 0.3928 0.4855 0.5738 0.7009 0.7838 0.9029 0.9283 1
x DMC + (1−x) ethanol 293.15 K 0 1.194 0 0.0498 1.070 −0.096 0.0978 0.974 −0.164 0.1760 0.853 −0.241 0.2928 0.740 −0.288 0.4053 0.675 −0.289 0.4981 0.646 −0.265 0.5982 0.625 −0.229 0.6962 0.613 −0.186 0.8024 0.609 −0.129 0.8894 0.607 −0.082 0.9516 0.618 −0.035 1 0.626 0 303.15 K 0 0.972 0 0.0673 0.832 −0.111 0.1142 0.752 −0.170 0.2249 0.627 −0.247 0.2894 0.588 −0.258 0.3906 0.541 −0.261 0.4848 0.521 −0.240 0.5996 0.512 −0.199 0.6931 0.513 −0.157 0.8038 0.512 −0.110 0.9072 0.520 −0.056 0.9462 0.527 −0.032 1 0.536 0
298.15 K 0 0.0598 0.0950 0.1692 0.2725 0.3854 0.4778 0.5686 0.6777 0.7915 0.8775 0.9366 1 313.15 K 0 0.0504 0.0934 0.2082 0.3087 0.3930 0.5026 0.6011 0.7052 0.7968 0.9075 0.9507 1
x DMC + (1−x) 1-propanol 293.15 K 0 2.198 0
298.15 K 0 1.97
0
169
Table 2 (Continued ) x
η (mPa s)
η (mPa s)
x
η (mPa s)
η (mPa s)
0.0508 0.0875 0.1647 0.2944 0.3858 0.5440 0.6026 0.7041 0.8900 0.9015 0.9510 1 303.15 K 0 0.0728 0.0829 0.1840 0.2605 0.3758 0.4849 0.6278 0.7071 0.8061 0.9018 0.9507 1
1.875 1.683 1.362 1.024 0.885 0.751 0.716 0.666 0.610 0.606 0.608 0.626
−0.243 −0.377 −0.577 −0.711 −0.706 −0.592 −0.535 −0.425 −0.189 −0.175 −0.095 0
1.675 1.493 1.147 0.936 0.803 0.725 0.673 0.631 0.598 0.579 0.576 0.585
−0.223 −0.353 −0.559 −0.633 −0.621 −0.555 −0.467 −0.367 −0.263 −0.145 −0.080 0
1.707 1.404 1.367 1.072 0.919 0.769 0.685 0.613 0.594 0.569 0.554 0.542 0.536
0 −0.218 −0.243 −0.420 −0.483 −0.498 −0.454 −0.359 −0.285 −0.194 −0.097 −0.052 0
0.0517 0.0898 0.1903 0.2896 0.3944 0.4980 0.5993 0.7016 0.8007 0.8994 0.9490 1 313.15 K 0 0.0498 0.0973 0.1985 0.3015 0.4025 0.5021 0.6029 0.7038 0.8033 0.9073 0.9510 1
1.361 1.198 1.066 0.860 0.721 0.639 0.584 0.546 0.521 0.500 0.489 0.489 0.494
0 −0.120 −0.211 −0.329 −0.379 −0.373 −0.342 −0.292 −0.230 −0.165 −0.085 −0.047 0
x DMC + (1−x) 2-propanol 293.15 K 0 2.386 0 0.0526 1.968 −0.325 0.0934 1.706 −0.516 0.2033 1.212 −0.816 0.3129 0.943 −0.892 0.4065 0.817 −0.854 0.5000 0.740 −0.766 0.6079 0.686 −0.630 0.7026 0.647 −0.502 0.8048 0.609 −0.361 0.9008 0.593 −0.208 0.9507 0.601 −0.112 1 0.626 0 303.15 K 0 1.763 0 0.0437 1.537 −0.172 0.1028 1.287 −0.350 0.2013 0.992 −0.524 0.3062 0.802 −0.585 0.3840 0.713 −0.579 0.4951 0.642 −0.514 0.5998 0.606 −0.421 0.7053 0.581 −0.317 0.8047 0.562 −0.214 0.9062 0.545 −0.106 0.9370 0.542 −0.071 1 0.536 0
298.15 K 0 0.0498 0.0979 0.2031 0.2999 0.3972 0.4892 0.5938 0.6971 0.7983 0.9012 0.9451 1 313.15 K 0 0.0507 0.0997 0.1984 0.2975 0.4001 0.4884 0.5959 0.7017 0.8014 0.9053 0.9492 1
2.098 1.733 1.454 1.046 0.844 0.740 0.690 0.654 0.625 0.589 0.567 0.567 0.585
0 −0.290 −0.496 −0.745 −0.800 −0.757 −0.668 −0.546 −0.418 −0.301 −0.167 −0.101 0
1.325 1.147 1.005 0.799 0.668 0.592 0.553 0.522 0.506 0.494 0.490 0.491 0.494
0 −0.136 −0.237 −0.361 −0.410 −0.401 −0.366 −0.308 −0.236 −0.165 −0.083 −0.045 0
x DMC + (1−x) 1-butanol 293.15 K 0 2.941 0 0.0518 2.461 −0.360 0.0975 2.119 −0.596 0.1961 1.586 −0.901 0.3064 1.218 −1.014 0.4108 1.023 −0.967
298.15 K 0 0.0527 0.1009 0.2002 0.2986 0.3974
2.620 2.192 1.877 1.411 1.127 0.952
0 −0.321 −0.538 −0.802 −0.885 −0.859
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Table 2 (Continued ) x
η (mPa s)
η (mPa s)
x
η (mPa s)
η (mPa s)
x
η (mPa s)
η (mPa s)
x
η (mPa s)
η (mPa s)
0.4769 0.6101 0.7043 0.8043 0.9052 0.9508 1 303.15 K 0 0.0249 0.0960 0.1911 0.2998 0.3877 0.4799 0.5865 0.6907 0.7931 0.8925 0.9464 1
0.929 0.794 0.719 0.644 0.607 0.605 0.626
−0.908 −0.735 −0.591 −0.435 −0.238 −0.135 0
0.831 0.748 0.673 0.611 0.572 0.569 0.585
−0.764 −0.649 −0.517 −0.379 −0.224 −0.117 0
−0.174 0
−0.139 0
1.754 1.536 1.351 1.018 0.880 0.752 0.662 0.598 0.557 0.520 0.497 0.494 0.494
0 −0.155 −0.277 −0.455 −0.496 −0.499 −0.455 −0.396 −0.327 −0.225 −0.121 −0.067 0
2.932 2.488 2.228 1.660 1.416 1.066 0.890 0.759 0.661 0.601 0.560 0.542 0.536
0 −0.315 −0.487 −0.798 −0.890 −0.931 −0.861 −0.755 −0.612 −0.433 −0.229 −0.040 0
0.9494 1 313.15 K 0 0.0467 0.1037 0.2514 0.3005 0.3996 0.5052 0.6059 0.7024 0.8053 0.9051 0.9651 1
0.586 0.585
0 −0.134 −0.424 −0.622 −0.694 −0.686 −0.643 −0.566 −0.460 −0.328 −0.174 −0.086 0
0.9503 1 303.15 K 0 0.0539 0.0906 0.1979 0.2613 0.3902 0.4928 0.5918 0.6923 0.7920 0.8943 0.9808 1
0.619 0.626
2.255 2.078 1.666 1.304 1.046 0.903 0.787 0.681 0.608 0.564 0.547 0.542 0.536
0.5039 0.6008 0.7028 0.8011 0.8965 0.9503 1 313.15 K 0 0.0499 0.0998 0.2234 0.3000 0.3991 0.5054 0.6030 0.6904 0.8009 0.9014 0.9471 1
2.256 1.972 1.678 1.161 1.046 0.876 0.750 0.659 0.596 0.540 0.502 0.494 0.494
0 −0.202 −0.395 −0.652 −0.680 −0.676 −0.616 −0.529 −0.422 −0.297 −0.159 −0.062 0
x DMC + (1−x) 2-butanol 293.15 K 0 3.619 0 0.0505 2.908 −0.560 0.0986 2.370 −0.954 0.2131 1.522 −1.459 0.2801 1.235 −1.546 0.4092 0.940 −1.454 0.5110 0.830 −1.260 0.6172 0.753 −1.019 0.7072 0.696 −0.806 0.7997 0.637 −0.589 0.8229 0.621 −0.535 0.9518 0.595 −0.175 1 0.626 0 303.15 K 0 2.503 0 0.0573 1.931 −0.459 0.0842 1.728 −0.609 0.1936 1.195 −0.927 0.2981 0.943 −0.974 0.3926 0.809 −0.922 0.4938 0.709 −0.823 0.5900 0.632 −0.710 0.6561 0.594 −0.618 0.7945 0.549 −0.391 0.8916 0.547 −0.202 0.9483 0.546 −0.092 1 0.536 0
298.15 K 0 0.0572 0.0994 0.1958 0.3029 0.3339 0.5075 0.6051 0.7037 0.808 0.9046 0.9523 1 313.15 K 0 0.0498 0.1005 0.2009 0.2952 0.4047 0.5109 0.6072 0.6982 0.7992 0.8977 0.9583 1
3.115 2.399 1.991 1.354 0.991 0.926 0.756 0.707 0.641 0.569 0.531 0.542 0.585
0 −0.571 −0.873 −1.266 −1.358 −1.344 −1.075 −0.877 −0.694 −0.502 −0.295 −0.164 0
1.784 1.512 1.289 0.975 0.795 0.669 0.600 0.561 0.529 0.502 0.486 0.486 0.494
0 −0.208 −0.365 −0.550 −0.608 −0.593 −0.525 −0.440 −0.354 −0.251 −0.140 −0.062 0
x DMC + (1−x) 1-pentanol 293.15 K 0 3.979 0 0.0482 3.367 −0.450 0.0991 2.836 −0.811 0.1941 2.110 −1.218 0.2974 1.605 −1.377 0.3939 1.304 −1.354 0.4993 1.092 −1.213 0.6000 0.939 −1.028 0.7013 0.810 −0.818 0.8013 0.704 −0.588 0.8915 0.635 −0.355
298.15 K 0 0.0457 0.1016 0.1979 0.3057 0.4024 0.5030 0.5793 0.7034 0.8003 0.9018
3.347 2.905 2.460 1.880 1.441 1.179 0.988 0.878 0.739 0.655 0.597
0 −0.316 −0.606 −0.920 −1.062 −1.057 −0.970 −0.869 −0.665 −0.482 −0.259
the pure component and k is the number of components in the mixture. The binary viscosity deviations were fitted to a Redlich– Kister type equation η (mPa s) = (x − x2 ) ·
M
Bp · (2x − 1)p
(2)
p=0
where x is the mole fraction, Bp are fitting parameters and M is the degree of the polynomic expansion, which was optimised using the F-test [14]. The viscosity deviations of the binary mixtures at several temperatures are given in Table 2. The fitting parameters are given in Table 3, together with the root-mean-square deviations. These ones are calculated by applying the values of the experimental and calculated viscosity deviations, and the number of experimental data are represented by ηexp , ηcal and nDAT , respectively. 1/2 n DAT (ηexp − ηcal )2 i σ= (3) nDAT Fig. 2 shows viscosity deviations for the binary mixtures dimethyl carbonate with alkanes at 293.15, 298.15, 303.15 and 313.15 K, respectively, plotted against mole fraction together with the fitted curve, obtained from the Redlich–Kister equation. The viscosity deviations for these systems at these temperatures are negative over the entire composition range for the whole of the binaries at the above temperatures. 3.1. Results obtained using UNIFAC-VISCO method To increase the application range of the predictive UNIFAC-VISCO method, based on a group contribution scheme, we have determined the interaction parameters corresponding to carbonate (–OCOO–) with alcohols (–OH) and methanol (CH3 OH) as other group. The UNIFAC-VISCO parameters have been calculated from our experimental values of dynamic viscosities, involving to the
A. Rodr´ıguez et al. / Fluid Phase Equilibria 216 (2004) 167–174
binary mixtures dimethyl carbonate or diethyl carbonate with methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol and 1-pentanol at 293.15, 398.15, 303.15 and 313.15 K, using the Nelder and Mead [15] equation for minimising the following objective function: N
O.F. =
1 |νi,exp − νi,calc | N νi,exp i=1
(4)
171
where N is the number of experimental data, and νexp and νcalc are the experimental and calculated kinematic viscosity, respectively. In this work it is necessary for the prediction of the viscosity of the binary mixtures to use the interaction parameters (–OCOO–) with alkanes which have been determined previously [5]. The carbonate–alcohol interaction parameters, obtained from our experimental data, are summarised in Table 4a.
Fig. 1. Dynamic viscosities (η) for the binary mixtures (a) dimethyl carbonate + methanol (b) dimethyl carbonate + ethanol (c) dimethyl + 1-propanol (d) dimethyl carbonate + 2-propanol (e) dimethyl carbonate + 1-butanol (f) dimethyl carbonate + 2-butanol (g) dimethyl + 1-pentanol at (䊊), 293.15 K (䊐), 298.15 K ( ), 303.15 K and (䉫), 313.15 K and the calculated values using UNIFAC-VISCO at (· · · · · · ), (-•-•-•-), 298.15 K; (— — —), 303.15 K and (– – –), 313.15 K. Comparison with literature data: in (a) Aminabhavi et al. (䉱), 298.15 K (䉲), In (b), (c) and (g) Romano et al. (䊉), 293.15 K (䊏), 303.15 K (䉬), 313.15 K.
carbonate carbonate 293.15 K; 303.15 K.
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Fig. 1. (Continued ).
The group volumes and surface areas are shown in Table 4b. In Table 5a the root-mean-square deviations between experimental and calculated viscosity deviations are shown. In view of the results shown in this table we can say that good results are obtained when we used the UNIFAC-VISCO method to calculate the dynamic viscosities of the binary mixtures for the linear alcohols, however these results are worse for the secondary alcohols with dimethyl carbonate. Figs. 1 and 2 show graphically the obtained values of viscosity and viscosity deviations, respectively, for the binary mixtures dimethyl carbonate with methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol and 1-pentanol at 293.15, 298.15, 303.15 and 313.15 K by applying the UNIFAC-VISCO method. Graphically we
Fig. 2. Curves (—) of viscosity deviations (η) from the Redlich–Kister equation, Eq. (2), for the binary mixtures (a) dimethyl carbonate + methanol (b) dimethyl carbonate + ethanol (c) dimethyl carbonate + 1-propanol (d) dimethyl carbonate + 2-propanol (e) dimethyl carbonate + 1-butanol (f) dimethyl carbonate + 2-butanol (g) dimethyl carbonate + 1-pentanol at (䊊), 293.15 K (䊐), 298.15 K ( ), 303.15 K and (䉫), 313.15 K and the calculated values using UNIFAC-VISCO at (· · · · · · ), 293.15 K; (-•-•-•-), 298.15 K; (— — —), 303.15 K and (– – –), 313.15 K.
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173
Table 4a The UNIFAC-VISCO interaction parameters αmn
Parameters CH3 OH–OCOO OCOO–CH3 OH OH–OCOO OCOO–OH
162.2 −208.1 3237.5 105.9
Table 4b Group volume and surface area parameters
Fig. 2. (Continued )
can observe in Fig. 1a how the binary mixture dimethyl carbonate + methanol obtains better results by applying UNIFAC-VISCO method at high temperatures; however, Table 3 Fitting parameters and root-mean-square deviations (σ) for the binary systems DMC with alcohols at several temperatures using the Eqs. (2) and (3), respectively T (K)
B0
−0.2695 −0.2155 −0.1598 −0.0966
DMC + ethanol 293.15 −1.0593 298.15 −1.0264 303.15 −0.9351 313.15 −0.8881
0.6456 0.5968 0.6421 0.5876
−0.4291 −0.4975 −0.3867 −0.4129
DMC + 1-propanol 293.15 −2.5276 298.15 −2.2148 303.15 −1.7944 313.15 −1.3705
1.6834 1.6064 1.2314 0.8546
−1.2080 −1.1026 0.5242 −0.5110
0.001 0.001 0.002 0.001
DMC + 2-propanol 293.15 −3.0545 298.15 −2.6210 303.15 −2.0383 313.15 −1.4474
2.3030 2.2993 1.5819 1.0290
−1.7407 −1.7397 −0.7629 −0.5614
0.001 0.001 0.001 0.001
DMC + 1-butanol 293.15 −3.5182 298.15 −3.0722 303.15 −2.5232 313.15 1.8425
2.4472 2.1869 1.3100 1.0678
−1.9536 −1.7230 −1.2399 −0.5936
0.001 0.001 0.001 0.001
DMC + 2-butanol 293.15 −5.1343 298.15 −4.3511 303.15 −3.2574 313.15 −2.1294
4.3486 3.9437 2.1835 1.5526
−3.2360 −3.4671 −2.4176 −1.0215
DMC + 1-pentanol 293.15 −4.8526 298.15 −3.8929 303.15 −3.4368 313.15 −2.4825
3.3560 2.3162 1.8503 1.4990
−2.3834 −1.4062 −1.0570 −0.8918
1.5821 1.3488 1.0000
1.3937 1.0800 1.200
a
The CH–CH3 group considers the R and Q parameters how 2 CH2 .
some differences are observed at 293.15 K. The same results can be observed in Fig. 2a. The results obtained from viscosity deviations using the calculated values are similar and they are not sensitive to the variation of the temperature.
The group contribution thermodynamic viscosity model GC-UNIMOD is based on the original UNIFAC method. The predictive equation has no theoretical foundation, but it is based on experience. The Van der Waals properties for the different subgroups and the group interaction energy parameters used in the GC-UNIMOD model have been calculated, previously [4], from our experimental VLE binary data carbonate with alcohols. When GC-UNIMOD predictive model for viscosities of the binary mixtures at 298.15 K is applied, we can observe worse predictive results than UNIFAC-VISCO because the group interaction energy parameters used have been obtained from VLE data while UNIFAC-VISCO one applies its own parameters. In Table 5b the root-mean-square deviations between experimental and calculated viscosity deviations are shown.
0.0306 0.0349 0.0225 0.0031
0.9162
OCOO CH–CH3 a OH
0.001 0.001 0.001 0.001
DMC + methanol 293.15 −0.2743 298.15 −0.2597 303.15 −0.2140 313.15 −0.1615
−0.1218
Qk
3.2. Results obtained using GC-UNIMOD method
B2
0.1099
Rk
σ
B1
B3
Group
0.001 0.001 0.002 0.001
Table 5a Root-mean-square deviations of dynamic viscosity σ(η) resulting by using UNIFAC-VISCO model at several temperatures and 13 number of data points for the binary mixtures System
1.9720
0.4186
0.002 0.001 0.002 0.001 0.002 0.002 0.002 0.002
DMC + Methanol Ethanol 1-Propanol 2-Propanol 1-Butanol 2-Butanol 1-Pentanol
T (K) 293.15
298.15
303.15
313.15
0.028 0.036 0.015 0.076 0.020 0.163 0.040
0.023 0.024 0.019 0.081 0.021 0.178 0.072
0.014 0.021 0.036 0.026 0.030 0.101 0.058
0.009 0.014 0.031 0.016 0.046 0.023 0.050
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Table 5b Root-mean-square deviations of dynamic viscosity σ(η) resulting by the prediction using GC-UNIMOD model at 298.15 K for the binary mixtures System DMC DMC DMC DMC DMC DMC DMC
+ methanol + ethanol + 1-propanol + 2-propanol + 1-butanol + 2-butanol + 1-pentanol
σ 0.024 0.120 0.242 0.323 0.346 0.566 0.414
4. Conclusions In this paper we have determined the experimental dynamic viscosities of the binary mixtures DMC with methanol, or ethanol, or 1-propanol, or 2-propanol, or 1-butanol, or 2-butanol, or 1-pentanol at 293.15, 298.15 303.15 and 313.15 K. In order to test the quality of the experimental values we have calculated the viscosity deviations for the above binary mixtures at the interval of temperatures and we have fitted these results at a Redlich–Kister equation. Comparison with literature data have been made for the binary mixtures dimethyl carbonate + methanol, + ethanol, + 1-propanol, and 1-pentanol. Serious discrepancies are shown in the viscosity data for the binary mixture dimethyl carbonate + methanol and dimethyl carbonate at 298.15 and 303.15 K. However similar results are obtained for the other mixtures. The UNIFAC-VISCO predictive method has been used to obtain calculated values of the viscosity at different temperatures. Due to the interaction parameters (–OCOO–) with alcohols were not calculated, we have used the experimental values to calculate them. The group contribution thermodynamic viscosity model GC-UNIMOD has already been used to predict the dynamic viscosities of the binary mixtures at 298.15 K. We have obtained good calculated results when we use UNIFAC-VISCO method using the calculated parameters for the binary mixtures. Analysing these results, we can say that the best ones are obtained for linear alcohols. The binary mixtures dimethyl carbonate + methanol obtain the worst results in calculated viscosity at low temperatures although the methanol is considered as a single group instead of the other alcohols that take into account only the OH group to difference them. The improvement of these values is increased when the temperature is increased too. Related to the GC-UNIMOD results, we can say that this predictive viscosity method obtains worse results than UNIFAC-VISCO due to the group interaction energy parameters of the GC-UNIMOD matrix have been obtained from VLE data however UNIFAC-VISCO obtains them from viscosity data. List of symbols xi the mole fraction k the number of components
x Bp M zexp , zpred nDAT N Greek letters η, ηoi νexp and νcalc
the mole fraction in the Redlich–Kister equation the fitting parameter the degree of the polynomic expansion the experimental and predictive property the number of experimental data the number of experimental data
the viscosity of the mixture and the pure component the experimental and calculated kinematic viscosity
References [1] Y. Katrib, G. Deiber, P. Mirabel, S. Le Calvé, C. George, A. Mellouki, G. Le Bras, J. Atmospheric Chem. 43 (2002) 151–174. [2] M.A. Pacheco, C.L. Marshall, Energy Fuel 11 (1997) 2–29. [3] A. Rodr´ıguez, J. Canosa, A. Dom´ınguez, J. Tojo, Fluid Phase Equilib. 198 (2002) 95–102. [4] A. Rodr´ıguez, J. Canosa, A. Dom´ınguez, J. Tojo, Fluid Phase Equilib. 201 (2002) 187–201. [5] A. Rodr´ıguez, J. Canosa, A. Dom´ınguez, J. Tojo, J. Chem. Eng. Data 48 (2003) 146–151. [6] O. Redlich, A.T. Kister, Ind. Eng. Chem. 40 (1948) 345–348. [7] T.M. Aminabhavi, K. Banerjee, J. Chem. Eng. Data 43 (1998) 1096– 1101. [8] E. Romano, J.L. Trenzado, E. González, J.S. Matos, L. Segade, E. Jiménez, Fluid Phase Equilib. 211 (2003) 219–240. [9] Y. Gaston-Bonhomme, P. Petrino, J.L. Chevalier, J. Chem. Eng. Sci. 49 (1994) 1799–1806. [10] A. Rodr´ıguez, ELV y estudio del comportamiento de los sistemas de dialquil carbonato con alcoholes y alcanos. Determinación de los correspondientes parámetros de interacción entre grupos, Ph Thesis, Vigo University, 2001. [11] W. Cao, K. Knudsen, A. Fredeslund, P. Rasmussen, Ind. Eng. Chem. Res. 32 (1993) 2088–2092. [12] J.A. Riddick, W.B. Bunger, T.K. Sakano, in: Organic Solvents Techniques of Chemistry, fourth ed., vol. 2, Wiley, New York, 1986. [13] A. Rodr´ıguez, J. Canosa, A. Dom´ınguez, J. Tojo, J. Chem. Eng. Data 46 (2001) 1476–1486. [14] P. Bevington, in: Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill, New York, 1969. [15] J.A. Nelder, R. Mead, Comput. J. 7 (1965) 308–313. [16] I. Garcia de la Fuente, J.A. Gonzalez, J.C. Cobos, C. Casanova, J. Solution Chem. 24 (1995) 827–835. [17] A. Pal, G. Dass, A. Kumar, J. Chem. Eng. Data 43 (1998) 738–741. [18] A. Das, M. Frenkel, N.M. Gadalla, K. Marsh, R.C. Wilhoit, in: TRC Thermodynamic Tables, Thermodynamic Research Center, Texas A&M University, College Station, TX, 1994. [19] J. Ortega, J. Chem. Eng. Data 27 (1982) 312–317. [20] D. Papaioannou, C. Panayiotou, J. Chem. Eng. Data 40 (1995) 202– 209. [21] T.M. Aminabhavi, B. Gopalakrishna, J. Chem. Eng. Data 40 (1995) 462–467. [22] M.N. Sovilj, J. Chem. Eng. Data 40 (1995) 1058–1061. [23] P. Cea, C. Lafuente, H. Artigas, F.M. Royo, J.S. Urieta, Can. J. Chem. 72 (1994) 1921–1924. [24] M.J.P. Comuñas, A. Baylaucq, C. Boned, J. Fernández, Int. J. Thermophys. 22 (2001) 749–768.
Viscosities of dimethyl carbonate with alcohols at several temperatures UNIFAC-VISCO interaction parameters (–OCOO–/alcohol) A. Rodr´ıguez, J. Canosa, A. Dom´ınguez, J. Tojo∗ Chemical Engineering Department, Vigo University, P.O. Box 36200 Vigo, Spain Received 28 March 2003; received in revised form 4 July 2003; accepted 29 October 2003
Abstract Viscosities have been determined for the binary mixtures dimethyl carbonate (DMC) + methanol, + ethanol, + 1-propanol, + 2-propanol, + 1-butanol, + 2-butanol, and + 1-pentanol at 293.15, 298.15, 303.15 and 313.15 K and atmospheric pressure. Viscosity deviations for the binary systems were fitted to the Redlich–Kister equation. From the experimental data (DMC or diethyl carbonate with above mentioned alcohols at the same temperatures) the interaction parameters (CH3 OH–OCOO) and (OH–OCOO) have been determined for their application in the UNIFAC-VISCO method, based on contribution groups, to predict the dynamic viscosities of the binary mixtures. Root-mean-square deviations are also gathered. The group contribution thermodynamic viscosity model GC-UNIMOD has been used to predict the dynamic viscosity of the binary mixtures at 298.15 K and their deviations have been shown. © 2003 Elsevier B.V. All rights reserved. Keywords: Viscosities; Dimethyl carbonate; Interaction parameters; UNIFAC-VISCO; Carbonate group
1. Introduction Organic carbonates have been suggested as fuel additives because their use may reduce the vapour pressure of fuels and in turn reduce their emissions to the atmosphere by evaporation [1]. DMC has about three times the oxygen content that MTBE this fact focus it as a strong contender to help the refining industry. DMC has a good blending octane, it does not phase separate in a water stream like some alcohols do, and it is both low toxicity and quickly biodegradable [2]. In this work, we continue our work [3–5] on the determination of interaction parameters of thermodynamic and transport properties of dialkyl carbonates with alkanes and alcohols. We present viscosity data for the binary systems DMC + methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol and 1-pentanol at 293.15, 298.15, 303.15 and 313.15 K. Viscosity deviations for the binary mixtures dimethyl carbonate with alcohols were correlated using the Redlich–Kister [6] equation. Comparison with literature has been made for the binary mixtures dimethyl
∗
Corresponding author. Tel.: +34-986-812287; fax: +34-986-812382. E-mail address: [email protected] (J. Tojo).
0378-3812/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2003.10.014
carbonate + methanol [7] at 298.15 and 303.15 K, dimethyl carbonate + ethanol, dimethyl carbonate + 1-propanol and dimethyl carbonate + 1-pentanol [8] at 293.15, 303.15 and 313.15 K. The predictive UNIFAC-VISCO method [9] can be used to predict viscosities using pure component data and group interaction parameters. As the interaction parameters (CH3 OH–COOO) and (OH–COOO) had not been determined, we have used our experimental data [10] to calculate them and incorporate them into the interaction parameter matrix. In a previous paper, we have determined the interaction parameters OCOO–alkanes [5]. The group contribution thermodynamic viscosity model GC-UNIMOD [11] has been used to predict the dynamic viscosities of the binary mixtures at 298.15 K and the root-mean-square deviations are shown.
2. Experimental 2.1. Chemicals Methanol (99.8 mass%), ethanol (99.9 mass%), 1-propanol (99.8 mass%), 2-propanol (99.9 mass%), 1-butanol (99.8 mass%), 2-butanol (99.5 mass%), and 1-pentanol (99.0
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Table 1a Comparison of physical properties at 298.15 K of pure components with literature data Component
ρ (g cm−3 )
η (mPa s)
Experimental
Literature
Experimental
Literature
Dimethyl carbonate
1.0635
1.0635a
0.585
0.589b
Methanol
0.7866
1.0632b 0.78664c,d
0.553
0.545c 0.5513d 1.0826d 1.9430d 1.968f 2.0436d
Ethanol 1-Propanol
0.7850 0.7995
2-Propanol
0.7809
1-Butanol
0.8059
2-Butanol
0.8024
1-Pentanol
0.8109
a b c d e f g h i
0.78509d 0.79950e
1.105 1.970
0.78126c 0.78090g 0.80575c
2.098
0.8026c 0.80250h 0.81080c
3.115
2.620
3.347
2.571c 2.600f 2.998c 3.084i 3.548c
From [16]. From [17]. From [18]. From [12]. From [19]. From [20]. From [21]. From [22]. From [23].
mass%) were supplied by Merck. DMC (99 mass%) by Fluka. They were degassed by ultrasound and dried over molecular sieves (Aldrich) Type 4 Å, in the case of methanol where Type 3 Å is used. The chemicals were kept in an inert argon atmosphere with a maximum water content of 2×10−6 in mass fraction. The maximum water content of the liquids was determined using a Metrohm 737 KF coulometer. The obtained values showed negligible quantities for the liquids (<0.1 mass%). The solvents were compared with recent published density and dynamic viscosity values at 298.15 K (Table 1a). In Table 1b dynamic viscosities of dimethyl Table 1b Comparison of dynamic viscosities at several temperatures of dimethyl carbonate with literature data Temperature (K)
η (mPa s) Experimental
Literature
293.15
0.626
298.15
0.585
303.15
0.536
313.15
0.494
0.623a 0.630b 0.579a 0.534c 0.548a 0.550b 0.503c 0.486a 0.495b
a b c
From [8]. From [24]. From [7].
carbonate have been compared with literature data at several temperatures. Analysing these experimental values, we consider that the discrepancies in the binary mixtures of the literature data [7] and our experimental data are due to the differences with the pure components. The densities were measured using an Anton Paar DSA-48 digital vibrating tube densimeter with an uncertainty of ±0.0001 g cm−3 . 2.2. Apparatus and procedure The mixtures were prepared by adding known masses of the pure liquids into stoppered bottles with a syringe to prevent preferential evaporation and to reduce possible errors in mole fraction calculations, using a Mettler AT-261 Delta Range balance with a precision of ±10−5 g. Viscosities were measured with an automated AMV 200 Anton Paar microviscometer. This apparatus is based on the rolling ball principle. A gold-covered steel ball rolls down the inside of inclined, sample-filled glass capillary. The apparatus is equipped with an automatic timer (±0.01 s) so the time taken for the ball to roll a fixed distance between two magnetic sensors allows one to evaluate the viscosity of the fluid mixture. The time measuring range is from (12–250 s), the accuracy and the precision in the time measurement is ±0.01 and ±0.1 s, respectively. The capillary was placed in a block, thermostated with a PolyScience controller bath model 9010 with a temperature stability of ±10−2 K. The calibration of the apparatus was done periodically, using three fluids of known viscosity, Millipore quality water and degassed and dried Fluka quality octane and 1-pentanol as reference liquids [12]. These reference fluids have mass fraction purities of 99.5 mass%. The uncertainty in the viscosity and the mole fraction were estimated as better than 2 × 10−3 mPa s and 5 × 10−5 , respectively.
3. Results and discussion The experimental viscosities of the binary mixtures DMC + methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol, 1-pentanol at 293.15, 298.15, 303.15 and 313.15 K, and atmospheric pressure are given in Table 2. Fig. 1 shows the experimental viscosity values at these temperatures and the comparison with the literature data. The experimental densities of these binary mixtures at these temperatures have been published previously [13]. The viscosity deviations are calculated from experimental viscosities of the pure components and the mixture by the equation η (mPa s) = η −
k i=1
(ηoi · xi )
(1)
where η and ηoi are the viscosity of the mixture and the pure component, respectively; xi represents the mole fraction of
A. Rodr´ıguez et al. / Fluid Phase Equilibria 216 (2004) 167–174 Table 2 Viscosity (η) and viscosity deviations (η) of the binary mixtures DMC with alcohols at several temperatures x
η (mPa s)
η (mPa s)
x
η (mPa s)
η (mPa s)
0.553 0.531 0.518 0.502 0.498 0.498 0.504 0.509 0.517 0.53 0.548 0.566 0.585
0 −0.024 −0.038 −0.058 −0.065 −0.068 −0.065 −0.063 −0.058 −0.049 −0.034 −0.018 0
0.450 0.437 0.434 0.428 0.426 0.428 0.429 0.437 0.444 0.451 0.471 0.476 0.494
0 −0.016 −0.020 −0.031 −0.037 −0.039 −0.042 −0.038 −0.037 −0.033 −0.019 −0.015 0
1.105 0.966 0.897 0.786 0.685 0.625 0.594 0.573 0.561 0.555 0.556 0.565 0.585
0 −0.108 −0.159 −0.231 −0.278 −0.280 −0.263 −0.236 −0.192 −0.138 −0.093 −0.053 0
0.826 0.731 0.662 0.535 0.472 0.450 0.440 0.438 0.440 0.445 0.463 0.475 0.494
0 −0.078 −0.133 −0.222 −0.252 −0.246 −0.219 −0.188 −0.152 −0.116 −0.062 −0.035 0
x DMC + (1−x) methanol 293.15 K 0 0.591 0 0.0537 0.567 −0.026 0.0996 0.551 −0.043 0.2058 0.536 −0.062 0.3135 0.533 −0.069 0.4100 0.535 −0.070 0.5086 0.540 −0.069 0.6104 0.545 −0.067 0.7229 0.554 −0.062 0.8338 0.570 −0.050 0.9067 0.586 −0.037 0.9509 0.600 −0.024 1 0.626 0 303.15 K 0 0.514 0 0.0260 0.503 −0.012 0.0707 0.489 −0.027 0.1832 0.469 −0.049 0.2839 0.467 −0.053 0.3823 0.468 −0.054 0.4869 0.472 −0.053 0.5847 0.475 −0.052 0.6832 0.480 −0.049 0.8119 0.496 −0.036 0.8969 0.512 −0.022 0.9581 0.525 −0.010 1 0.536 0
298.15 K 0 0.0506 0.1042 0.2079 0.3011 0.3963 0.4931 0.5890 0.6927 0.8137 0.8997 0.9575 1 313.15 K 0 0.0648 0.1008 0.1978 0.3027 0.3928 0.4855 0.5738 0.7009 0.7838 0.9029 0.9283 1
x DMC + (1−x) ethanol 293.15 K 0 1.194 0 0.0498 1.070 −0.096 0.0978 0.974 −0.164 0.1760 0.853 −0.241 0.2928 0.740 −0.288 0.4053 0.675 −0.289 0.4981 0.646 −0.265 0.5982 0.625 −0.229 0.6962 0.613 −0.186 0.8024 0.609 −0.129 0.8894 0.607 −0.082 0.9516 0.618 −0.035 1 0.626 0 303.15 K 0 0.972 0 0.0673 0.832 −0.111 0.1142 0.752 −0.170 0.2249 0.627 −0.247 0.2894 0.588 −0.258 0.3906 0.541 −0.261 0.4848 0.521 −0.240 0.5996 0.512 −0.199 0.6931 0.513 −0.157 0.8038 0.512 −0.110 0.9072 0.520 −0.056 0.9462 0.527 −0.032 1 0.536 0
298.15 K 0 0.0598 0.0950 0.1692 0.2725 0.3854 0.4778 0.5686 0.6777 0.7915 0.8775 0.9366 1 313.15 K 0 0.0504 0.0934 0.2082 0.3087 0.3930 0.5026 0.6011 0.7052 0.7968 0.9075 0.9507 1
x DMC + (1−x) 1-propanol 293.15 K 0 2.198 0
298.15 K 0 1.97
0
169
Table 2 (Continued ) x
η (mPa s)
η (mPa s)
x
η (mPa s)
η (mPa s)
0.0508 0.0875 0.1647 0.2944 0.3858 0.5440 0.6026 0.7041 0.8900 0.9015 0.9510 1 303.15 K 0 0.0728 0.0829 0.1840 0.2605 0.3758 0.4849 0.6278 0.7071 0.8061 0.9018 0.9507 1
1.875 1.683 1.362 1.024 0.885 0.751 0.716 0.666 0.610 0.606 0.608 0.626
−0.243 −0.377 −0.577 −0.711 −0.706 −0.592 −0.535 −0.425 −0.189 −0.175 −0.095 0
1.675 1.493 1.147 0.936 0.803 0.725 0.673 0.631 0.598 0.579 0.576 0.585
−0.223 −0.353 −0.559 −0.633 −0.621 −0.555 −0.467 −0.367 −0.263 −0.145 −0.080 0
1.707 1.404 1.367 1.072 0.919 0.769 0.685 0.613 0.594 0.569 0.554 0.542 0.536
0 −0.218 −0.243 −0.420 −0.483 −0.498 −0.454 −0.359 −0.285 −0.194 −0.097 −0.052 0
0.0517 0.0898 0.1903 0.2896 0.3944 0.4980 0.5993 0.7016 0.8007 0.8994 0.9490 1 313.15 K 0 0.0498 0.0973 0.1985 0.3015 0.4025 0.5021 0.6029 0.7038 0.8033 0.9073 0.9510 1
1.361 1.198 1.066 0.860 0.721 0.639 0.584 0.546 0.521 0.500 0.489 0.489 0.494
0 −0.120 −0.211 −0.329 −0.379 −0.373 −0.342 −0.292 −0.230 −0.165 −0.085 −0.047 0
x DMC + (1−x) 2-propanol 293.15 K 0 2.386 0 0.0526 1.968 −0.325 0.0934 1.706 −0.516 0.2033 1.212 −0.816 0.3129 0.943 −0.892 0.4065 0.817 −0.854 0.5000 0.740 −0.766 0.6079 0.686 −0.630 0.7026 0.647 −0.502 0.8048 0.609 −0.361 0.9008 0.593 −0.208 0.9507 0.601 −0.112 1 0.626 0 303.15 K 0 1.763 0 0.0437 1.537 −0.172 0.1028 1.287 −0.350 0.2013 0.992 −0.524 0.3062 0.802 −0.585 0.3840 0.713 −0.579 0.4951 0.642 −0.514 0.5998 0.606 −0.421 0.7053 0.581 −0.317 0.8047 0.562 −0.214 0.9062 0.545 −0.106 0.9370 0.542 −0.071 1 0.536 0
298.15 K 0 0.0498 0.0979 0.2031 0.2999 0.3972 0.4892 0.5938 0.6971 0.7983 0.9012 0.9451 1 313.15 K 0 0.0507 0.0997 0.1984 0.2975 0.4001 0.4884 0.5959 0.7017 0.8014 0.9053 0.9492 1
2.098 1.733 1.454 1.046 0.844 0.740 0.690 0.654 0.625 0.589 0.567 0.567 0.585
0 −0.290 −0.496 −0.745 −0.800 −0.757 −0.668 −0.546 −0.418 −0.301 −0.167 −0.101 0
1.325 1.147 1.005 0.799 0.668 0.592 0.553 0.522 0.506 0.494 0.490 0.491 0.494
0 −0.136 −0.237 −0.361 −0.410 −0.401 −0.366 −0.308 −0.236 −0.165 −0.083 −0.045 0
x DMC + (1−x) 1-butanol 293.15 K 0 2.941 0 0.0518 2.461 −0.360 0.0975 2.119 −0.596 0.1961 1.586 −0.901 0.3064 1.218 −1.014 0.4108 1.023 −0.967
298.15 K 0 0.0527 0.1009 0.2002 0.2986 0.3974
2.620 2.192 1.877 1.411 1.127 0.952
0 −0.321 −0.538 −0.802 −0.885 −0.859
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A. Rodr´ıguez et al. / Fluid Phase Equilibria 216 (2004) 167–174 Table 2 (Continued )
Table 2 (Continued ) x
η (mPa s)
η (mPa s)
x
η (mPa s)
η (mPa s)
x
η (mPa s)
η (mPa s)
x
η (mPa s)
η (mPa s)
0.4769 0.6101 0.7043 0.8043 0.9052 0.9508 1 303.15 K 0 0.0249 0.0960 0.1911 0.2998 0.3877 0.4799 0.5865 0.6907 0.7931 0.8925 0.9464 1
0.929 0.794 0.719 0.644 0.607 0.605 0.626
−0.908 −0.735 −0.591 −0.435 −0.238 −0.135 0
0.831 0.748 0.673 0.611 0.572 0.569 0.585
−0.764 −0.649 −0.517 −0.379 −0.224 −0.117 0
−0.174 0
−0.139 0
1.754 1.536 1.351 1.018 0.880 0.752 0.662 0.598 0.557 0.520 0.497 0.494 0.494
0 −0.155 −0.277 −0.455 −0.496 −0.499 −0.455 −0.396 −0.327 −0.225 −0.121 −0.067 0
2.932 2.488 2.228 1.660 1.416 1.066 0.890 0.759 0.661 0.601 0.560 0.542 0.536
0 −0.315 −0.487 −0.798 −0.890 −0.931 −0.861 −0.755 −0.612 −0.433 −0.229 −0.040 0
0.9494 1 313.15 K 0 0.0467 0.1037 0.2514 0.3005 0.3996 0.5052 0.6059 0.7024 0.8053 0.9051 0.9651 1
0.586 0.585
0 −0.134 −0.424 −0.622 −0.694 −0.686 −0.643 −0.566 −0.460 −0.328 −0.174 −0.086 0
0.9503 1 303.15 K 0 0.0539 0.0906 0.1979 0.2613 0.3902 0.4928 0.5918 0.6923 0.7920 0.8943 0.9808 1
0.619 0.626
2.255 2.078 1.666 1.304 1.046 0.903 0.787 0.681 0.608 0.564 0.547 0.542 0.536
0.5039 0.6008 0.7028 0.8011 0.8965 0.9503 1 313.15 K 0 0.0499 0.0998 0.2234 0.3000 0.3991 0.5054 0.6030 0.6904 0.8009 0.9014 0.9471 1
2.256 1.972 1.678 1.161 1.046 0.876 0.750 0.659 0.596 0.540 0.502 0.494 0.494
0 −0.202 −0.395 −0.652 −0.680 −0.676 −0.616 −0.529 −0.422 −0.297 −0.159 −0.062 0
x DMC + (1−x) 2-butanol 293.15 K 0 3.619 0 0.0505 2.908 −0.560 0.0986 2.370 −0.954 0.2131 1.522 −1.459 0.2801 1.235 −1.546 0.4092 0.940 −1.454 0.5110 0.830 −1.260 0.6172 0.753 −1.019 0.7072 0.696 −0.806 0.7997 0.637 −0.589 0.8229 0.621 −0.535 0.9518 0.595 −0.175 1 0.626 0 303.15 K 0 2.503 0 0.0573 1.931 −0.459 0.0842 1.728 −0.609 0.1936 1.195 −0.927 0.2981 0.943 −0.974 0.3926 0.809 −0.922 0.4938 0.709 −0.823 0.5900 0.632 −0.710 0.6561 0.594 −0.618 0.7945 0.549 −0.391 0.8916 0.547 −0.202 0.9483 0.546 −0.092 1 0.536 0
298.15 K 0 0.0572 0.0994 0.1958 0.3029 0.3339 0.5075 0.6051 0.7037 0.808 0.9046 0.9523 1 313.15 K 0 0.0498 0.1005 0.2009 0.2952 0.4047 0.5109 0.6072 0.6982 0.7992 0.8977 0.9583 1
3.115 2.399 1.991 1.354 0.991 0.926 0.756 0.707 0.641 0.569 0.531 0.542 0.585
0 −0.571 −0.873 −1.266 −1.358 −1.344 −1.075 −0.877 −0.694 −0.502 −0.295 −0.164 0
1.784 1.512 1.289 0.975 0.795 0.669 0.600 0.561 0.529 0.502 0.486 0.486 0.494
0 −0.208 −0.365 −0.550 −0.608 −0.593 −0.525 −0.440 −0.354 −0.251 −0.140 −0.062 0
x DMC + (1−x) 1-pentanol 293.15 K 0 3.979 0 0.0482 3.367 −0.450 0.0991 2.836 −0.811 0.1941 2.110 −1.218 0.2974 1.605 −1.377 0.3939 1.304 −1.354 0.4993 1.092 −1.213 0.6000 0.939 −1.028 0.7013 0.810 −0.818 0.8013 0.704 −0.588 0.8915 0.635 −0.355
298.15 K 0 0.0457 0.1016 0.1979 0.3057 0.4024 0.5030 0.5793 0.7034 0.8003 0.9018
3.347 2.905 2.460 1.880 1.441 1.179 0.988 0.878 0.739 0.655 0.597
0 −0.316 −0.606 −0.920 −1.062 −1.057 −0.970 −0.869 −0.665 −0.482 −0.259
the pure component and k is the number of components in the mixture. The binary viscosity deviations were fitted to a Redlich– Kister type equation η (mPa s) = (x − x2 ) ·
M
Bp · (2x − 1)p
(2)
p=0
where x is the mole fraction, Bp are fitting parameters and M is the degree of the polynomic expansion, which was optimised using the F-test [14]. The viscosity deviations of the binary mixtures at several temperatures are given in Table 2. The fitting parameters are given in Table 3, together with the root-mean-square deviations. These ones are calculated by applying the values of the experimental and calculated viscosity deviations, and the number of experimental data are represented by ηexp , ηcal and nDAT , respectively. 1/2 n DAT (ηexp − ηcal )2 i σ= (3) nDAT Fig. 2 shows viscosity deviations for the binary mixtures dimethyl carbonate with alkanes at 293.15, 298.15, 303.15 and 313.15 K, respectively, plotted against mole fraction together with the fitted curve, obtained from the Redlich–Kister equation. The viscosity deviations for these systems at these temperatures are negative over the entire composition range for the whole of the binaries at the above temperatures. 3.1. Results obtained using UNIFAC-VISCO method To increase the application range of the predictive UNIFAC-VISCO method, based on a group contribution scheme, we have determined the interaction parameters corresponding to carbonate (–OCOO–) with alcohols (–OH) and methanol (CH3 OH) as other group. The UNIFAC-VISCO parameters have been calculated from our experimental values of dynamic viscosities, involving to the
A. Rodr´ıguez et al. / Fluid Phase Equilibria 216 (2004) 167–174
binary mixtures dimethyl carbonate or diethyl carbonate with methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol and 1-pentanol at 293.15, 398.15, 303.15 and 313.15 K, using the Nelder and Mead [15] equation for minimising the following objective function: N
O.F. =
1 |νi,exp − νi,calc | N νi,exp i=1
(4)
171
where N is the number of experimental data, and νexp and νcalc are the experimental and calculated kinematic viscosity, respectively. In this work it is necessary for the prediction of the viscosity of the binary mixtures to use the interaction parameters (–OCOO–) with alkanes which have been determined previously [5]. The carbonate–alcohol interaction parameters, obtained from our experimental data, are summarised in Table 4a.
Fig. 1. Dynamic viscosities (η) for the binary mixtures (a) dimethyl carbonate + methanol (b) dimethyl carbonate + ethanol (c) dimethyl + 1-propanol (d) dimethyl carbonate + 2-propanol (e) dimethyl carbonate + 1-butanol (f) dimethyl carbonate + 2-butanol (g) dimethyl + 1-pentanol at (䊊), 293.15 K (䊐), 298.15 K ( ), 303.15 K and (䉫), 313.15 K and the calculated values using UNIFAC-VISCO at (· · · · · · ), (-•-•-•-), 298.15 K; (— — —), 303.15 K and (– – –), 313.15 K. Comparison with literature data: in (a) Aminabhavi et al. (䉱), 298.15 K (䉲), In (b), (c) and (g) Romano et al. (䊉), 293.15 K (䊏), 303.15 K (䉬), 313.15 K.
carbonate carbonate 293.15 K; 303.15 K.
172
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Fig. 1. (Continued ).
The group volumes and surface areas are shown in Table 4b. In Table 5a the root-mean-square deviations between experimental and calculated viscosity deviations are shown. In view of the results shown in this table we can say that good results are obtained when we used the UNIFAC-VISCO method to calculate the dynamic viscosities of the binary mixtures for the linear alcohols, however these results are worse for the secondary alcohols with dimethyl carbonate. Figs. 1 and 2 show graphically the obtained values of viscosity and viscosity deviations, respectively, for the binary mixtures dimethyl carbonate with methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol and 1-pentanol at 293.15, 298.15, 303.15 and 313.15 K by applying the UNIFAC-VISCO method. Graphically we
Fig. 2. Curves (—) of viscosity deviations (η) from the Redlich–Kister equation, Eq. (2), for the binary mixtures (a) dimethyl carbonate + methanol (b) dimethyl carbonate + ethanol (c) dimethyl carbonate + 1-propanol (d) dimethyl carbonate + 2-propanol (e) dimethyl carbonate + 1-butanol (f) dimethyl carbonate + 2-butanol (g) dimethyl carbonate + 1-pentanol at (䊊), 293.15 K (䊐), 298.15 K ( ), 303.15 K and (䉫), 313.15 K and the calculated values using UNIFAC-VISCO at (· · · · · · ), 293.15 K; (-•-•-•-), 298.15 K; (— — —), 303.15 K and (– – –), 313.15 K.
A. Rodr´ıguez et al. / Fluid Phase Equilibria 216 (2004) 167–174
173
Table 4a The UNIFAC-VISCO interaction parameters αmn
Parameters CH3 OH–OCOO OCOO–CH3 OH OH–OCOO OCOO–OH
162.2 −208.1 3237.5 105.9
Table 4b Group volume and surface area parameters
Fig. 2. (Continued )
can observe in Fig. 1a how the binary mixture dimethyl carbonate + methanol obtains better results by applying UNIFAC-VISCO method at high temperatures; however, Table 3 Fitting parameters and root-mean-square deviations (σ) for the binary systems DMC with alcohols at several temperatures using the Eqs. (2) and (3), respectively T (K)
B0
−0.2695 −0.2155 −0.1598 −0.0966
DMC + ethanol 293.15 −1.0593 298.15 −1.0264 303.15 −0.9351 313.15 −0.8881
0.6456 0.5968 0.6421 0.5876
−0.4291 −0.4975 −0.3867 −0.4129
DMC + 1-propanol 293.15 −2.5276 298.15 −2.2148 303.15 −1.7944 313.15 −1.3705
1.6834 1.6064 1.2314 0.8546
−1.2080 −1.1026 0.5242 −0.5110
0.001 0.001 0.002 0.001
DMC + 2-propanol 293.15 −3.0545 298.15 −2.6210 303.15 −2.0383 313.15 −1.4474
2.3030 2.2993 1.5819 1.0290
−1.7407 −1.7397 −0.7629 −0.5614
0.001 0.001 0.001 0.001
DMC + 1-butanol 293.15 −3.5182 298.15 −3.0722 303.15 −2.5232 313.15 1.8425
2.4472 2.1869 1.3100 1.0678
−1.9536 −1.7230 −1.2399 −0.5936
0.001 0.001 0.001 0.001
DMC + 2-butanol 293.15 −5.1343 298.15 −4.3511 303.15 −3.2574 313.15 −2.1294
4.3486 3.9437 2.1835 1.5526
−3.2360 −3.4671 −2.4176 −1.0215
DMC + 1-pentanol 293.15 −4.8526 298.15 −3.8929 303.15 −3.4368 313.15 −2.4825
3.3560 2.3162 1.8503 1.4990
−2.3834 −1.4062 −1.0570 −0.8918
1.5821 1.3488 1.0000
1.3937 1.0800 1.200
a
The CH–CH3 group considers the R and Q parameters how 2 CH2 .
some differences are observed at 293.15 K. The same results can be observed in Fig. 2a. The results obtained from viscosity deviations using the calculated values are similar and they are not sensitive to the variation of the temperature.
The group contribution thermodynamic viscosity model GC-UNIMOD is based on the original UNIFAC method. The predictive equation has no theoretical foundation, but it is based on experience. The Van der Waals properties for the different subgroups and the group interaction energy parameters used in the GC-UNIMOD model have been calculated, previously [4], from our experimental VLE binary data carbonate with alcohols. When GC-UNIMOD predictive model for viscosities of the binary mixtures at 298.15 K is applied, we can observe worse predictive results than UNIFAC-VISCO because the group interaction energy parameters used have been obtained from VLE data while UNIFAC-VISCO one applies its own parameters. In Table 5b the root-mean-square deviations between experimental and calculated viscosity deviations are shown.
0.0306 0.0349 0.0225 0.0031
0.9162
OCOO CH–CH3 a OH
0.001 0.001 0.001 0.001
DMC + methanol 293.15 −0.2743 298.15 −0.2597 303.15 −0.2140 313.15 −0.1615
−0.1218
Qk
3.2. Results obtained using GC-UNIMOD method
B2
0.1099
Rk
σ
B1
B3
Group
0.001 0.001 0.002 0.001
Table 5a Root-mean-square deviations of dynamic viscosity σ(η) resulting by using UNIFAC-VISCO model at several temperatures and 13 number of data points for the binary mixtures System
1.9720
0.4186
0.002 0.001 0.002 0.001 0.002 0.002 0.002 0.002
DMC + Methanol Ethanol 1-Propanol 2-Propanol 1-Butanol 2-Butanol 1-Pentanol
T (K) 293.15
298.15
303.15
313.15
0.028 0.036 0.015 0.076 0.020 0.163 0.040
0.023 0.024 0.019 0.081 0.021 0.178 0.072
0.014 0.021 0.036 0.026 0.030 0.101 0.058
0.009 0.014 0.031 0.016 0.046 0.023 0.050
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Table 5b Root-mean-square deviations of dynamic viscosity σ(η) resulting by the prediction using GC-UNIMOD model at 298.15 K for the binary mixtures System DMC DMC DMC DMC DMC DMC DMC
+ methanol + ethanol + 1-propanol + 2-propanol + 1-butanol + 2-butanol + 1-pentanol
σ 0.024 0.120 0.242 0.323 0.346 0.566 0.414
4. Conclusions In this paper we have determined the experimental dynamic viscosities of the binary mixtures DMC with methanol, or ethanol, or 1-propanol, or 2-propanol, or 1-butanol, or 2-butanol, or 1-pentanol at 293.15, 298.15 303.15 and 313.15 K. In order to test the quality of the experimental values we have calculated the viscosity deviations for the above binary mixtures at the interval of temperatures and we have fitted these results at a Redlich–Kister equation. Comparison with literature data have been made for the binary mixtures dimethyl carbonate + methanol, + ethanol, + 1-propanol, and 1-pentanol. Serious discrepancies are shown in the viscosity data for the binary mixture dimethyl carbonate + methanol and dimethyl carbonate at 298.15 and 303.15 K. However similar results are obtained for the other mixtures. The UNIFAC-VISCO predictive method has been used to obtain calculated values of the viscosity at different temperatures. Due to the interaction parameters (–OCOO–) with alcohols were not calculated, we have used the experimental values to calculate them. The group contribution thermodynamic viscosity model GC-UNIMOD has already been used to predict the dynamic viscosities of the binary mixtures at 298.15 K. We have obtained good calculated results when we use UNIFAC-VISCO method using the calculated parameters for the binary mixtures. Analysing these results, we can say that the best ones are obtained for linear alcohols. The binary mixtures dimethyl carbonate + methanol obtain the worst results in calculated viscosity at low temperatures although the methanol is considered as a single group instead of the other alcohols that take into account only the OH group to difference them. The improvement of these values is increased when the temperature is increased too. Related to the GC-UNIMOD results, we can say that this predictive viscosity method obtains worse results than UNIFAC-VISCO due to the group interaction energy parameters of the GC-UNIMOD matrix have been obtained from VLE data however UNIFAC-VISCO obtains them from viscosity data. List of symbols xi the mole fraction k the number of components
x Bp M zexp , zpred nDAT N Greek letters η, ηoi νexp and νcalc
the mole fraction in the Redlich–Kister equation the fitting parameter the degree of the polynomic expansion the experimental and predictive property the number of experimental data the number of experimental data
the viscosity of the mixture and the pure component the experimental and calculated kinematic viscosity
References [1] Y. Katrib, G. Deiber, P. Mirabel, S. Le Calvé, C. George, A. Mellouki, G. Le Bras, J. Atmospheric Chem. 43 (2002) 151–174. [2] M.A. Pacheco, C.L. Marshall, Energy Fuel 11 (1997) 2–29. [3] A. Rodr´ıguez, J. Canosa, A. Dom´ınguez, J. Tojo, Fluid Phase Equilib. 198 (2002) 95–102. [4] A. Rodr´ıguez, J. Canosa, A. Dom´ınguez, J. Tojo, Fluid Phase Equilib. 201 (2002) 187–201. [5] A. Rodr´ıguez, J. Canosa, A. Dom´ınguez, J. Tojo, J. Chem. Eng. Data 48 (2003) 146–151. [6] O. Redlich, A.T. Kister, Ind. Eng. Chem. 40 (1948) 345–348. [7] T.M. Aminabhavi, K. Banerjee, J. Chem. Eng. Data 43 (1998) 1096– 1101. [8] E. Romano, J.L. Trenzado, E. González, J.S. Matos, L. Segade, E. Jiménez, Fluid Phase Equilib. 211 (2003) 219–240. [9] Y. Gaston-Bonhomme, P. Petrino, J.L. Chevalier, J. Chem. Eng. Sci. 49 (1994) 1799–1806. [10] A. Rodr´ıguez, ELV y estudio del comportamiento de los sistemas de dialquil carbonato con alcoholes y alcanos. Determinación de los correspondientes parámetros de interacción entre grupos, Ph Thesis, Vigo University, 2001. [11] W. Cao, K. Knudsen, A. Fredeslund, P. Rasmussen, Ind. Eng. Chem. Res. 32 (1993) 2088–2092. [12] J.A. Riddick, W.B. Bunger, T.K. Sakano, in: Organic Solvents Techniques of Chemistry, fourth ed., vol. 2, Wiley, New York, 1986. [13] A. Rodr´ıguez, J. Canosa, A. Dom´ınguez, J. Tojo, J. Chem. Eng. Data 46 (2001) 1476–1486. [14] P. Bevington, in: Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill, New York, 1969. [15] J.A. Nelder, R. Mead, Comput. J. 7 (1965) 308–313. [16] I. Garcia de la Fuente, J.A. Gonzalez, J.C. Cobos, C. Casanova, J. Solution Chem. 24 (1995) 827–835. [17] A. Pal, G. Dass, A. Kumar, J. Chem. Eng. Data 43 (1998) 738–741. [18] A. Das, M. Frenkel, N.M. Gadalla, K. Marsh, R.C. Wilhoit, in: TRC Thermodynamic Tables, Thermodynamic Research Center, Texas A&M University, College Station, TX, 1994. [19] J. Ortega, J. Chem. Eng. Data 27 (1982) 312–317. [20] D. Papaioannou, C. Panayiotou, J. Chem. Eng. Data 40 (1995) 202– 209. [21] T.M. Aminabhavi, B. Gopalakrishna, J. Chem. Eng. Data 40 (1995) 462–467. [22] M.N. Sovilj, J. Chem. Eng. Data 40 (1995) 1058–1061. [23] P. Cea, C. Lafuente, H. Artigas, F.M. Royo, J.S. Urieta, Can. J. Chem. 72 (1994) 1921–1924. [24] M.J.P. Comuñas, A. Baylaucq, C. Boned, J. Fernández, Int. J. Thermophys. 22 (2001) 749–768.