Isobaric vapor–liquid equilibria for mixtures of tetrahydrofuran, 2-propanol, and 2,2,4-trimethylpentane at 101.3 kPa

Isobaric vapor–liquid equilibria for mixtures of tetrahydrofuran, 2-propanol, and 2,2,4-trimethylpentane at 101.3 kPa

Available online at www.sciencedirect.com Journal of the Chinese Institute of Chemical Engineers 39 (2008) 265–273 www.elsevier.com/locate/jcice Iso...

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Available online at www.sciencedirect.com

Journal of the Chinese Institute of Chemical Engineers 39 (2008) 265–273 www.elsevier.com/locate/jcice

Isobaric vapor–liquid equilibria for mixtures of tetrahydrofuran, 2-propanol, and 2,2,4-trimethylpentane at 101.3 kPa Chia-Chiang Hsu, Chein-Hsiun Tu * Department of Applied Chemistry, Providence University, Taichung 433, Taiwan Received 1 September 2007; accepted 18 December 2007

Abstract Vapor–liquid equilibrium (VLE) at 101.3 kPa have been determined for a ternary system (tetrahydofuran + 2-propanol + 2,2,4-trimethylpentane) and its constituent binary systems (tetrahydrofuran + 2-propanol, tetrahydrofuran + 2,2,4-trimethylpentane, and 2-propanol + 2,2,4-trimethylpentane). The activity coefficients of liquid mixtures were calculated from the modified Raoult’s law. Thermodynamic consistency tests were performed for all VLE data. The VLE data of the binary mixtures and ternary mixtures were correlated using the Margules, Wilson, NRTL, and UNIQUAC activity-coefficient models. The models with their best-fitted interaction parameters of the binary systems were used to predict the ternary vapor–liquid equilibrium. All VLE data are also used to calculate the reduced excess molar Gibbs free energy gE/RT and the deviations in the boiling point DT. The calculated quantities of gE/RT and DT were fitted to variable-degree polynomials in terms of liquid composition. # 2008 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Experiments; Isobaric VLE; Tetrahydrofuran; 2-Propanol; 2,2,4-Trimethylpentane

1. Introduction Certain oxygenated compounds are usually added to gasoline in order to improve the octane number and reduce pollution. This work has been carried out as part of the project to study the thermophysical behavior of liquid mixtures including oxygenated compounds and hydrocarbon liquids. The present paper is concerned with an experimental determination of vapor–liquid equilibrium (VLE) for the system formed by the oxygenated compounds of the type {cyclic ether or aliphatic alcohol} and the alkane liquids that generally appears in gasoline. Such data of oxygenated mixtures are important for predicting the vaporphase composition that would be in equilibrium with different hydrocarbon liquids. From the view point of association, cyclic ethers can be regarded as an intermediate case between alkanes (inert compounds) and alkanols (highly self-associated compounds). For these reasons, we measured VLE data for a ternary system (tetrahydrofuran + 2-propanol + 2,2,4-trimethylpentane) and three binary systems (tetrahydrofuran + 2-propanol, tetrahydrofuran + 2,2,4-trimethylpentane, and 2-propanol + 2,2,4-tri* Corresponding author. Tel.: +886 4 26328001x15214; fax: +886 4 26327554. E-mail address: [email protected] (C.-H. Tu).

methylpentane) at 101.3 kPa. Tetrahydrofuran and 2-propanol were chosen for the present study because they are two potential candidates as blending agents for reformulated gasoline. The third added compound, 2,2,4-trimethylpentane, represents the hydrocarbon in gasoline. In the literature there are isobaric VLE data for these three binary systems (Bures et al., 1959; Du et al., 2001; Hiaki et al., 1994; Yoshikawa et al., 1980). However, we are not aware of any VLE data existed for the ternary system. 2. Experimental 2.1. Chemicals The source and mass purities of the chemicals employed are as follows: tetrahydrofuran (Merck, >99.5%); 2-propanol (Tedia, >99.5%); 2,2,4-trimethylpentane (Merck, >99.7%). All chemicals were used without further purification after gas chromatography failed to show any significant impurities. Before measurements the liquids were dried over molecular sieves (Merck, type 0.3 nm pellets). The purity of each component was further ascertained by comparing its boiling point, density, and refractive index with the corresponding literature values as shown in Table 1. The density r was measured at (298.15  0.01) K using a DMA-5000 vibrating-tube densimeter (Anton-Paar; Graz, Austria) with an uncertainty of

0368-1653/$ – see front matter # 2008 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jcice.2007.12.015

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Nomenclature ak

binary coefficients of the Redlich–Kister equation a, b, c, d, e coefficients in the liquid molar volume equation A, B, C, D, E coefficients in the vapor pressure equation Aij, Aji binary parameters for liquid activity coefficient models Cij ternary coefficients of the gE/RT and DT equations D local deviation in the method of McDermott– Ellis Dmax maximum deviation used by Wisniak and Tamir gE excess molar Gibbs energy gij, gjj NRTL parameters n number of experimental data nD refractive index N number of components OF objective function p number of parameters of fitted equations P system pressure (Pa) P8 vapor pressure of pure component (Pa) q surface area parameter of the UNIQUAC model DQ gE/RT or DT (K) function for binary mixtures DQ123 gE/RT or DT (K) function for ternary mixtures r volume parameter of the UNIQUAC model R universal gas constant RMSD root mean squared deviation T boiling temperature (K) Uij, Ujj UNIQUAC parameters v molar volume of pure liquid (m3/kmol) VLE vapor–liquid equilibrium xi mole fraction of component i in liquid-phase yi mole fraction of component i in vapor-phase

0.01 kg/m3. The refractive index nD was measured at (298.15  0.05) K using an automatic Anton Paar RXA-156 refractometer, with an uncertainty of 0.00002. 2.2. Apparatus and procedure The VLE measurements were carried out by circulation for both vapor and liquid in an all-glass equilibrium still (NGW, Wertheim, Germany) of the Hunsmann type (Hunsmann, 1967) connected to a manostat as used by Fowler and Hunt (1941). The boiling temperature was measured with a precision thermometer (Hart Scientific, Model 1560/2560) with a platinum RTD probe to within 0.01 K, the uncertainty of the measurement being estimated at 0.05 K. Constant pressure was maintained by the manostat within 0.1 kPa. The equilibrium pressures were determined comparatively via the boiling temperature of pure water, measured in a S´wie˛tosławski type ebulliometer (Ha´la et al., 1967) connected to the system. The equilibrium still was insulated by an oil jacket and its temperature was maintained at a temperature of approximately 6 K above the boiling point of the mixture in the boiling chamber to ensure that no phase change occurred. Equilibrium compositions of sampled liquid and condensed vapor phases were analyzed with a PerkinElmer Autosystem gas chromatograph (GC). A flame ionization detector was used along with a capillary column packed (60 m long, 0.25 mm i.d., 0.5 mm film) with Petrocol DH (SUPELCO, PA/USA). The GC response peaks were integrated by using PerkinElmer Turbochrom software. Calibration analyses using gravimetrically prepared standard solutions were carried out to convert the peak area ratios to mole fractions of the sample. The uncertainty of equilibrium composition measurements was estimated to be within 0.003 mol fraction. 3. Results and discussion

Greek symbols D deviation used for boiling temperature T a NRTL parameter d deviation between experimental and calculated value g liquid-phase activity coefficient lij,lii Wilson parameters r density (kg/cm3) s standard deviation

The VLE data for the binary systems of tetrahydrofuran + 2propanol, tetrahydrofuran + 2,2,4-trimethylpentane, and 2-propanol + 2,2,4-trimethylpentane at the pressure of 101.3 kPa are presented in Tables 2–4, respectively. The activity coefficients of pure liquid i (gi) were calculated from the equality of component fugacity in both liquid and vapor-phase under the assumptions of an ideal vapor-phase and a unity in the Poynting factor, i.e.

Superscripts calc calculated value expt experimental value E excess value L liquid state o pure component

where xi and yi are the liquid and vapor mole fractions at equilibrium for pure component i, Poi is the vapor pressure for pure component i, and P is the total pressure. Eq. (1) is also known as the modified Raoult’s law. The temperature dependence of the pure component vapor pressure (P8) was calculated from

Subscripts 1, 2, 3, i, j components 123 ternary mixture

ln Po ðPaÞ ¼ A þ

gi ¼

yi P xi Poi

(1)

B þ C ln T þ DT E T

(2)

where A, B, C, D, and E are the component specific coefficients for vapor pressure and T is the equilibrium temperature in

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Table 1 Comparison of measured boiling points T at 101.3 kPa and densities r and refractive indices nD at 298.15 K with literature values Compounds

r (kg/m3)

T (K) Experiment

Literature

nD

Experiment

Literature

Experiment

Literature

a

Tetrahydrofuran

339.11

339.1 339.08b

882.35

881.91 882.30b

1.40461

1.4046a 1.4050b

2-Propanol

355.39

355.42c 355.392d

780.96

780.86c 781.26d 781.29e

1.37525

1.37512d 1.3752e

2,2,4-Trimethylpentane

372.37

372.38c 372.40f 372.50g

687.75

687.67c 687.64g 687.64h

1.38890

1.3890g 1.3892h

a b c d e f g h

a

Loras et al. (1999). Kobe et al. (1956). Hiaki et al. (1994). Riddick et al. (1986). Nagata et al. (2000). Font et al. (2003). Martinez-Soria et al. (1999). Aralaguppi et al. (1999).

Kelvin. The constants A, B, C, D, and E for tetrahydrofuran and 2-propanol were obtained after regressing from the experimental vapor pressure data of Scott (1970) and data of Ambrose and Sprake (1970), respectively. The corresponding parameters for 2,2,4-trimethylpentane were obtained directly from CHEMCAD Data Bank (1998). Table 5 lists the values of these constants A, B, C, D, and E. The reduced excess molar Gibbs energy (gE/RT) was calculated according to the definition

where N is the number of components.

Figs. 1–3 are the temperature-composition diagrams for the binary systems of tetrahydrofuran (1) + 2-propanol (2), tetrahydrofuran (1) + 2,2,4-trimethylpentane (3), and 2-propanol (2) + 2,2,4-trimethylpentane (3), respectively. Only the binary system 2-propanol + 2,2,4-trimethylpentane shows the azeotrope of a minimum boiling temperature. The azeotropic composition was obtained by determining the xi value that makes the function ((xi  yi) = f(xi)) zero. The corresponding azeotropic temperature was computed from the experimental results around the azeotropic point, using the xi values previously determined. The azeotropic point thus obtained for 2-propanol + 2,2,4-trimethylpentane is xaz = 0.630 (0.635) of 2-propanol, T az = 349.45 K (349.58 K) and the values shown

Table 2 VLE data for the binary system of tetrahydofuran (1) + 2-propanol (2) at 101.3 kPa

Table 3 VLE data for the binary system of tetrahydofuran (1) + 2,2,4-trimethylpentane (3) at 101.3 kPa

N X gE ¼ xi ln g i RT i¼1

(3)

T (K)

x1

y1

g1

355.39 354.39 353.15 352.35 350.74 350.39 348.82 348.42 347.09 346.86 346.11 344.79 344.58 343.45 342.97 342.37 341.34 340.77 340.21 339.70 339.11

0.000 0.040 0.089 0.123 0.193 0.208 0.281 0.302 0.378 0.390 0.434 0.515 0.528 0.607 0.643 0.689 0.779 0.831 0.885 0.939 1.000

0.000 0.077 0.164 0.220 0.324 0.345 0.437 0.463 0.541 0.551 0.595 0.661 0.669 0.729 0.756 0.786 0.852 0.886 0.925 0.960 1.000

1.202 1.194 1.186 1.168 1.167 1.147 1.144 1.113 1.106 1.099 1.071 1.065 1.046 1.039 1.028 1.018 1.011 1.009 1.003 1.000

g2

gE/RT

T (K)

x1

y1

g1

1.000 1.001 1.005 1.007 1.012 1.016 1.027 1.026 1.041 1.049 1.056 1.089 1.103 1.138 1.152 1.191 1.216 1.253 1.242 1.278

0.000 0.009 0.021 0.027 0.040 0.044 0.058 0.059 0.066 0.069 0.071 0.077 0.080 0.078 0.075 0.073 0.057 0.047 0.033 0.018 0.000

372.37 370.04 366.71 365.00 363.34 361.12 356.38 356.26 352.21 350.41 349.98 348.18 345.03 343.66 342.42 341.45 340.64 340.06 339.83 339.33 339.11

0.000 0.028 0.073 0.098 0.124 0.161 0.254 0.257 0.354 0.405 0.419 0.479 0.607 0.675 0.745 0.808 0.871 0.918 0.938 0.974 1.000

0.000 0.091 0.207 0.265 0.318 0.387 0.523 0.527 0.632 0.676 0.690 0.732 0.809 0.843 0.876 0.905 0.934 0.956 0.966 0.980 1.000

1.314 1.253 1.251 1.242 1.238 1.214 1.213 1.189 1.173 1.173 1.149 1.104 1.080 1.058 1.039 1.021 1.010 1.006 0.999 1.000

g3

gE/RT

1.000 0.993 1.000 1.002 1.006 1.010 1.023 1.022 1.040 1.054 1.051 1.071 1.125 1.171 1.230 1.295 1.377 1.456 1.494 2.167

0.000 0.001 0.017 0.024 0.032 0.042 0.066 0.066 0.087 0.096 0.096 0.103 0.106 0.103 0.095 0.080 0.059 0.040 0.031 0.019 0.000

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Table 4 VLE data for the binary system of 2-propanol (2) + 2,2,4-trimethylpentane (3) at 101.3 kPa T (K)

x2

y2

g2

372.37 369.30 364.90 357.74 355.12 354.80 351.35 351.15 350.42 349.74 349.59 349.53 349.49 349.50 349.55 349.70 350.03 350.48 351.50 352.77 355.39

0.000 0.010 0.029 0.083 0.121 0.127 0.240 0.253 0.318 0.444 0.527 0.574 0.603 0.673 0.718 0.759 0.816 0.846 0.905 0.949 1.000

0.000 0.090 0.209 0.388 0.453 0.459 0.542 0.548 0.569 0.599 0.611 0.619 0.625 0.637 0.651 0.673 0.704 0.728 0.790 0.861 1.000

5.255 4.964 4.255 3.785 3.702 2.665 2.577 2.194 1.702 1.472 1.373 1.322 1.206 1.153 1.121 1.075 1.053 1.024 1.010 1.000

g3

gE/RT

1.000 0.997 1.004 1.023 1.036 1.042 1.132 1.143 1.223 1.427 1.632 1.782 1.884 2.207 2.464 2.688 3.153 3.411 4.130 4.888

0.000 0.014 0.050 0.141 0.192 0.202 0.330 0.340 0.387 0.434 0.436 0.428 0.420 0.386 0.357 0.325 0.271 0.232 0.156 0.090 0.000

in the parentheses were obtained from the literature (Hiaki et al., 1994). A good agreement was found between them. Figs. 1–3 also contain a comparison of our experimental T– x–y values with those from open literature (Bures et al., 1959; Du et al., 2001; Hiaki et al., 1994; Yoshikawa et al., 1980) for these three binary systems. A reasonable agreement between our experimental and the literature results is obtained for these three systems except for those from Bures et al. (1959) for 2propanol + 2,2,4-trimethylpentane, which show higher values in equilibrium temperature. Fig. 4 plots the reduced excess molar Gibbs energy as function of liquid composition for these three binary systems. All these systems exhibit a positive deviation from ideal behavior. The thermodynamic consistency for three binary systems was treated using the direct test proposed by Van Ness (1995). In the direct test, a proposed consistency index associated with

Fig. 1. Experimental T–x1–y1 diagram of tetrahydrofuran (1) + 2-propanol (2) at 101.3 kPa: (~,~) this work; (*,*) Yoshikawa et al., 1980; (—) NRTL equation. Full symbols refer to liquid-phase compositions and open symbols to vapor-phase compositions.

the test characterizes the degree of departure of a data set from consistency. The consistency index starts at 1 for highly consistent data and goes to 10 for data of very poor quality based on an appropriate measure in the RMSD value of d ln(gi/gj). The residual in the logarithms of the activitycoefficient ratio d ln(gi/gj) is calculated between two sets of activity coefficients coming from the experimental data and from the correlation. For this test, the values of gE/RT in this study were calculated from experimental activity coefficients and were correlated with the three-suffix Margules equation (Gess et al., 1991) with a temperature dependence assumed for each parameter. With constants from this fit, the RMSD values

Table 5 Parameters of vapor pressure, of liquid molar volume, and of UNIQUAC equation for the pure components used in this study Parameters

Tetrahydrofuran

2-Propanol

2,2,4-Trimethylpentane

P8 (Pa) A B C D E

66.272 5644.7 6.6228 4.23  106 2.0

73.032 7215.9 7.1145 4.62  106 2.0

120.81 7550 16.111 1.71  102 1.0

vL (m3/kmol) a b c d UNIQUAC q UNIQUAC r

1.2543 0.2808 540.15 0.2912 2.72 2.9414

1.18 0.26475 508.31 0.243 2.5078 2.7790

0.5886 0.27373 543.96 0.2846 5.0079 5.8463

Fig. 2. Experimental T–x1–y1 diagram of tetrahydrofuran (1) + 2,2,4-trimethylpentane (3) at 101.3 kPa: (~,~) this work; (*,*) Du et al., 2001; (—) NRTL equation. Full symbols refer to liquid-phase compositions and open symbols to vapor-phase compositions.

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Table 6 Results of the thermodynamic consistency test for binary VLE data Systems i + j

RMSDa

Index

b

1+2 1 + 3c 2 + 3d a

Margulese

Consistency test

Aij

0.040 2 86.091 0.071 3 97.449 0.037 2 633.525 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffi Pn   expt calc 2 ln g i =g j Þ ðln g i =g j Þ gi k¼1 ð k k RMSD d ln g ¼ : n

Aji 124.593 194.073 609.007

j

b c d e

Fig. 3. Experimental T–x2–y2 diagram of 2-propanol (2) + 2,2,4-trimethylpentane (3) at 101.3 kPa: (~,~) this work; (*,*) Bures et al., 1959; (^,^) Hiaki et al., 1994; (—) NRTL equation. Full symbols refer to liquid-phase compositions and open symbols to vapor-phase compositions.

of d ln(gi/gj) were determined. Table 6 shows the results for the thermodynamic consistency test. The consistency-index values for tetrahydrofuran + 2-propanol, tetrahydrofuran + 2,2,4-trimethylpentane, and 2-propanol + 2,2,4-trimethylpentane systems were found to be 2, 3, and 2, respectively, suggesting that all binary VLE data are of acceptable quality. The equilibrium phase compositions were also measured for the ternary system of tetrahydrofuran (1) + 2-propanol (2) + 2,2,4-trimethylpentane (3) at 101.3 kPa, and the results are presented in Table 7. Similarly, Eq. (1) was applied to calculate the activity coefficients for each component. Fig. 5 shows the experimental tie-lines between the saturated vapor and liquid phases, indicating the absence of a ternary azeotrope.

1 + 2: tetrahydrofuran (1) + 2-propanol (2). 1 + 3: tetrahydrofuran (1) + 2,2,4-trimethylpentane (3). 2 + 3: 2-propanol (2) + 2,2,4-trimethylpentane (3).  0  0 0 0 A A gE Margules equation RT ¼ xi x j A ji xi þ Ai j x j ; Ai j ¼ Ti j ; A ji ¼ Tji .

The ternary system was found to be thermodynamically consistent as tested by the McDermott–Ellis method (McDermott and Ellis, 1965) modified by Wisniak and Tamir (1977). According to this method, two experimental points a and b are considered to be thermodynamically consistent if D < Dmax where D is a local deviation and Dmax is a maximum deviation, both related to the equilibrium data a and b. The errors in the present measurements as dP = 0.1 kPa, dT = 0.05 K, and dx = 0.003 mol fraction units were used for the method. The calculated Dmax  D values were greater than zero for all experimental points with a mean value of 0.051, which indicates that the system is thermodynamically consistent according to the method. The VLE experimental data of the three binary systems and the ternary system were then calculated with the various activity coefficient models, including the three-suffix Margules (Gess et al., 1991) the Wilson (1964), the NRTL (Renon and Prausnitz, 1968), and the UNIQUAC (Abrams and Prausnitz, 1975) models by a bubble temperature calculation procedure (Smith and Van Ness, 1987). All the activity coefficient models gave satisfactory representations for the investigated binary systems, as shown in Table 8. Generally, the NRTL equation gives the best correlation. The correlation results for the ternary VLE data using the above four models are show in Table 9. There are no significant differences in the correlation between the various equations. Estimation of energy parameters of all the models studied was based on minimization of the following objective function: 2  n X N  expt X g i  g calc i OF ¼ (4) g expt i k k¼1 i¼1 where n is the number of data points and N is the number of components. The liquid molar volume (vL ) of pure component for the Wilson equation was evaluated from d

b½1þð1T=cÞ v ðm =kmolÞ ¼ a L

Fig. 4. Experimental gE/RT vs. xi diagram at 101.3 kPa for the systems: (*) tetrahydrofuran (1) + 2-propanol (2), xi = x1; (~) tetrahydrofuran (1) + 2,2,4trimethylpentane (3), xi = x1; (&) 2-propanol (2) + 2,2,4-trimethylpentane (3), xi = x2; (—) Redlich–Kister equation; (- - - ) NRTL equation.

3



(5)

where a, b, c, and d are the component specific coefficients for liquid molar volume and T is the equilibrium temperature in Kelvin. The constants a, b, c, and d of liquid molar volume were obtained from CHEMCAD Data Bank (1998). These constants a, b, c, and d along with the parameters required for the UNIQUAC equation were also shown in Table 5.

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Table 7 VLE Data for the ternary system of tetrahydrofuran (1) + 2-propanol (2) + 2,2,4-trimethylpentane (3) at 101.3 kPa T (K)

x1

x2

y1

y2

g1

g2

g3

gE/RT

340.22 341.24 341.49 342.19 342.50 342.84 343.26 343.53 343.61 343.63 343.91 344.33 344.44 344.61 344.97 345.25 345.62 345.67 345.84 346.12 346.16 346.32 346.33 347.08 347.31 347.96 348.07 348.31 348.33 348.58 348.63 349.43 349.52 349.56 349.58 349.61 349.62 349.69 349.75 349.77 349.89 349.95 350.88 351.16 351.33 351.96 353.47 353.49 357.38 361.47

0.897 0.804 0.796 0.689 0.714 0.573 0.739 0.592 0.589 0.517 0.519 0.584 0.486 0.475 0.429 0.313 0.284 0.410 0.389 0.293 0.386 0.276 0.387 0.230 0.314 0.185 0.185 0.172 0.108 0.143 0.383 0.050 0.098 0.101 0.086 0.051 0.128 0.107 0.064 0.048 0.175 0.054 0.050 0.186 0.051 0.066 0.104 0.252 0.103 0.053

0.046 0.154 0.061 0.269 0.174 0.171 0.064 0.366 0.290 0.290 0.178 0.058 0.458 0.378 0.171 0.411 0.486 0.481 0.368 0.568 0.562 0.264 0.259 0.295 0.635 0.579 0.473 0.686 0.41 0.293 0.058 0.503 0.765 0.612 0.749 0.398 0.295 0.699 0.337 0.757 0.777 0.668 0.303 0.14 0.842 0.216 0.144 0.059 0.062 0.051

0.939 0.855 0.889 0.781 0.765 0.691 0.802 0.689 0.680 0.591 0.632 0.768 0.602 0.545 0.514 0.394 0.369 0.482 0.469 0.385 0.494 0.376 0.474 0.331 0.438 0.249 0.234 0.265 0.148 0.227 0.584 0.072 0.148 0.142 0.136 0.078 0.170 0.152 0.097 0.074 0.276 0.072 0.078 0.289 0.081 0.104 0.160 0.407 0.186 0.096

0.034 0.113 0.043 0.184 0.137 0.172 0.058 0.270 0.229 0.268 0.194 0.068 0.351 0.326 0.221 0.387 0.434 0.380 0.344 0.476 0.417 0.336 0.289 0.370 0.490 0.517 0.482 0.554 0.513 0.431 0.102 0.569 0.663 0.567 0.657 0.534 0.428 0.608 0.502 0.667 0.641 0.616 0.499 0.297 0.734 0.438 0.329 0.144 0.217 0.178

1.010 0.993 1.035 1.027 0.961 1.070 0.950 1.011 1.000 0.990 1.045 1.114 1.045 0.963 0.995 1.036 1.057 0.955 0.974 1.053 1.024 1.085 0.975 1.119 1.077 1.019 0.954 1.154 1.026 1.179 1.131 1.042 1.090 1.014 1.140 1.101 0.956 1.020 1.087 1.105 1.126 0.950 1.081 1.068 1.086 1.057 0.987 1.036 1.034 0.924

1.407 1.335 1.268 1.193 1.355 1.705 1.509 1.214 1.295 1.514 1.764 1.863 1.212 1.354 1.997 1.438 1.342 1.185 1.392 1.233 1.090 1.856 1.627 1.771 1.079 1.214 1.379 1.082 1.675 1.949 2.325 1.446 1.104 1.178 1.114 1.702 1.840 1.100 1.879 1.110 1.034 1.153 1.981 2.523 1.029 2.333 2.470 2.637 3.232 2.743

1.294 2.008 1.242 2.125 2.208 1.335 1.747 2.378 1.827 1.773 1.381 1.086 1.982 2.060 1.537 1.823 1.943 2.868 1.733 2.231 3.813 1.388 1.483 1.360 3.027 2.080 1.736 2.644 1.458 1.247 1.153 1.605 2.749 2.018 2.495 1.399 1.384 2.452 1.324 2.626 3.405 2.205 1.246 1.160 3.248 1.174 1.192 1.142 1.108 1.108

0.039 0.068 0.073 0.098 0.113 0.204 0.099 0.114 0.148 0.225 0.222 0.128 0.148 0.203 0.288 0.326 0.312 0.177 0.245 0.245 0.127 0.336 0.256 0.341 0.128 0.289 0.332 0.217 0.396 0.343 0.176 0.399 0.222 0.303 0.243 0.402 0.362 0.243 0.386 0.272 0.106 0.312 0.354 0.242 0.155 0.302 0.261 0.158 0.162 0.139

The experimental VLE data of the ternary system of tetrahydrofuran + 2-propanol + 2,2,4-trimethylpentane have been predicted using the three-suffix Margules, Wilson, NRTL, and UNIQUAC models for the activity coefficients of the components with the binary interaction parameters from Table 8. The average deviations of the predicted bubble temperatures and saturated vapor compositions for the ternary system are summarized in Table 10. As can be seen, the Wilson model exhibits a somewhat smaller deviation from the experimental result than the other models.

Fig. 5. Tie-lines for the ternary system tetrahydrofuran (1) + 2-propanol (2) + 2,2,4-trimethylpentane (3) system at 101.3 kPa: (*) liquid-phase; (*) vapor-phase.

The deviation in the boiling temperature for mixture is defined by DT ¼ T 

N X

xi T i

(6)

i¼1

where T is the boiling temperature of a mixture and Ti is the boiling temperature of pure components i. The mixing functions gE/RT and DT for binary mixtures were represented Table 8 VLE data reduction for three binary systems with the three-suffix Margules, Wilson, NRTL, and UNIQUAC models Models

System

Aija

RMSDb

Ajia

i+j c

Margules

1+2 1 + 3d 2 + 3e

Wilson

1+2 1+3 2+3

44.61 88.37 671.21

149.14 184.18 151.92

1+2 1+3 2+3

115.94 715.27 375.70

20.43 396.05 378.21

1+2 1+3 2+3

88.18 93.27 88.84

46.76 30.54 376.77

NRTL

UNIQUAC

0.240 0.218 1.711

0.280 0.564 1.730

0.256 0.204 0.372

dT (K)

dyi

0.18 0.11 0.24

0.004 0.007

0.13 0.17 0.34

0.004 0.004

0.18 0.18 0.17

0.004 0.005

0.17 0.20 0.23

0.004 0.004

dyj

0.006

0.007

0.005

0.005

a

The binary adjustable parameters for Wilson: Aij = (lij  lii)/R, Aji = (lji  ljj)/R; NRTL: Aij = (gij  gjj)/R, Aji = (gji  gii)/R; UNIQUAC: Aij = (Uij  Ujj)/R, Aji = (Uji  Uii)/R. b

RMSD: root mean squared deviation, defined as: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ffi Pn  expt calc 2 Pn  expt calc 2 j¼1

Tj

T j

j¼1

; RMSD dyi ¼ RMSD dT ¼ n c 1 + 2: tetrahydrofuran (1) + 2-propanol (2). d 1 + 3: tetrahydrofuran (1) + 2,2,4-trimethylpentane (3). e 2 + 3: 2-propanol (2) + 2,2,4-trimethylpentane (3).

yi; j yi; j n

.

C.-C. Hsu, C.-H. Tu / Journal of the Chinese Institute of Chemical Engineers 39 (2008) 265–273

271

Table 9 VLE correlation for the ternary system of tetrahydrofuran (1) + 2-propanol (2) + 2,2,4-trimethylpentane (3) with the three-suffix Margules, Wilson, NRTL, and UNIQUAC models Models

Margules Wilson NRTLa UNIQUAC a

A21

A12

0.203 24.555 118.420 213.64

A13

0.160 179.530 14.393 119.920

A31

0.114 199.630 464.571 64.937

0.414 217.510 240.310 31.287

A32

1.461 1034.501 461.820 83.143

RMS

1.707 406.270 169.182 523.740

dT (K)

dy1

dy2

0.73 0.97 0.95 0.98

0.025 0.017 0.018 0.018

0.021 0.017 0.017 0.017

a = 0.3 for NRTL model.

Table 10 VLE prediction for the ternary system of tetrahydrofuran (1) + 2-propanol (2) + 2,2,4-trimethylpentane (3) from the determined binary parameters of Table 8 Models

RMSDa dT (K)

dy1

dy2

dy3

Margules Wilson NRTL UNIQUAC

1.24 0.69 0.94 0.79

0.028 0.016 0.021 0.018

0.028 0.024 0.035 0.024

0.032 0.028 0.030 0.028

a

A23

mathematically by the following type of the Redlich–Kister equation (Redlich and Kister, 1948) for correlating the data: DQðxi ; x j Þ ¼ xi x j

" s¼

2 n X ðDQexpt  DQcalc Þ i

ak ðxi  x j Þ

DQ123 ¼ DQðx1 ; x2 Þ þ DQðx1 ; x3 Þ þ DQðx2 ; x3 Þ

E

where DQ refers to g /RT or DT (K) as a function of mole fractions xi of pure component i and xj of pure component j. The values of the binary coefficients ak for each binary system were determined by a nonlinear regression analysis based on the least-squares method and are summarized along with the standard deviations between the experimental and fitted values of the respective functions in Table 11. The standard deviation

2 X 2i X C i j xi1 x2j

(9)

i¼0 j¼0

(7)

k¼0

(8)

where n is the number of experimental points and p is the number of parameters. The largest standard deviations occurred for the 2-propanol + 2,2,4-trimethylpentane system with 0.06 K for DT and 0.002 for gE/RT. The derived properties, gE/RT and DT (K), for the ternary system of tetrahydrofuran (1) + 2-propanol (2) + 2,2,4-trimethylpentane (3) were correlated using the equation:

þ x1 x2 x3 k

#1=2

i

n p

i¼1

RMSD as defined in Table 7.

m X

(s) is defined by

where DQ123 refers to gE/RT or DT (K) for ternary mixtures, x3 = 1  x1  x2, and DQ is the binary contribution function to the gE/RT or DT (K) given by Eq. (7) with the parameters shown in Table 11. The ternary parameters Cij were determined with the optimization algorithm similar to that for the binary parameters of Eq. (7). The ternary parameters Cij and the corresponding standard deviations defined as Eq. (8) are given in Table 11. The standard deviations occurred for the

Table 11 Binary coefficients ak of the Redlich–Kister equation and ternary coefficients Cij of Eq. (9) and their standard deviations s for gE/RT and DT DQ

a1

a0

Tetrahydrofuran (1) + 2-propanol (2) 0.309 gE/RT DT (K) 8.88

a2

0.084 1.57

Tetrahydrofuran (1) + 2,2,4-trimethylpentane (3) 0.421 0.131 gE/RT DT (K) 32.62 12.41 2-Propanol (2) + 2,2,4-trimethylpentane (3) 1.756 0.048 gE/RT DT (K) 56.85 30.10 DQ123

C00

C10

a3

a4

a5

a6

a7

s

0.029 0.98

0.065 0.17

2.49

0.001 0.02

0.018 3.15

0.064 2.29

1.64

0.002 0.03

0.110 58.35

0.075 28.57

21.29

C01

Tetrahydrofuran (1) + 2-propanol (2) + 2,2,4-trimethylpentane (3) 4.103 0.211 16.714 gE/RT DT (K) 299.49 843.64 702.16

22.31

98.91

76.78

0.002 0.06

C11

C20

C02

s

20.368 786.40

9.238 744.70

11.364 572.93

0.016 0.56

272

C.-C. Hsu, C.-H. Tu / Journal of the Chinese Institute of Chemical Engineers 39 (2008) 265–273

Fig. 6. The iso-lines of the reduced Gibbs energy gE/RT for the ternary system tetrahydrofuran (1) + 2-propanol (2) + 2,2,4-trimethylpentane (3) system at 101.3 kPa.

deviation from ideal behavior. The azeotropic point for the binary system of 2-propanol + 2,2,4-trimethylpentane is in good agreement with that from Hiaki et al. (1994). No azeotropic behavior was found for the ternary system from the ternary VLE data measured. The activity coefficients of pure liquid were obtained from the assumptions of an ideal vaporphase and a unity in the Poynting factor. The thermodynamic consistency of the VLE data was tested for the three binary systems using the Van Ness direct test. All the binary VLE data were shown to be acceptable by the test. Using the test of McDermott and Ellis (1965) as modified by Wisniak and Tamir (1977) for ternary VLE data, the ternary system adequately fulfilled the criterion of thermodynamic consistency. Reduction of the VLE data using the three-suffix Margules, Wilson, NRTL, and UNIQUAC models showed that all four models gave satisfactory correlations. The NRTL equation seems to have the best result. Based on the information of the constituent binaries, the Wilson model yielded the best prediction for the ternary equilibrium. The derived data, gE/RT and DT of three binary systems were correlated using the Redlich–Kister equation and those of the ternary system were represented using variable-degree polynomials. The results are used to construct the curves of constant gE/RT and DT for the ternary mixtures. Acknowledgement The authors wish to extend their deep gratitude for the support by the National Science Council of Republic of China under grant NSC 95-2221-E-126-010-MY3. References

Fig. 7. The iso-lines of the boiling temperature T (K) of the liquid-phase for the ternary system tetrahydrofuran (1) + 2-propanol (2) + 2,2,4-trimethylpentane (3) system at 101.3 kPa.

ternary system with 0.56 K in DT and 0.016 in gE/RT. The iso-lines for gE/RT of liquid-phase in Fig. 6 and the iso-lines for boiling temperature in Fig. 7 were obtained from Eq. (9) using the parameters reported in Table 11. As can be expected from the behavior of binary mixtures, the ternary system of tetrahydofuran + 2-propanol + 2,2,4-trimethylpentane shows positive values of gE/RT at all equilibrium compositions. The maximum gE/RT value is located at x  0.5 of 2-propanol near the binary 2-propanol + 2,2,4trimethylpentane. 4. Conclusion Isobaric VLE data were determined experimentally for the systems composed of tetrahydrofuran, 2-propanol, and 2,2,4trimethylpentane at 101.3 kPa. All systems exhibited a positive

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