Low-Pressure VLE Measurements and Thermodynamic Modeling

Article Cite This: J. Chem. Eng. Data 2018, 63, 4614−4625

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Low-Pressure VLE Measurements and Thermodynamic Modeling, with PSRK and NRTL, of Binary 1‑Alcohol + n-Alkane Systems Machelle Ferreira and Cara E. Schwarz*

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Department of Process Engineering, Stellenbosch University, Private Bag X1, Stellenbosch, Matieland 7602, South Africa ABSTRACT: New subatmospheric vapor−liquid equilibrium (VLE) data for five binary 1-alcohol + n-alkane systems are presented. An all-glass dynamic recirculating still was used to measure the phase behavior of the 1-pentanol + n-nonane, 1-hexanol + n-decane, 1-heptanol + n-undecane, 1-octanol + n-dodecane, and 1-decanol + n-tetradecane systems at 40 kPa. Each of the five systems displayed an azeotrope, indicating complex molecular interactions. Thermodynamic modeling was conducted with (1) the NRTL activity coefficient model, (2) the predictive Soave− Redlich−Kwong (PSRK) group contribution equation of state (EoS) with original UNIFAC model parameters, and (3) PSRK with newly regressed NRTL parameters. The models, in order of decreasing performance, were NRTL > PSRK (with UNIFAC) > PSRK (with NRTL). Therefore, the PSRK with UNIFAC parameters GE-EoS investigated in this article showed that accurate 1-alcohol + n-alkane VLE data can be predicted without the need to first measure experimental data.

1. INTRODUCTION The design of separation processes usually requires thermodynamic data, more specifically, phase equilibria data. As more than 40% of the cost in industrial processes is related to their specific separation units, the need for accurate thermodynamics is imperative.1 Several studies on CO2 + hydrocarbon systems have shown a large variety of phase behavior and interesting thermodynamic properties. For example, the solubility behavior of a solute in supercritical CO2 is strongly affected when a second low-volatility component is added.2 Investigations on the phase behavior of the ternary CO2 + 1-decanol + n-dodecane system revealed significant interactions between the detergentrange 1-alcohol and n-alkane in the presence of supercritical CO2.3−5 Another study conducted on the separation of 1dodecanol and n-tetradecane in the presence of supercritical CO2 shows similar interactions between the 1-alcohol and nalkane.6,7 Recently, the complex phase behavior of the CO2 + 1decanol + n-tetradecane ternary system8 was studied. The highpressure phase equilibria data measured by Ferreira and Schwarz8 confirmed the significant solute + solute interactions taking place between 1-decanol and n-tetradecane in the presence of near-critical and supercritical CO2, and the solute + solute interactions were directly connected to the cosolvency effects observed. This finding encouraged an experimental study on the fluid-phase behavior of 1-alcohol + n-alkane binary systems. This article presents experimental measurement results on similar-boiling-point 1-alcohol + n-alkane binary systems and thermodynamic modeling of the measured data. In so doing, the data presented in this article will provide further insight into the distinct solute + solute binary interactions that occur in these complex systems. The following five 1-alcohol + n-alkane binary systems will be measured and evaluated in this study at p = 40 © 2018 American Chemical Society

kPa: (i) 1-pentanol + n-nonane, (ii) 1-hexanol + n-decane, (iii) 1-heptanol + n-undecane, (iv) 1-octanol + n-dodecane, and (v) 1-decanol + n-tetradecane. These five binary systems were selected as they contain components with similar boiling points, with the 1-alcohol always being slightly more volatile than the nalkane. As the molecular mass of the compounds increases, measurements become increasingly difficult, through studying the homologous series’ future extrapolation to high molecular masses may be possible. The reason for selecting a vacuum pressure of 40 kPa was to produce good and operable lowpressure data at temperatures close to high-pressure phase equilibrium data. When commencing with the design of a separation unit it is often questioned whether sufficient data and/or suitable models are available for the specific process. The answer to this question varies with respect to the availability of suitable models in process simulators. Fortunately, several commercial simulators, e.g., Aspen Plus, have a wide spectrum of thermodynamic models from which to choose.9 The purpose of evaluating, selecting, and improving thermodynamic models found in Aspen Plus is to ultimately end with a working process model, such as that designed by Zamudio et al.10 Over the last several decades, various new excess Gibbs (GE) mixing rules have been developed, optimized, and incorporated into Aspen Plus11−13 to enable vapor−liquid equilibrium (VLE) predictions at high and low temperatures or pressures as well as for supercritical compounds. As a result, predictive models are becoming increasingly popular for correlating thermodynamic properties and predicting phase equilibria data. Since being Received: August 1, 2018 Accepted: October 30, 2018 Published: November 12, 2018 4614

DOI: 10.1021/acs.jced.8b00680 J. Chem. Eng. Data 2018, 63, 4614−4625

Journal of Chemical & Engineering Data

Article

Table 1. Chemicals Used with Their Structures,40 Suppliers, CAS Numbers, and Mass Fraction Purities (Specified by Supplier)

Table 2. Measured Vapor Pressures, p, at Various Temperatures, T, for the 1-Alcohol and n-Alkane Components of Interest in This Worka n-tetradecane T/K

p/kPa

498.07 497.96 496.08 495.18 492.53 491.29 489.26 489.17

50.70 50.50 48.13 46.96 43.80 42.42 40.04 40.00

1-decanol

n-dodecane T/K 478.47 474.33 470.69 467.52 465.47 461.72 459.31 456.87 453.92 1-octanol

n-undecane

n-decane

n-nonane

p/kPa

T/K

p/kPa

T/K

p/kPa

T/K

p/kPa

77.75 69.97 63.63 58.41 55.35 49.93 46.71 43.58 40.08

458.59 454.55 451.59 448.68 445.40 442.20 438.71 434.60

78.59 70.48 65.09 60.13 54.82 50.04 45.18 40.04

446.01 443.51 439.77 435.60 431.14 425.83 420.50 414.08

98.88 92.72 83.97 75.05 66.32 57.04 48.74 40.00

423.88 420.83 417.05 413.23 409.14 404.65 399.76 392.77

101.70 93.72 84.18 75.48 66.68 58.04 49.24 39.96

1-heptanol

1-hexanol

1-pentanol

T/K

p/kPa

T/K

p/kPa

T/K

p/kPa

T/K

p/kPa

T/K

p/kPa

496.88 494.46 492.56 491.16 487.90 484.05 481.36 479.42 476.80 475.40 472.98 469.83

85.24 79.92 76.32 73.44 67.43 61.26 57.04 54.07 50.19 47.97 44.40 40.03

466.80 463.50 460.31 457.08 454.35 450.45 445.86 443.61 437.67

97.64 89.16 81.52 74.25 67.60 60.03 52.15 48.62 40.08

444.34 441.44 438.22 433.75 430.35 426.27 423.00 420.40

88.14 81.04 73.40 63.50 56.78 49.44 44.20 40.12

429.19 427.54 425.15 421.90 418.35 413.31 407.89 403.66

99.78 92.07 85.63 77.40 69.27 58.84 48.72 40.02

410.73 407.17 404.59 400.95 398.11 392.76 384.85

101.20 90.21 82.75 72.93 66.15 54.41 40.01

a

Standard uncertainties are u(T) = 0.2 K and u(p) = 0.36 kPa.

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introduced by Huron and Vidal in 1979,14,15 the aim of these GE mixing rules has been to form group contribution equations of state (EoS), e.g., the predictive Soave−Redlich−Kwong (PSRK) mixing rule as suggested by Holderbaum and Gmehling.16 Here, the universal quasichemical functional group activity coefficient (UNIFAC) GE model was combined with the Soave−Redlich−Kwong (SRK) EoS.16,17 Several other predictive EoS’s have been proposed, e.g., the group contribution EoS based on the modified Huron−Vidal mixing rule (MHV2)18,19 and the Wong−Sandler modified Huron− Vidal mixing rule (W−S).20,21 Previous publications have indicated that the PSRK mixing rule is a more vigorous method than the MHV2 and W−S mixing rules as it has a well-defined reference state.11 Furthermore, the PSRK method contains the largest parameter matrix in the Dortmund data bank (DDB), allowing the mixing rule to produce reliable VLE results over larger temperature and pressure ranges.11 Pertinent 1-alcohol + n-alkane literature data (within the range of C5−C14) were investigated and implied that in 1alcohol + n-alkane systems with m < n, where m and n represent the number of carbon atoms in the alkyl chains of the 1-alcohol and n-alkane, respectively, an azeotrope will form in the T−x−y phase-behavior envelope.22−35 Predictive models are not always equipped to account for complexities arising from complex molecular interactions. Therefore, the nonrandom two-liquid (NRTL) composition-dependent model36 will be considered alongside the PSRK model in this article. In a study conducted by Fischer and Gmehling,17 it was shown that the PSRK mixing rules could produce accurate model correlations with UNIQUAC or NRTL binary interaction parameters (BIPs). Therefore, their work implies that any activity coefficient model can be used with the PSRK mixing rules when its BIPs are known.17 To verify this for the binary 1-alcohol + n-alkane systems of interest here, the NRTL parameters regressed in this work will be used. The aim of this article thus is twofold: (1) to measure and study new VLE data of five pertinent 1-alcohol + n-alkane binary systems at p = 40 kPa for n = m + 4 with 5 ≤ m ≤ 10 and (2) to evaluate the predictive capabilities of the PSRK model, first with UNIFAC BIPs obtained from the literature (DDB)17,37 and second with the NRTL BIPs regressed in this work, alongside the NRTL model as implemented in the Aspen Plus process simulation program.

Figure 1. Vapor pressure ln(psat*) against temperature T to compare the experimental data: ◊, 1-pentanol; ○, 1-hexanol; □, 1-heptanol; Δ, 1-octanol; □, 1-decanol; gray ◊, n-nonane; gray ○, n-decane; gray □, nundecane; gray Δ, n-dodecane; and □, n-tetradecane to the DIPPR correlations: −··−··−, 1-alcohol systems; ···, n-alkane systems.

uniform composition and temperature for the mixture throughout the experiment. The mixture was returned to the immersion heater for recirculation. A maximum operating temperature of T = 523 K is enforced to avoid damage to the glass still and prevent any possible harm to the operator. 2.2. Experimental Procedure. The still was prepared by adding approximately 110 mL of the feed mixture to the mixing chamber. Once the immersion heater rod was completely submerged in the mixture, the magnetic stirrer and immersion heater were switched on. The pressure was also set accordingly (p = 40 kPa) and balanced using the vacuum pump. After approximately 1 h, equilibrium was achieved and confirmed with a steady vapor temperature on the display unit as well as steady liquid and vapor returns. Thereafter, condensed vapor and liquid samples were collected through the two sampling ports. Upon completion of the runs, the contents of the still were drained and approximately 110 mL of acetone was fed into the mixing chamber to wash out the still. The samples were prepared for gas chromatography (GC) analysis by adding approximately 30 mg of sample to 1.5 mL of solvent (n-hexane). Approximately 30 mg of an internal standard (1-pentanol or 1-octanol), measured accurately to 10−5 g, was added to the solvent, after which the samples were analyzed via GC. 2.3. Materials. Table 1 contains the list of components with their respective suppliers, CAS numbers, purity, and chemical structures.40 Prior to experimentation, each of the components listed in Table 1 was analyzed by GC to rule out any impurities. The GC analysis results agreed with or exceeded the listed mass fraction purities provided by the suppliers. Additionally, Karl Fischer titrations were conducted and showed negligible amounts of water (at least 99 mass % pure). Technical-grade air and high-purity helium, supplied by Afrox, were used for the GC. Nitrogen, also supplied by Afrox, was used for overpressure control in the phase equilibrium still. The pure-component vapor pressures provided in Table 2 were measured using the apparatus and compared to literature correlations available in the DIPPR 801 data bank41 (Figure 1). The experimental results correlate well with the literature data of

2. MATERIALS AND METHODS 2.1. Experimental Setup. An all-glass dynamic recirculating still, manufactured by Pilodist, was used to measure the VLE phase behavior of the five binary systems at a subatmospheric pressure of p = 40 kPa. A full schematic representation and detailed discussion of the commercial VLE 100 D still that was utilized in this work have been provided previously.38,39 The heart of the still consists of a mixing chamber, a boiling chamber, a Cottrell tube (spiral contact line), a demixing chamber, and a return system. The electrical immersion heater supplies enough heat to the liquid mixture for partial evaporation. The Cottrell tube connects the boiling chamber to the separation chamber to enable the required phase equilibrium. In the separation chamber, the two-phase mixture is sent over the thermometer to measure the bubble-point (equilibrium) temperature before the two phases are separated, condensed, and returned to the mixing chamber. The compositions of the two coexisting phases are determined through sampling the liquid and condensed vapor phases. A magnet in the mixing chamber ensures a 4616



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each pure component, as shown in Figure 1. Therefore, the measured vapor pressure data confirmed the purity of the chemicals, and all components given in Table 1 were used without further purification. 2.4. Uncertainty. The measurement uncertainties are as follows: (i) After the temperature calibration was complete, the Pt100 temperature probe connected to a digital Hart Scientific thermometer measured the equilibrium temperature of the mixture to an accuracy of 0.1 K. Fluctuations of 0.03 K in the temperature were observed during sampling. However, the deviation never exceeded 0.1 K. The maximum absolute uncertainty in the temperature is 0.2 K, i.e., u(T) = 0.2 K. (ii) A Wika UT-10 unit with a maximum operating pressure of 160 kPa absolute and a quoted accuracy of 0.1% (0.16 kPa) of full scale output, per the most recent calibration certificate, was utilized to measure the pressure. Furthermore, pressure fluctuations of up to 0.2 kPa were observed during sampling. Therefore, the maximum absolute uncertainty in the pressure transducer is 0.36 kPa, i.e., u(p) = 0.36 kPa. (iii) After manually completing several repeatability tests on the GC, for samples with a known composition, a maximum uncertainty of 0.022 g·g−1 for the analysis was calculated, i.e., u(x) = u(y) = 0.022 mol·mol−1.

Figure 2. Temperature, T, against liquid, x1, and vapor, y1, mole fractions for the ethanol (1) + 2,2,4-trimethylpentane (2) binary system at a pressure p = 101.3 kPa. Experimental VLE data (⧫, x1; and gray ○, y1) compared to published data by □, Pienaar et al.;38 ○, Brits;44 × , Wen and Tu;46 Δ, Ku and Tu;45 and ◊, Hiaki et al.33

The L/W test42 was selected to confirm the experimental data as a representation of the system dynamics by means of the following: (i) A point-to-point test, where Lk = Wk, must be satisfied for each experimental point measured. However, because of experimental errors and the assumptions made to derive the thermodynamic test, a deviation factor must be specified. (ii) An area test where the deviation value D, D = [100|L − W|/(L + W)], is less than 3 to 5 across the entire composition range is required to ensure thermodynamic consistency. However, the Gibbs−Duhem equation is disregarded when using the L/W consistency test as the relationship between the excess Gibbs energy of the binary system is compared to its boiling-point temperature at equilibrium.42 Therefore, a second test is recommended to be used in conjunction with the L/W test. One method that has been proven to be useful in literature is that of McDermott and Ellis,43 who used a two-point consistency test to evaluate each consecutive data point separately. If a deviation (Dev) within the maximum deviation (Dmax) is obtained for each data point, then the data will be consistent. Results of both the L/W and McDermott−Ellis consistency tests are given together with the experimental results. 3.2. Reproducibility Test. Although both the L/W and McDermott−Ellis consistency tests are necessary, they are not sufficient on their own to prove the experimental data as accurate due to composition, temperature, and pressure inaccuracies during measurements. Theoretically, these inaccuracies are considered in the McDermott−Ellis consistency test; however, reproducibility tests are required as with any new experimental procedure to validate the equipmental setup. The experimental setup and method were verified by measuring VLE data for the binary ethanol + 2,2,4trimethylpentane system. This binary system was previously measured by Pienaar et al.38 and Brits44 on the experimental

3. VERIFICATION 3.1. Thermodynamic Consistency. To test for systematic errors in the data, a thermodynamic consistency test can be used. Table 3. Experimental VLE Data for the Reference System Ethanol (1) + 2,2,4-Trimethylpentane (2) at Temperature T, Liquid Mole Fraction x1, and Vapor Mole Fraction y1 at Pressure p = 101.3 kPaa T/K

x1

y1

351.44 351.17 350.63 350.03 349.29 349.17 348.16 346.77 345.54 344.84 344.58 344.53 344.48 344.42 344.40 344.33 344.37 344.35 344.49 344.73 346.37 355.43 372.26

1.000 0.996 0.984 0.982 0.966 0.966 0.957 0.935 0.864 0.674 0.618 0.591 0.564 0.532 0.494 0.462 0.419 0.353 0.255 0.251 0.184 0.0381 0.000

1.000 0.995 0.922 0.967 0.903 0.841 0.826 0.782 0.730 0.682 0.641 0.661 0.635 0.627 0.653 0.624 0.620 0.612 0.594 0.594 0.575 0.393 0.000

a

Standard uncertainties are u(T) = 0.2 K, u(x1) = u(y1) = 0.022 mol· mol−1, and u(p) = 0.36 kPa. 4617



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Figure 3. Temperature, T, against liquid, x1, and vapor, y1, mole fractions at pressure p = 40 kPa. Experimental VLE data are represented by □, x1 and Δ, y1. Repeatability data are represented by ■, x1 and ▲, y1 for (a) 1-pentanol (1) + n-nonane (2); (b) 1-hexanol + n-decane (2); (c) 1-heptanol (1) + nundecane (2); (d) 1-octanol (1) + n-dodecane (2); and (e) 1-decanol + n-tetradecane (2).

system measured in this work and are indicated in Figure 2 by means of error bars. The measured data were used in combination with PRO-VLE 2.0 and the maximum temperature, pressure, and composition errors observed to calculate the necessary thermodynamic consistency parameters. A maximum D value of 1.670 was obtained for the system, well below the lower threshold value of 3 for the L/W test. For the McDermott−Ellis point-to-point test, all D values were found to be lower than their respective

setup used in this work, and several other research groups have investigated and published measured data on this system.33,45 The measured data are presented in Table 3, and a visual comparison of the results to published literature by Pienaar et al.,38 Brits,44 Wen and Tu,46 Ku and Tu,45 and Hiaki et al.33 is shown in Figure 2. Good agreement is seen between the new data measured in this work and literature measurements. Maximum errors of T = 0.2 K for temperature and x = y = 0.022 mol·mol−1 for composition are observed for the binary 4618



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Table 5. Experimental VLE Data for 1-Hexanol (1) + nDecane (2) at Temperature T, Liquid Mole Fraction x1, and Vapor Mole Fraction y1 at Pressure p = 40 kPaa

maximum deviations, Dmax. Therefore, the data of the verification system adheres to the L/W and McDermott−Ellis tests for thermodynamic consistency.

4. RESULTS AND DISCUSSION The experimental T−x−y data generated for the five 1-alcohol + n-alkane systems are presented in Figure 3a−e, and the Table 4. Experimental VLE Data for 1-Pentanol (1) + nNonane (2) at Temperature T, Liquid Mole Fraction x1, and Vapor Mole Fraction y1 at Pressure p = 40 kPaa T/K

x1

y1

T/K

x1

y1

384.45 384.09 383.61 383.50 382.89 382.36 381.87 381.04 380.69 380.66 380.37 380.27 380.09 379.57 379.20 378.81 378.57 378.64 378.59 378.44 378.39 378.40 378.17

1.000 0.990 0.979 0.979 0.959 0.945 0.930 0.897 0.892 0.885 0.875 0.870 0.857 0.826 0.795 0.765 0.742 0.729 0.719 0.698 0.690 0.692 0.641

1.000 0.966 0.934 0.934 0.893 0.853 0.824 0.773 0.764 0.749 0.744 0.734 0.724 0.703 0.666 0.642 0.626 0.619 0.617 0.605 0.602 0.602 0.579

378.09 378.09 377.93 377.98 378.18 378.32 378.78 378.49 379.16 379.59 379.95 379.76 380.17 380.46 381.03 382.71 383.36 383.85 385.23 385.89 389.38 390.17 392.17

0.621 0.552 0.493 0.463 0.402 0.359 0.318 0.323 0.254 0.216 0.211 0.209 0.188 0.182 0.151 0.101 0.0950 0.0900 0.0610 0.0590 0.0220 0.0160 0.000

0.571 0.543 0.522 0.512 0.491 0.477 0.470 0.466 0.440 0.422 0.418 0.416 0.411 0.393 0.375 0.324 0.308 0.288 0.242 0.219 0.100 0.0680 0.000

T/K

x1

y1

T/K

x1

y1

402.36 402.07 401.87 401.66 401.43 401.16 400.83 400.34 400.21 399.84 399.47 399.45 399.38 399.23 399.12 399.00 398.84 398.75 398.67 398.63 398.54 398.38 398.50

1.000 0.994 0.986 0.977 0.968 0.959 0.948 0.921 0.903 0.896 0.875 0.869 0.861 0.844 0.833 0.816 0.797 0.779 0.768 0.763 0.742 0.725 0.543

1.000 0.982 0.961 0.940 0.922 0.904 0.883 0.836 0.820 0.803 0.768 0.766 0.754 0.734 0.725 0.715 0.699 0.684 0.695 0.671 0.660 0.654 0.574

398.49 398.59 398.65 398.67 398.79 398.81 398.86 398.92 398.87 399.07 399.19 399.25 399.64 400.04 400.78 402.73 403.95 405.92 408.68 409.70 410.66 411.62 414.18

0.507 0.497 0.469 0.462 0.444 0.439 0.430 0.418 0.407 0.397 0.374 0.355 0.319 0.287 0.239 0.167 0.125 0.0940 0.0490 0.0340 0.0240 0.0120 0.000

0.566 0.561 0.542 0.551 0.533 0.539 0.528 0.529 0.525 0.529 0.519 0.507 0.500 0.478 0.453 0.397 0.355 0.297 0.200 0.160 0.125 0.0910 0.000

a Standard uncertainties are u(T) = 0.2 K, u(x1) = u(y1) = 0.022 mol· mol−1, and u(p) = 0.36 kPa.

Table 6. Experimental VLE Data for 1-Heptanol (1) + nUndecane (2) at Temperature T, Liquid Mole Fraction x1, and Vapor Mole Fraction y1 at Pressure p = 40 kPaa


measured data are provided in Tables 4−8. The experimental results were analyzed with both the L/W test and the McDermott−Ellis test. Final D values below the higher threshold value of 5 were obtained for the L/W consistency test, namely, 2.427 (1-pentanol + n-nonane), 3.712 (1-hexanol + n-decane), 2.514 (1-heptanol + n-undecane), 4.588 (1-octanol + n-dodecane), and 3.894 (1-decanol + n-tetradecane). With respect to the McDermott−Ellis consistency test for each binary system, all D values were found to be lower than their respective Dmax values. Therefore, the binary VLE data measured in this work are confirmed to be thermodynamically consistent. Furthermore, repeatability tests were conducted for each binary system and are in good agreement, as shown by the small error bars in Figure 3. In Figure 4, the 1-pentanol + n-nonane data measured in this work is compared to previously measured low-pressure VLE data.47,48 The data measured by Kirss and co-workers47,48 at p = 26.66 kPa, p = 53.33 kPa, p = 79.99 kPa, and p = 101.32 kPa helps to illustrate the effect of pressure and shows how the data from this work (at p = 40 kPa) lies well between their data in terms of temperature and pressure. For the 1-hexanol + n-decane and 1-heptanol + n-undecane systems, T−x−y data at p = 101.32 kPa was published by Kushner et al.49 Similarly, 1-pentanol + nnonane, 1-hexanol + n-decane, and 1-heptanol + n-undecane

T/K

x1

y1

T/K

x1

y1

419.40 419.26 419.03 418.52 418.24 417.86 417.75 417.47 417.12 416.95 416.87 416.84 416.92 416.86 416.90 416.79 416.84 416.85 416.80 416.72 416.73 416.78 416.78

1.000 0.989 0.978 0.958 0.941 0.920 0.901 0.870 0.841 0.828 0.805 0.792 0.781 0.761 0.759 0.738 0.720 0.705 0.698 0.669 0.645 0.628 0.615

1.000 0.980 0.957 0.924 0.897 0.870 0.847 0.813 0.782 0.773 0.761 0.741 0.741 0.731 0.730 0.716 0.709 0.701 0.691 0.688 0.662 0.653 0.659

417.52 418.12 418.26 418.66 419.09 419.47 419.98 420.00 420.10 420.59 421.15 422.23 423.30 423.33 423.42 424.02 424.99 425.97 426.63 428.56 431.70 433.25 434.50

0.478 0.407 0.383 0.352 0.324 0.311 0.297 0.284 0.270 0.242 0.223 0.187 0.158 0.157 0.152 0.136 0.116 0.0970 0.0860 0.0700 0.0310 0.0170 0.000

0.595 0.552 0.561 0.549 0.529 0.515 0.493 0.505 0.490 0.468 0.453 0.417 0.375 0.378 0.383 0.365 0.339 0.313 0.297 0.226 0.108 0.0610 0.000

a

Standard uncertainties are u(T) = 0.2 K, u(x1) = u(y1) = 0.022 mol· mol−1, and u(p) = 0.36 kPa.

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Table 7. Experimental VLE Data for 1-Octanol (1) + nDodecane (2) at Temperature T, Liquid Mole Fraction x1, and Vapor Mole Fraction y1 at Pressure p = 40 kPaa T/K

x1

y1

T/K

x1

y1

436.67 436.42 436.13 436.07 435.82 435.62 435.38 435.26 435.14 435.08 435.13 435.16 435.13 435.18 435.22 435.29 435.59 435.79 436.07 436.47

1.000 0.998 0.985 0.973 0.945 0.923 0.902 0.879 0.860 0.840 0.837 0.799 0.736 0.723 0.709 0.673 0.574 0.551 0.503 0.425

1.000 0.993 0.968 0.948 0.913 0.886 0.862 0.836 0.812 0.799 0.800 0.773 0.726 0.721 0.719 0.703 0.653 0.651 0.617 0.598

436.94 437.32 437.54 437.94 438.25 438.49 439.11 439.64 440.57 441.75 442.73 443.33 443.90 445.45 446.86 447.76 449.91 452.99 453.92

0.389 0.353 0.332 0.299 0.276 0.272 0.227 0.190 0.150 0.117 0.0950 0.0850 0.0800 0.0480 0.0350 0.0270 0.0140 0.00400 0.000

0.604 0.570 0.575 0.554 0.553 0.540 0.521 0.496 0.453 0.427 0.379 0.361 0.354 0.293 0.258 0.235 0.145 0.0410 0.000

Figure 4. Temperature, T, against liquid, x1, and vapor, y1, mole fractions for the 1-pentanol (1) + n-nonane (2) binary system at varying pressures: ×, p = 26.66 kPa (Kirss et al.48); △, p = 40 kPa (this work); ◊, p = 53.33 kPa (Kirss et al.48); □, p = 79.99 kPa (Kirss et al.48); and ○, p = 101.32 kPa (Kirss et al.47).


Table 8. Experimental VLE Data for 1-Decanol (1) + nTetradecane (2) at Temperature T, Liquid Mole Fraction x1, and Vapor Mole Fraction y1 at Pressure p = 40 kPaa T/K

x1

y1

T/K

x1

y1

469.23 469.01 468.92 468.77 468.72 468.65 468.66 468.56 468.60 468.74 468.73 468.88 468.90 468.69 468.92 469.03 469.40 469.39 469.17 469.68 469.91 470.22 470.40

1.000 0.994 0.984 0.961 0.943 0.922 0.865 0.858 0.835 0.809 0.805 0.787 0.785 0.773 0.737 0.700 0.667 0.651 0.650 0.616 0.573 0.535 0.532

1.000 0.991 0.978 0.952 0.935 0.916 0.869 0.866 0.853 0.834 0.836 0.818 0.820 0.811 0.790 0.765 0.748 0.739 0.736 0.722 0.698 0.682 0.683

470.80 471.26 471.77 472.08 472.62 473.61 473.61 474.09 474.47 474.12 474.88 475.67 476.52 477.70 478.64 478.50 479.47 481.54 483.34 481.17 485.76 487.63 489.17

0.495 0.440 0.411 0.372 0.342 0.306 0.301 0.274 0.267 0.259 0.249 0.208 0.176 0.135 0.116 0.105 0.104 0.0690 0.0430 0.0750 0.0250 0.0110 0.000

0.661 0.635 0.623 0.604 0.587 0.570 0.572 0.555 0.545 0.543 0.540 0.505 0.473 0.421 0.392 0.382 0.366 0.289 0.233 0.321 0.139 0.0720 0.000

Figure 5. Experimental mole fraction differences between the vapor and liquid phases y1 − x1 against x1 at pressure p = 40 kPa for □, 1-pentanol (1) + n-nonane (2); gray □, 1-hexanol (1) + n-decane (2); •, 1heptanol (1) + n-undecane (2); gray ◊, 1-octanol (1) + n-dodecane (2); and ◊, 1-decanol (1) + n-tetradecane (2) to find the azeotropic points.

Table 9. Experimentally Determined Azeotropic Liquid Mole Fraction x1 and Temperature T for All 1-Alcohol + n-Alkane Systems Measured at Pressure p = 40 kPa 1-pentanol (1) + n-nonane (2) 1-hexanol (1) + n-decane (2) 1-heptanol (1) + n-undecane (2) 1-octanol (1) + n-dodecane (2) 1-decanol (1) + n-tetradecane (2)

a

Standard uncertainties are u(T) = 0.2 K, u(x1) = u(y1) = 0.022 mol· mol−1, and u(p) = 0.36 kPa.

data was measured by Seymour et al.50 at p = 101.32 kPa. Thus, a direct comparison between the literature data and the experimental data measured in this work cannot be made due to a difference in isobaric conditions. Similarly, comparisons

x1

T/K

0.501 0.572 0.676 0.712 0.889

378.03 398.46 416.79 435.34 468.72

cannot be made for the 1-octanol + n-dodecane system because the T−x−y data at p = 101.32 kPa predicted by Góral et al.51 was 4620



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Table 10. Critical Temperature Tc, Critical Pressure pc, Critical Molar Volume νc, Acentric Factor ωi, and Mathias and Copeman53 Constants ci Obtained from the Literature37 for Each Pure Component component

Tc/K

pc/MPa

νc/cm3·mol

ωi

c1

c2

c3

1-pentanol 1-hexanol 1-heptanol 1-octanol 1-decanol n-nonane n-decane n-undecane n-dodecane n-tetradecane

586.0 610.0 633.0 652.5 684.4 594.7 617.9 638.4 658.8 691.8

3.850 3.420 3.040 2.860 2.314 2.280 2.099 1.948 1.810 1.573

326.0 381.0 435.0 490.0 600.0 555.2 603.0 688.6 713.0 893.7

0.580 0.560 0.560 0.596 0.692 0.444 0.490 0.535 0.562 0.679

1.3176 1.3039 1.1804 1.4849 1.4847 0.9922 1.2407 1.3766 1.3026 1.4596

−0.0103 1.1676 0.5364 −1.1138 0.0000 1.1157 −0.3494 −0.9838 −0.00586 −0.5074

1.3301 −2.6225 1.4631 3.6068 0.0000 −2.3143 0.7327 2.1446 0.1852 1.4459

based on P−x−y data published by Schmelzer and Taummler.29 Furthermore, no data for the 1-decanol + n-tetradecane binary system has been previously published. A small temperature range is available for analyzing each binary system because of the similar boiling-point temperatures of 1-alcohol and n-alkane. Although it is a small temperature range, it is evident from Figure 3, along with the temperature minimum observed in each data set (Tables 4−8), that there exists a minimum-boiling azeotrope for each of the systems at p = 40 kPa. One can obtain the approximate location of each azeotrope graphically by plotting (y − x) against x and finding the x intercept (zero point). By applying this method, Figure 5 is obtained. The estimated azeotropic temperature (through cross interpolation with the zero point) and azeotropic composition for each of the binary systems measured in this work are presented in Table 9. The azeotrope temperature increases and the azeotrope composition shifts toward the 1-alcohol-rich region when increasing the alkyl chain lengths of both molecules in the mixture. The shifting of the azeotropic point (Table 9) and change in the phase envelopes (Figure 5) highlight the effect of the increase in the alkyl chain lengths on the experimental phase behavior. These observations support the idea that the degree of association is dependent on the size of the 1-alcohol molecule: the shorter the chain length, the more polar the molecule.

Table 12. Regressed NRTL Correlation Parameters A and B for Each of the Binary 1-Alcohol + n-Alkane Systems 1-pentanol (1) + n-nonane (2) 1-hexanol (1) + n-decane (2) 1-heptanol (1) + n-undecane (2) 1-octanol (1) + n-dodecane (2) 1-decanol (1) + ntetradecane (2)

CH2 CH2 OH

1 1 5

CH3 CH2 OH

1 2 14

Aspen Plus group number

Qi

Ri

1015 1010 1200

0.8480 0.5400 1.2000

0.9011 0.6744 1.0000

A21

B21/K

−21.47

8596.89

10.60

−3903.29 366.32

1.70

−421.33 167.49

47.63

536.49

−57.93

517.58

Ψij = e(−aij / T )

(1)

The group interaction parameters, aij = 156.4 and aji = 986.5, where i represents the alcohol group (OH) and j represents the alkane group (CH2) used in this work, were obtained directly from the DDB.37 5.2. Application of the NRTL Model. To evaluate the predictive capabilities of the PSRK + UNIFAC model, it is assessed alongside the NRTL activity coefficient model. The NRTL BIPs were regressed using Aspen Plus and are provided in Table 12. The nonrandomness parameter, αij, was set equal to a constant value of 0.3 for each binary system to comply with the specifications of polar liquids displaying small deviations from ideality.13 The energy parameter, τij, was calculated using eq 2. The molecule + molecule binary parameters (Aij, Aji, Bij, and Bji) were obtained by minimizing the objective function (OF) shown in eq 3.39 Bij τij = Aij + (2) T

Table 11. van der Waals Group Assignment, Volume Parameter Qk, and Area Parameter Rk for All PSRK Groups Used37 subgroup

B12/K −7521.06

pure components of interest in this study were obtained from the literature37 and are provided in Table 10. The van der Waals area, Qk, and volume, Rk, parameters for the structural groups (required for calculating activity coefficients) were obtained using Aspen Plus and are provided in Table 11. The UNIFAC group contribution method has the largest number of available parameters stored in the DDB.54,55 The UNIFAC parameters for the 1-alcohol and n-alkane components investigated in this work are independent of temperature, allowing GE model parameter Ψij to be calculated using a constant:16,56

5. THERMODYNAMIC MODELING 5.1. Application of the PSRK + UNIFAC Model. The PSRK mixing rules, as developed by Holderbaum and

main group

A12 20.36

Gmehling,16 make use of a thermodynamic relationship between the excess Helmholtz energy AE and the SRK EoS. For the EoS to predict accurate VLE data of polar systems, the temperaturedependent alpha parameter, αi(T), in the SRK EoS52 was calculated with the Mathias and Copeman53 expression. The Mathias and Copeman constants c1,i, c2,i, and c3,i, the critical temperature Tc, and the critical pressure pc constants for the

1

OF =

∑ n

4621

1

(γ1exp

−

γ1calc)i2

+

∑ (γ2exp − γ2calc)i2 n

(3)



Article

Figure 6. Temperature, T, against liquid, x1, and vapor, y1, mole fractions for (a) 1-pentanol (1) + n-nonane (2); (b) 1-hexanol + n-decane (2); (c) 1heptanol (1) + n-undecane (2); (d) 1-octanol (1) + n-dodecane (2); and (e) 1-decanol + n-tetradecane (2). Experimental VLE data represented by □, x1 and Δ, y1. Repeatability data represented by ■, x1 and ▲, y1. Model correlations represented by ···, NRTL; −−− PSRK + UNIFAC; and −·−·− PSRK + NRTL.

5.3. Application of the PSRK + NRTL Model. Besides

NRTL interaction parameters regressed as described in section 5.2 were used to form the PSRK + NRTL model. 5.4. Phase Behavior. Figure 6 compares the NRTL activity coefficient model to the PSRK mixing rules with (1) the UNIFAC BIPs obtained from the literature (DDB)17,37 and (2) the NRTL BIPs regressed in this work, for each of the five

using the UNIFAC model, the interaction parameters from any activity coefficient model can be used without needing to modify the PSRK mixing rules.17 Therefore, to assess this theory for the 1-alcohol + n-alkane systems measured in this work, the new 4622



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Table 13. Percentage Absolute Average Deviations %AADa and Root Mean Square Deviations RMSDb for Each Model Prediction of the Binary 1-Alcohol + n-Alkane Systems 1pentanol (1) + nnonane (2) %AADT RMSDT %AADy RMSDy

0.100 0.148 1.68 0.00707

%AADT RMSDT %AADy RMSDy

0.188 0.289 3.67 0.0165

%AADT RMSDT %AADy RMSDy

0.318 0.542 3.92 0.0184

1-hexanol (1) + ndecane (2)

1-heptanol (1) + nundecane (2)

NRTL 0.172 0.145 0.280 0.256 2.48 2.82 0.0224 0.00949 PSRK + UNIFAC 0.122 0.250 0.323 0.560 3.41 3.53 0.0232 0.0124 PSRK + NRTL 0.155 0.223 0.228 0.448 5.37 3.42 0.0286 0.0175

1-octanol (1) + ndodecane (2)

1-decanol (1) + ntetradecane (2)

0.244 0.505 4.50 0.0224

0.268 0.604 6.85 0.0368

0.236 0.509 7.40 0.0309

0.100 0.295 7.17 0.0354

0.181 0.395 6.92 0.0301

0.314 0.694 8.17 0.0407

slightly better than the PSRK + NRTL model. Therefore, second to the NRTL model, the PSRK + UNIFAC model produced the most accurate predictions of each binary system. The qualitative results are confirmed by the deviations calculated for each modeled system (Table 12). This proves that experimental data is not necessary to predict the 1-alcohol + n-alkane data measured in this work. Furthermore, the PSRK + UNIFAC model shows adequate predictions of each binary system, regardless of the azeotrope. However, to validate the proposed modeling approach suggested for these 1-alcohol + n-alkane systems, it is pertinent that similar systems be investigated and their predictions be evaluated in future studies. An analysis of the PSRK + UNIFAC model was conducted by calculating the excess GE residuals for each of the binary systems. The difference between the model and experimental data is typically within 10%, as shown in Figure 7. Thus, the scatter is within the quoted experimental uncertainty and indicates an acceptable model fit. This work shows that to predict the VLE data of ternary systems such as the CO2 + 1-decanol + n-tetradecane system only the CO2 + 1-decanol and CO2 + n-tetradecane BIPs will need to be obtained.17 Fortunately, gases such as CO2 have been introduced as new UNIFAC groups, and the missing PSRK + UNIFAC interaction parameters can be obtained from experimental data or the DDB.37,57 Therefore, the use of these mixing rules allows for the advantages of the group contribution models to be directly connected with the EoS. Subsequently, a strictly predictive tool is available for the prediction of VLE data at low and high pressures, irrespective of the presence of polar compounds.58

%AAD(F)=[(∑n1|(Fexp − Fcalc)/Fexp|/n] × 100%, where n is the number of data points. bRMSD(F) = [(∑n1(Fexp − Fcalc)2)/n]1/2, where n is the number of data points. a

6. CONCLUSIONS New subatmospheric VLE data for five pertinent binary 1alcohol + n-alkane systems were measured. Each of the systems showed an azeotrope that shifted toward the 1-alcohol-rich region when increasing the alkyl chain lengths of the molecules in the binary system. A comparative study of the NRTL activity coefficient model and the PSRK group contribution EoS with (1) UNIFAC parameters and (2) NRTL parameters highlighted that experimental data is not a prerequisite for the generation of accurate 1-alcohol + n-alkane VLE data. The NRTL model produced the most accurate representation of the experimental phase envelopes. Second to the NRTL model was the PSRK + UNIFAC model predictions, followed closely by the PSRK + NRTL model lagging only in its liquid composition predictions. Therefore, the model results verified that the PSRK mixing rule can be used with the NRTL activity coefficient model to predict the 1-alcohol + n-alkane data measured in this work if the BIPs are known. However, to validate that the PSRK mixing rules can be used with any GE model, it is pertinent that a wide range of 1alcohol + n-alkane systems be investigated and evaluated in the future.

E Figure 7. Excess Gibbs energy residuals (δGE = [GE/RT]calc 1 − [G / exp RT]1 ) against liquid mole fraction, x1, calculated between the PSRK + UNIFAC group contribution EoS and experimental data for the binary systems: □, 1-pentanol (1) + n-nonane (2); ○, 1-hexanol (1) + ndecane (2); gray ◊, 1-heptanol (1) + n-undecane (2); □, 1-octanol (1) + n-dodecane (2); and Δ, 1-decanol (1) + n-tetradecane (2).

■

measured systems. In Table 13, the temperature, T, and vapor mole fraction, y1, percentage absolute average deviations (% AAD) and root mean square deviations (RMSD) for each model are provided. Overall, the lowest deviations were obtained with the NRTL model quantitatively and qualitatively. This could be expected, as the correlations are based on BIPs regressed using the true experimental data. In Figure 6, the PSRK envelopes (with UNIFAC and NRTL parameters) are identical for the vapor phase. However, from the deviations in the liquid-phase composition it is seen that the PSRK + UNIFAC model is

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +27 21 808 4487. Fax: +27 21 808 2059. ORCID

Cara E. Schwarz: 0000-0001-5513-2105 Funding

This work is based on the research supported in part by the National Research Foundation of South Africa (grant specific 4623



Article

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unique reference number (UID) 103214) and Sasol Technology (Pty) Ltd. The financial assistance of the National Research Foundation (NRF) and Sasol Technology (Pty) Ltd. for this research is hereby acknowledged. Opinions expressed and conclusions arrived at are those of the authors and are not necessarily to be attributed to the NRF or Sasol Technology. Aspen Plus is a registered trademark of Aspen Technology Inc. Notes

The authors declare no competing financial interest.

■

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Low-Pressure VLE Measurements and Thermodynamic Modeling

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