VaporâLiquid Equilibrium Measurements of Ethanol and - American

Article Cite This: J. Chem. Eng. Data 2018, 63, 1240−1248

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Vapor−Liquid Equilibrium Measurements of Ethanol and n‑Nonane or n‑Decane Binary Mixtures with Large Relative Volatility Caleb Narasigadu,*,† Kuveneshan Moodley,‡ and Johan David Raal‡ †

Department of Chemical Engineering, Mangosuthu University of Technology, 511 Mangosuthu Highway, Umlazi 4031, South Africa Thermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Howard College Campus, King George V Avenue, Durban 4041, South Africa

‡

ABSTRACT: A specialized still was used for the measurement of vapor−liquid equilibrium (VLE) data by the dynamic-analytic approach at low pressures. The specialized apparatus improves the measurement of VLE in high relative volatility systems. Isothermal measurements were conducted for the ethanol (1) + n-nonane (2) systems at 323.21, 333.21, and 343.21 K and the ethanol (1) + ndecane (2) systems at 328.17, 338.17, and 348.16 K. The experimental data was modeled by the combined approach using the NRTL activity coefficient model for the liquid phase and with the virial equation of state for the vapor phase with the Hayden and O’Connell correlation. The experimental data was fitted by minimizing the pressure residual. UNIFAC predictions were also conducted, and there was significant discrepancy between experimental and predicted data, highlighting the importance of precise experimental data in these types of systems. Thermodynamic consistency tests showed all data to be consistent.

1. INTRODUCTION Binary systems with large relative volatility (LRV) ranges that do not exhibit azeotropic behavior are generally simple to separate by conventional distillation, albeit an energy intensive procedure. However, systems that exhibit complex, azeotropic, and rapidly changing relative volatilities over the composition range require an accurate description of their vapor−liquid equilibrium (VLE) behavior, in order to design and control separation strategies for such systems. Such behaviors are known to exist at broad ranges of temperatures and pressures,1−4 hence it is important that suitable methods of measurement are applied on a case by case basis, e.g., the staticanalytic method or the low-pressure dynamic-analytic method. For instance, Narasigadu et al.5 used a static-analytical type apparatus for VLE measurement. This type of apparatus employs sampling of the liquid phase as a liquid, and sampling of the vapor phase as a vapor (no condensation of the vapor phase prior to sampling), using online gas chromatography. Such apparatuses are well suited to the measurement of VLE in systems with LRV ranges, as the closed system temperature is generally simple to control, the cell pressure can be easily measured, good mixing can be achieved in theory by overhead magnetic stirring, and sampling can be performed by employing a unit-dedicated online gas chromatograph. An alternate strategy for the measurement of systems of LRV ranges is to employ the dynamic method of VLE measurement by using a circulating still that is similar in construction and operation to a packed distillation column operating under total reflux. Such apparatuses are generally constructed from glass © 2018 American Chemical Society

and are thus limited to operate in the near vacuum to moderate-pressure range. The central advantages of utilizing this apparatus are that, due to the omission of steel-to-steel connections, leak detection is rapid and usually easily resolvable, the glass material allows the experimentalist to view the contents of the still at most points and can, for example, help establish whether sufficient mixing of the contents is occurring, there is a single liquid phase, or if the still has been thoroughly cleaned prior to measurement. Additionally the vapor phase is sampled as a condensed liquid which eliminates the need for an online dedicated gas chromatograph. Furthermore, it is generally simpler and less expensive to commission and operate than a static-analytic apparatus. Alcohol hydrocarbon systems can have very steep P-x or T-x gradients in the dilute regions (with activity coefficients >406) and may require specialized equipment to manage measurements in these regions. A specialized dynamic still, with a novel annular Cottrell pump and a vapor bubbling chamber as the equilibrium mechanism, has previously been shown to be capable of producing very accurate, thermodynamically consistent data in the dilute regions for the methanol + hexane and ethanol + heptane systems.6 A version of this apparatus was also used successfully7 for the difficult water + methyl-butenol system to cope with extremely steep P-x gradients in the waterReceived: October 5, 2017 Accepted: March 21, 2018 Published: March 28, 2018 1240

DOI: 10.1021/acs.jced.7b00875 J. Chem. Eng. Data 2018, 63, 1240−1248

Journal of Chemical & Engineering Data

Article

Table 1. Chemical Suppliers and Purities refractive index (RI) at 293.15 K and 0.101 MPaa component

CAS No.

d

ethanol n-nonane n-decane

64-17-5 111-84-2 124-18-5

supplier Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich

experimental 1.3616 1.4074 1.4122

literature

minimum stated mass fraction purity

GC peak relative area (mass fraction purity)

≥0.990 ≥0.990 ≥0.990

0.9999 0.9999 0.9999

b

1.3611 1.4058b 1.4112c

a

Standard uncertainties, u, are u(RI) = 0.001, u(T) = 0.01 K, and u(P) = 0.002 MPa. bLide12 at 293.15 K. cLechner33 at 293.15 K. dPurified by molecular sieving.

rich region and activity coefficients, γi > 50. An adaptation of this apparatus was therefore adopted for this study and commissioned accordingly. Data verification is performed by comparing the systems of ethanol (1) + n-decane (2) at 101.3 kPa and ethanol (1) + nnonane (2) at 343.21 K to literature. Additionally, novel measurements are performed for ethanol (1) + n-decane (2) at 328.17, 338.17, and 348.16 K and ethanol (1) + n-nonane (2) at 323.21 and 333.21 K. Thermodynamic modeling is performed using the γ−Φ formulation with the non-random two-liquid (NRTL)8 activity coefficient model for the liquid phase description and the virial equation of state with the Hayden and O’Connell 9 correlation for vapor phase description. Thermodynamic consistency tests, estimation of infinite dilution activity coefficients, and prediction of excess enthalpies are performed by using the experimental data.

In order to calculate the activity coefficient for correlation purposes, the NRTL model8 was used. The NRTL activity coefficient for a binary system is ⎡ ⎛

ln γi =

v

Gij = exp( −αijτij)

τij =

(1)

where is the fugacity of species i in solution in the vapor, v, or liquid phase, l. For systems at low pressures, the ideal solution reference state can be used for the liquid phase, and hence an activity coefficient can be used to estimate liquid phase mixture nonidealities. It can thus be shown from eq 1 that

φi

⎡ −V l(P − P sat) ⎤ i i ⎢ ⎥ ⎢⎣ ⎥⎦ RT

sat exp

(2)

N

GE = RT ∑ xi ln γi

(10)

i=1

The change of the Gibbs excess energy with temperature is given by the Gibbs−Helmholtz relation:

(3)

⎛ nGE ⎜ ∂ RT HE = −RT 2⎜ ⎜ ∂T ⎝

( ) ⎞⎟⎟

⎟ ⎠P , x

i

(11)

(4)

3. EXPERIMENTAL SECTION 3.1. Materials. All organic solvents used were reagent grade (>0.99 mass fraction), and purities were confirmed by gas chromatography using a thermal conductivity detector. A Shimadzu GC 2014 with a POROPAK-Q column (2 m × 2.2

where

δij = 2Bij − Bii − Bjj

(9)

where aij and bij are adjustable fitting parameters. The infinite dilution activity coefficient (γi) by the NRTL model can be estimated by substituting xi = 0 into eq 6. Alternatively, the method of Maher and Smith11 provides a model-independent approach for the calculation of the infinite dilution activity coefficient. Details of the required procedure are provided in the work of Maher and Smith.11 At constant temperature and pressure, the excess Gibbs energy can be determined by the summability relation.

If the virial equation of state is used then for a binary system eq 3 can be expressed by ⎡ (B − V l)(P − P sat) + Py 2 δ ⎤ ii i i j ij ⎥ Φi = exp⎢ ⎥ ⎢ RT ⎦ ⎣

(8)

RT

τij = aij + bij /T

where yi and xi are the vapor and liquid mole fractions, respectively, P is the total system pressure, and Psat is the i saturation pressure of the pure component i. γi is the activity coefficient of species i in the liquid phase, and Φi is the vapor correction factor given by φî

gij − gjj

T is the temperature in Kelvin, and R is the universal gas constant in J mol−1·K−1. The cross interaction parameters (gij − gii) were determined by regression. Walas10 recommends that αij (the nonrandomness parameter) be set to a value of 0.3 for nonaqueous systems, but this parameter can also be regressed if it provides a superior fit to the experimental data. For simultaneous regression of multiple isotherms, τij can incorporate temperature dependence:

fαî

Φi =

(7)

and

l

yi ΦiP = xiγiPisat

(6)

where

2. THEORY At vapor−liquid equilibrium the isofugacity condition applies: fi ̂ = fi ̂

⎞⎤ ⎞2 ⎛ τijGij ⎟⎥ ⎟⎟ + ⎜⎜ 2 ⎟⎥ x x G + ( x + x G ) j ji ⎠ ⎝ j i ij ⎠⎦ ⎣ ⎝ i Gji

xj2⎢τji⎜⎜ ⎢

(5)

Bij are the second virial coefficients and were estimated by the method of Hayden and O’Connell in this work.9 1241



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Figure 1. A schematic of the dynamic equilibrium still used in this work, taken from a previous work.7

Table 2. Experimental Vapor Pressure Data and Comparison to Literaturea P/kPa literature T/K

experimental

ethanol

323.21 328.17 333.21 338.17 343.21 348.16

29.580 37.530 47.042 58.600 72.387 88.830

n-nonane

323.21 333.21 343.21

2.417 4.027 6.331

n-decane

328.17 338.17 348.16

1.180 1.930 3.240

component

a

Poling et al.

25

29.630 37.453 47.134 58.650 72.700 89.154 Poling et al.25 2.423 3.989 6.332 Poling et al.25 1.152 1.966 3.222

Ambrose and Sprake26

Kretschmer and Wiebe27

29.575 37.377 47.025 58.492 72.469 88.822 Ahmad et al.28 1.817 2.992 4.750 Morgan and Kobayashi29 1.160 1.972 3.224

29.524 37.311 46.947 58.411 72.399 88.785

Standard uncertainties, u, are u(T) = 0.10 K and u(P) = 0.46 kPa.

capillary outlet. The disengaged vapor stream flowed downward and bubbled through liquid in the inner equilibrium chamber before taking off through the superheated arm shown. This vapor stream was an effective insulating mechanism for the interior of the bubbling chamber. At equilibrium, compositions in the inner and outer chambers were found to have identical compositions,6 ensuring effective adiabaticity of the inner equilibrium chamber. The exterior of the still was, however, insulated to reduce heat loss to the surroundings. The bubbling chamber, with rounded contours at the bottom, was considered to be a very effective equilibration mechanism with highly efficient mixing, which is particularly effective for systems with the major mass transfer resistance in the liquid phase. The experimental procedure using the specialized apparatus was analogous to the procedure using the original apparatus described in a similar previous work.13,14

mm) was utilized with helium as a carrier gas. This GC was also used for phase analysis. The refractive indices of the organic solvents used were determined at T = 293.15 K by employing an ATAGO RX-7000α refractometer (sodium D-line = 589 nm) with an uncertainty of 0.001 in the reported values. The ethanol used was dehydrated by molecular sieves for 24 h prior to measurement. The purities and chemical suppliers are provided in Table 1. No unexpected or significant hazards were associated with this experimental work. 3.2. Equipment. The specialized dynamic still used in this study is shown in Figure 1. Heating in the magnetically stirred boiling chamber produced a two-phase vapor−liquid flow in the ±1.5 mm annular space between the outer and inner chambers, impinging on the Pt-100 temperature sensor, as shown. Liquid from the separating chamber, after passing through loose stainless steel packing, emerged into the boiling chamber via a 1242



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3.3. Uncertainties. The temperature was measured with a Pt-100 temperature probe and was calibrated against a WIKA CTB 9100 temperature calibration standard. The standard uncertainty in temperature was determined to be 0.10 K. The pressure transducer (P-10) was supplied by WIKA and had a measured range of 0−101.3 kPa with a supplier uncertainty of 50 Pa. This transducer was calibrated against a WIKA CPH 6000 pressure transducer. The standard uncertainty in pressure was calculated to be 0.46 kPa. The equilibrium phase samples were analyzed by the same GC that was used for purity checks mentioned above. The estimated uncertainty in the phase composition at equilibrium wass 0.005 mole fraction, which includes the GC calibration uncertainty. The GC detector was calibrated using the area ratio method outlined by Raal and Mü h lbauer.15 All uncertainties were calculated according to IUPAC guidelines.16

Figure 3. VLE data for the ethanol (1) + n-decane (2) system at 101.3 kPa. (x1, y1): (●, ○) this work, (■, □) Koshel’kov et al.,18 (+, × ) Ellis and Spur,19 and (⧫,◊) Ortega and Espiau.32 (x1): (red triangle) Garner and Ellis.31

4. RESULTS AND DISCUSSION The vapor pressure data measured in this work are presented in Table 2 along with literature sources at similar conditions. It can be seen that the vapor pressure data measured here compare well with the literature. The experimental vapor pressures measured here were used in the data reduction. In Figure 2, a comparison of the isothermal system of ethanol (1) + n-nonane (2) at approximately 343 K is made to

Espiau.32 Furthermore, analysis by densitometry was used in the work of Ortega and Espiau,32 whereas gas chromatography was used here. The authors here are confident with the data presented as they correlate well with the majority of the literature sources. For this study, the minimization of the sum of the squares of the differences between the model and experimental pressures, as suggested by Van Ness and Abbott,14 was used as the objective function to correlate the experimental data in order to determine model parameters. To fit the experimental data, the following objective function, suggested by Van Ness and Abbott,20 which minimizes the pressure residual (δP), was used: N

δP =

∑ (P exp − P calc)2 (12)

k=1 exp

calc

N is the number of experimental points, and P and P are the experimental and model-calculated pressures. The root-mean-square deviation (RMSD) was also calculated to provide an indication of the quality of the model fit:

Figure 2. VLE data for the ethanol (1) + n-nonane (2) system at 343.21 K. (x1, y1): (●, ○) this work, (+, × ) Berro et al.,17 and (▲,Δ) Ortega and Espiau at 344.17 K.32

RMSD =

17

literature. There is good agreement with this source, except in the composition range of 0.2−0.4 mol fraction ethanol with a difference of approximately 2.5 kPa. This difference is attributed to the differences in the apparatus used for measurement and the differences in the analysis procedure, (mixture density measurement in Berro et al.17 vs gas chromatography used in this work). A comparison for one approximate experimental point from the isobaric data of Ortega and Espiau32 was also made. This compares well with the data measured in this work. In Figure 3, a comparison of the isobaric system of ethanol (1) + n-decane (2) at approximately 101.3 kPa is made to literature. There is good agreement between the data measured here and the various literature sources, except in the case of the work of Ortega and Espiau32 for liquid compositions less than 0.25 mol fraction ethanol. A maximum deviation of approximately 0.08 mol fraction is apparent. This result is interesting as the vapor compositions measured here compare well with the data of Ortega and Espiau.32 The differences are attributed to the method of measurement as well as the pressure control of the VLE apparatus used by Ortega and

δP N

(13)

The experimental data measured in this work for the ethanol (1) + n-nonane (2) system at 323.21, 333.21, and 343.21 K are presented in Table 3 and in Figures 3, 4, and 5 along with modeling by the NRTL model and the virial equation of state with the Hayden and O’Connell correlation for the vapor correction factor. Similarly, the results for the ethanol (1) + ndecane (2) at 328.17, 338.17, and 348.16 K and at 101.3 kPa are presented in Table 4 and in Figures 6, 7, and 8 along with the respective thermodynamic modeling. The isobaric system was excluded from the regression. The regressed NRTL model parameters were determined using ASPEN Plus V.9 software and are reported in Table 5. A single simultaneous temperature dependent regression was performed for all three isotherms of each data set, and it substantiates the relatively high RMSD in pressure. From Figures 4−9 it is evident that both ethanol + alkane systems exhibit a large relative volatility with large distances between the P-x and P-y curves for the majority of the composition range. However, in both systems a maximum pressure azeotrope was found, which increased in ethanol 1243



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Table 3. VLE Data for the Ethanol (1) + n-Nonane (2) Systema T/K = 323.21

a

T/K = 333.21

P/kPa

x1

y1

lnγ1

2.42 19.21 23.28 26.65 28.10 28.56 28.64 28.68 28.74 28.73 29.15 29.24 29.50 29.61 29.77 29.80 29.58

0.000 0.061 0.083 0.114 0.208 0.288 0.330 0.396 0.495 0.602 0.757 0.800 0.892 0.930 0.956 0.972 1.000

0.0000 0.875 0.900 0.910 0.912 0.915 0.916 0.917 0.918 0.925 0.930 0.931 0.940 0.949 0.960 0.971 1.000

2.231 2.142 1.972 1.427 1.120 0.990 0.810 0.588 0.400 0.191 0.140 0.050 0.022 0.011 0.006 0

T/K = 343.21

lnγ2

P/kPa

x1

y1

lnγ1

0 0.059 0.045 0.111 0.253 0.347 0.390 0.483 0.658 0.804 1.245 1.430 1.909 2.181 2.411 2.543

4.03 33.87 35.83 39.43 43.51 44.85 45.12 45.35 45.48 46.11 46.30 46.78 46.95 47.06 47.15 47.04

0.000 0.072 0.094 0.132 0.210 0.301 0.413 0.543 0.609 0.789 0.837 0.898 0.930 0.957 0.972 1.000

0.000 0.884 0.891 0.902 0.907 0.914 0.916 0.918 0.924 0.930 0.933 0.941 0.950 0.961 0.971 1.000

2.175 1.980 1.746 1.384 1.063 0.755 0.489 0.383 0.145 0.093 0.041 0.020 0.005 0.002 0

lnγ2

P/kPa

x1

y1

lnγ1

lnγ2

0 0.050 0.067 0.101 0.239 0.314 0.473 0.707 0.790 1.329 1.548 1.914 2.107 2.356 2.473

6.33 50.49 61.94 64.67 66.24 67.51 67.98 68.83 69.16 69.53 69.83 70.20 70.54 70.69 70.80 70.91 71.16 71.53 71.68 71.93 72.19 72.39 72.58 72.65 72.65 72.58 72.39

0.000 0.089 0.216 0.295 0.374 0.458 0.508 0.592 0.629 0.673 0.714 0.750 0.781 0.799 0.808 0.819 0.841 0.864 0.878 0.899 0.919 0.937 0.953 0.967 0.979 0.989 1.000

0.000 0.879 0.905 0.910 0.913 0.916 0.917 0.919 0.920 0.922 0.923 0.925 0.927 0.928 0.929 0.930 0.932 0.935 0.938 0.942 0.947 0.953 0.960 0.969 0.978 0.987 1.000

1.933 1.276 1.015 0.805 0.624 0.529 0.390 0.335 0.274 0.221 0.179 0.146 0.127 0.118 0.107 0.086 0.067 0.056 0.040 0.027 0.017 0.010 0.006 0.002 0.001 0

0.059 0.173 0.264 0.372 0.504 0.591 0.768 0.854 0.966 1.083 1.201 1.311 1.380 1.418 1.463 1.566 1.682 1.759 1.880 2.010 2.143 2.270 2.381 2.491 2.578

Standard uncertainties, u, are u(T) = 0.10 K, u(P) = 0.46 kPa, u(xi) = 0.005, and u(yi) = 0.005.

Figure 4. VLE data for the ethanol (1) + n-nonane (2) system at 323.21 K. (x1, y1): (●, ○) experimental, (, - - -) NRTL model, and (red −--−, red ····) UNIFAC prediction.


composition with increasing temperature. This indicates that conventional distillation does not suit the separation of ethanol from these alkanes, and an enhanced technique, such as pressure swing or extractive distillation, may be required. The UNIFAC model predictions using ASPEN Plus V.9 software are also presented along with the experimental data in Figures 4−9. It is evident that there is a significant difference between experimental and UNIFAC-predicted data, which indicates that the data measured here are essential for the precise description of the phase behavior of these systems. In Figures 10 and 11, the experimental activity coefficient data at selected temperatures are presented along with the NRTL model fit. The

shapes of these logarithmic activity coefficient plots are quite conventional and typical of mixtures of polar and nonpolar substances. Thermodynamic consistency testing is a necessary tool that can indicate the quality of experimental VLE data. In this work, the area test of Redlich and Kister21 and the point to point test of Van Ness et al., 22 modified by Christiansen and Fredenslund,23 were used to determine the consistency of the experimental data. This was conducted on ASPEN Plus V9 software, with the default criterion for consistency. For the area test, a 10% deviation from 0 was assumed to be thermodynamically consistent. All measured isotherms were individually 1244


a

1.18 24.00 34.21 35.32 35.42 35.61 35.76 36.10 36.52 37.15 37.53

y1

0.000 0.938 0.963 0.971 0.972 0.974 0.975 0.976 0.980 0.994 1.000

2.813 2.024 1.075 0.710 0.377 0.217 0.133 0.044 0.001 0

lnγ1

lnγ2 0 0.269 0.193 0.232 0.426 0.763 1.101 1.417 1.962 2.408

x1 0.000 0.041 0.113 0.335 0.448 0.680 0.792 0.848 0.931 0.983 1.000

P/kPa 1.93 32.10 46.15 54.70 55.15 55.79 56.16 56.32 57.15 58.00 58.60

0.000 0.943 0.956 0.966 0.969 0.972 0.973 0.975 0.981 0.994 1.000

y1

T/K = 338.17

2.534 1.897 0.990 0.711 0.308 0.163 0.100 0.027 0.001 0

lnγ1

lnγ2 0 0.012 0.171 0.371 0.473 0.928 1.329 1.569 2.098 2.361

Standard uncertainties, u, are u(T) = 0.10 K, u(P) = 0.46 kPa, u(xi) = 0.005, and u(yi) = 0.005.

x1

0.000 0.036 0.116 0.312 0.451 0.634 0.748 0.822 0.913 0.983 1.000

P/kPa

T/K = 328.17

Table 4. VLE Data for the Ethanol (1) + n-Decane (2) Systema x1 0.000 0.054 0.117 0.354 0.482 0.695 0.816 0.871 0.938 0.983 1.000

P/kPa 3.24 49.01 66.80 81.08 82.05 84.38 85.96 86.45 87.12 88.17 88.83

0.000 0.930 0.939 0.962 0.965 0.969 0.971 0.974 0.981 0.995 1.000

y1

T/K = 348.16

2.252 1.798 0.908 0.615 0.281 0.141 0.085 0.025 0.005 0

lnγ1

lnγ2 0 0.113 0.354 0.387 0.537 0.973 1.431 1.682 2.109 2.080

x1 0.000 0.027 0.041 0.061 0.123 0.368 0.482 0.716 0.807 0.864 0.938 0.962 0.983 1.000

T/K 446.84 405.65 389.15 375.76 362.36 354.36 353.26 352.46 352.26 351.96 351.46 351.36 351.26 351.06

0.000 0.653 0.801 0.887 0.938 0.961 0.963 0.967 0.970 0.973 0.982 0.988 0.996 1.000

y1

P/kPa = 101.3

4.338 4.125 3.829 3.184 2.112 1.844 1.453 1.336 1.271 1.198 1.179 1.165 1.152

lnγ1

lnγ2 0 0.162 0.183 0.140 0.157 0.375 0.572 1.095 1.395 1.654 2.057 2.146 1.856

Journal of Chemical & Engineering Data Article


Figure 7. VLE data for the ethanol (1) + n-decane (2) system at 328.17 K. (x1, y1): (●, ○) experimental, (, - - -) NRTL model, and (red −--−, red ····) UNIFAC

Figure 8. VLE data for the ethanol (1) + n-decane (2) system at 338.17 K. (x1, y1): (●, ○) experimental, (, - - -) NRTL model, and (red −--−, red ····) UNIFAC prediction.

tested and were found to pass both consistency tests when using a single set of temperature dependent NRTL model parameters for each binary system. In Table 6, the estimations of the infinite dilution activity coefficients (γ∞ i ) by the NRTL model are presented. This was calculated by setting xi = 0 in eq 6. Additionally, estimations by the model-independent method of Maher and Smith11 are also presented, where a linear extrapolation was possible. The γ∞ 1 tends to decrease with increasing temperature for both systems and are higher in the system of ethanol (1) + n-decane (2) than in ethanol (1) + n-nonane (2). For the ethanol (1) + n-decane

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Table 5. Regressed NRTL Model Parameters system

a

parameter

ethanol (1) + n-nonane (2)

ethanol (1) + n-decane (2)

a12 a21 b12 /K b21/K α12 RMSD/kPa δy1a

0.1059 −1.3119 530.6878 1057.9296 0.4210 0.6343 0.0024

−0.3922 −2.4277 752.0831 1527.5734 0.4190 1.7719 0.0036

calc Average absolute deviation: δy1 = abs(yexp 1 − y1 )/N.

Figure 11. lnγi vs x1 for the ethanol (1) + n-decane (2) system at 328.17 K. lnγ1-x1: (▲) experimental and () NRTL model. lnγ2-x1: (■) experimental and (− − −) NRTL model.

Table 6. Estimated Infinite Dilution Activity Coefficient NRTL extrapolation system

γ∞ 1

ethanol (1) + n-nonane (2) T/K = 323.21 16.423 T/K = 333.21 14.789 T/K = 343.21 13.391 ethanol (1) + n-decane (2) T/K = 328.17 21.850 T/K = 338.17 18.912 T/K = 348.16 16.491

Figure 9. Vapor−liquid equilibrium data for the ethanol (1) + ndecane (2) system at 348.16 K. (x1, y1): (●, ○) experimental, (, - -) NRTL model, and (red −--−, red ····) UNIFAC prediction. a

Figure 10. lnγi vs x1 for the ethanol (1) + n-nonane (2) system at 343.21 K. lnγ1-x1: (▲) experimental and () NRTL model. lnγ2-x1: ( ■) experimental and (− − −) NRTL model.

method of Maher and Smith11

γ∞ 2

γ∞ 1

γ∞ 2

13.555 12.797 12.090

14.094 12.759 9.199

18.236

16.047 14.916 13.876

61.080 26.323 20.885

12.583 11.791

literature30 γ∞ 1

γ∞ 2 24.2a 18.6b

14.865 25.5c 15.9d

T/K = 323.65. bT/K = 333.85. cT/K = 321.35. dT/K = 338.65.

Figure 12. α12 vs x1 for the ethanol (1) + n-nonane (2) system at (experimental, NRTL model) 323.21 K (●, − ), 333.21 K (▲, − − − ), and 343.21 K (■, − - − ).

(2) system at 328.17 K, the value for γ∞ 1 seems significantly larger than that of the extrapolation from the NRTL model, albeit the method of Maher and Smith11 yielded a 99% linearity. In Figures 12 and 13, the calculated and experimental relative volatility plots are presented. It can be seen that the model follows the experimental trend of an increase of relative volatility with decreasing temperature for a given liquid composition. Furthermore, the extremely high relative volatility of the mixtures studied are apparent, especially in the alcoholrich region. The new apparatus design does however allow for accurate VLE measurements in this region. The model parameters from the VLE data regression were used to predict the excess enthalpies of the systems considered here at the measured VLE conditions, as well as at 313.15 K, where reliable literature data was found. A good prediction of

excess enthalpy from the VLE model parameters was obtained. These results are presented in Figures 14 and 15 and are useful in tray to tray calculations in separation processes.

5. CONCLUSION A specialized apparatus for dynamic-analytical vapor−liquid equilibrium measurement for systems of high relative volatility was commissioned and tested. Test measurements were performed for the ethanol + n- nonane and ethanol + n-decane binary systems and compared well with literature data. Novel isothermal measurements were subsequently performed. The experimental isothermal data was modeled using the γ−Φ approach and the NRTL activity coefficient model with the virial equation of state with the Hayden and O’Connell 1246



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Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is based upon research supported by Sasol R&D, Ltd.

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Figure 13. α12 vs x1 for the ethanol (1) + n-decane (2) system at (experimental, NRTL model) 328.17 K (●, − ), 338.17 K (▲, − − − ), and 348.16 K (■, − - − ).

Figure 14. Excess enthalpy data for the ethanol (1) + n-nonane (2) system at various temperatures. Predicted from VLE model parameters at: ( - ) 313.15 K, (- - -) 323.21, (······) 333.21 K, and () 333.21 K. (○) Experimental data at 313.15 K.24

Figure 15. Excess enthalpy data for the ethanol (1) + n-decane (2) system at various temperatures. Predicted from VLE model parameters at: ( - ) 313.15 K, (- - -) 328.17, (······) 338.17 K, and () 348.16 K. (○) Experimental data at 313.15 K.24

correlation. Thermodynamic consistency tests were conducted, and the data passed the area and point tests. Excess enthalpy values were very reasonably predicted from the VLE datacorrelated model parameters.

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REFERENCES

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