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Vapor–liquid equilibrium in the system ethanethiol+tetraethylene glycol
Fluid Phase Equilibria 182 (2001) 209–215
Vapor–liquid equilibrium in the system ethanethiol + tetraethylene glycol F.-Y. Jou, K.A.G. Schmidt1 , A.E. Mather∗ Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2G6 Received 4 August 2000; accepted 5 December 2000
Abstract The vapor–liquid equilibrium in the system ethanethiol+tetraethylene glycol has been determined at temperatures in the range 25–130◦ C at pressures up to 1000 kPa. The experimental results were correlated by the Peng–Robinson equation of state, and interaction parameters have been obtained for this system. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Experimental method; Vapor–liquid equilibria; Equation of state; Data
1. Introduction Mercaptans (thiols) are sulfur compounds which are impurities in natural gas. Ethanethiol has an overpowering offensive odor and, while small amounts are added to natural gas and liquefied petroleum gas for safety purposes, larger quantities must be removed to meet specifications on the total sulfur content. Sokolina et al. [1] measured the solubility of ethanethiol in a number of organic solvents. In this laboratory the solubility of ethanethiol in an aqueous solution of methyldiethanolamine was measured at 40 and 70◦ C [2]; similar data were obtained in a diethanolamine solution at the same temperatures [3]. This work was undertaken to ascertain the usefulness of tetraethylene glycol for the removal of ethanethiol; measurements were extended to cover the complete range of ethanethiol concentration. 2. Experimental details The apparatus and experimental technique used in the present investigation are similar to those described by Jou et al. [4]. The equilibrium cell is mounted in an air bath. The temperature of the contents of the cell was measured by a calibrated iron–constantan thermocouple and the pressure in the cell was measured ∗
Corresponding author. Tel.: +1-780-492-3957; fax: +1-780-492-2881. E-mail address: [email protected] (A.E. Mather). 1 Present address: DB Robinson Research Ltd., Edmonton, Alberta, Canada. 0378-3812/01/$20.00 © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 ( 0 1 ) 0 0 3 9 6 - X
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Table 1 Vapor–liquid equilibrium data P (kPa)
yCH4
yH 2 O
yEtSH
xCH4
xH 2 O
xEtSH
xTeEG
t=25◦ C 200 200 207 200 200 220 63 101
0.998 0.998 0.993 0.996 0.963 0.820 – 0.3255
1.45 × 10−3 4.50 × 10−4 2.17 × 10−3 – – 2.55 × 10−3 – 1.19 × 10−3
2.35 × 10−4 1.35 × 10−3 5.07 × 10−3 3.65 × 10−3 3.73 × 10−3 0.178 1.00 0.6733
1.06 × 10−3 1.25 × 10−3 1.30 × 10−3 1.25 × 10−3 1.26 × 10−3 1.82 × 10−3 – 6.57 × 10−4
2.50 × 10−2 2.02 × 10−2 1.95 × 10−2 2.83 × 10−2 1.22 × 10−2 1.27 × 10−2 4.15 × 10−3 4.21 × 10−4
3.36 × 10−4 1.95 × 10−3 7.01 × 10−3 5.07 × 10−3 4.24 × 10−2 0.305 0.750 0.964
0.974 0.977 0.965 0.965 0.944 0.681 0.246 0.0353
t = 40◦ C 200 200 200 200 200 170 150
0.997 0.997 0.997 0.942 0.662 0.359 0.192
2.90 × 10−3 2.50 × 10−3 1.00 × 10−3 4.00 × 10−4 4.15 × 10−3 – 1.33 × 10−3
3.15 × 10−4 4.10 × 10−4 2.52 × 10−3 5.75 × 10−2 0.333 0.641 0.807
1.19 × 10−3 1.20 × 10−3 1.21 × 10−3 9.68 × 10−4 1.10 × 10−3 – 4.99 × 10−4
2.47 × 10−2 2.45 × 10−2 2.50 × 10−2 1.32 × 10−2 1.24 × 10−2 4.66 × 10−3 1.53 × 10−4
3.09 × 10−4 3.40 × 10−4 2.08 × 10−3 4.21 × 10−2 0.283 0.737 0.993
0.974 0.974 0.972 0.944 0.703 0.259 0.00630
t =70◦ C 180 220 220 220 200 200 350 320 300
0.999 0.990 0.982 0.989 0.950 0.875 0.580 0.209 0.037
6.11 × 10−4 9.54 × 10−3 1.45 × 10−2 6.36 × 10−3 9.50 × 10−3 2.70 × 10−3 2.86 × 10−3 – –
2.16 × 10−4 8.64 × 10−4 3.10 × 10−3 4.51 × 10−3 4.05 × 10−2 0.122 0.417 0.791 0.963
1.11 × 10−3 1.34 × 10−3 1.35 × 10−3 1.40 × 10−3 1.10 × 10−3 9.17 × 10−4 1.97 × 10−3 4.41 × 10−4 –
6.15 × 10−3 2.60 × 10−2 2.01 × 10−2 2.43 × 10−2 1.42 × 10−2 1.30 × 10−2 1.13 × 10−2 5.09 × 10−3 1.09 × 10−3
5.45 × 10−5 3.13 × 10−4 1.11 × 10−3 1.56 × 10−3 1.35 × 10−2 3.92 × 10−2 0.290 0.689 0.956
0.993 0.972 0.977 0.973 0.971 0.947 0.697 0.306 0.0429
0.9997 0.985 0.981 0.953 0.796 0.433 6.04 × 10−3
– 1.41 × 10−2 1.42 × 10−2 1.17 × 10−2 5.54 × 10−3 4.33 × 10−3 3.58 × 10−3
3.23 × 10−4 1.42 × 10−3 4.83 × 10−3 3.58 × 10−2 0.199 0.562 0.990
1.26 × 10−3 1.15 × 10−3 1.52 × 10−3 1.46 × 10−3 1.23 × 10−3 2.43 × 10−3 –
2.02 × 10−2 2.37 × 10−2 2.47 × 10−2 2.02 × 10−2 1.55 × 10−2 1.27 × 10−2 5.24 × 10−3
5.00 × 10−5 2.36 × 10−4 9.60 × 10−4 6.50 × 10−3 3.69 × 10−2 0.329 0.670
0.978 0.975 0.973 0.972 0.946 0.655 0.325
0.991 0.969 0.967 0.928 0.549 0.219 1.23 × 10−2 1.40 × 10−3
8.0 × 10−3 2.64 × 10−2 2.64 × 10−2 2.40 × 10−2 1.09 × 10−2 7.23 × 10−3 6.75 × 10−3 3.30 × 10−3
4.68 × 10−4 4.14 × 10−3 7.12 × 10−3 4.80 × 10−2 0.441 0.774 0.981 0.995
1.43 × 10−3 1.84 × 10−3 1.54 × 10−3 1.50 × 10−3 7.88 × 10−4 2.53 × 10−3 – –
4.09 × 10−3 1.87 × 10−2 2.46 × 10−2 2.22 × 10−2 1.26 × 10−2 1.20 × 10−2 6.26 × 10−3 4.11 × 10−4
5.05 × 10−5 5.57 × 10−4 7.43 × 10−4 5.56 × 10−3 4.96 × 10−2 0.283 0.535 0.970
0.994 0.979 0.973 0.971 0.937 0.702 0.459 0.0291
t = 100◦ C 220 220 240 240 220 600 530 t = 130◦ C 250 280 250 250 220 650 800 1000
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by digital Heise gauges. The thermocouple had an accuracy of ±0.1◦ C by comparison with a platinum resistance thermometer. The pressure gauges had an accuracy of ±0.1% of full scale by comparison with a dead-weight gauge. The apparatus and experimental technique were checked by determination of the critical point and the vapor pressure of propane, carbon dioxide, and hydrogen sulphide. Differences of ±0.1◦ C between the measured critical temperature and literature values and ±0.1% in vapor pressure between the measured pressures and literature values were found. The tetraethylene glycol (Chemical Abstracts Registry No. (112-60-7)) of purity 99% and the ethanethiol (75-08-1) of purity 97% were purchased from Aldrich Chemical. Methane (UHP grade) was supplied by Praxair. The ethanethiol (EtSH) was first transferred from the glass bottle in which it was supplied to a 500 ml stainless steel cylinder. This cylinder was connected to a vacuum pump, a length of 0.5 m×12.5 mm o.d. stainless steel tubing containing a 3A molecular sieve, and a second cylinder. A vacuum was drawn on the EtSH to remove air and then the first cylinder was closed. The tubing and the second cylinder were evacuated overnight. The EtSH was distilled over into the second cylinder by maintaining the first cylinder at 30◦ C with heating tape and cooling the second cylinder with an ice-water bath. The second cylinder was then disconnected from the vacuum system and attached to the manifold of the equilibrium cell. Using a hand pump, the EtSH was loaded into the evacuated equilibrium cell and the vapor pressure of EtSH measured over a range of temperatures. The tetraethylene glycol (TeEG) was purged with methane while being evacuated at a total pressure of 10 kPa at 100◦ C to remove any water. After being purged, the TeEG was stored in a 300 ml cylinder. TeEG was then tranferred into the cell by the application of pressure by methane. To maintain smooth operation of the magnetic pump, which circulates the vapor phase to the bottom of the cell, methane was added to the cell to ensure the total pressure was greater than 200 kPa. The analysis of both phases was done with a gas chromatograph equipped with a thermal conductivity detector maintained at 250◦ C. The components in the vapor phase were separated with a 2 m × 3.175 mm o.d. stainless steel column packed with Haye Sep Q and operated at 180◦ C. The liquid phase was analyzed by injection of a 3.3 l sample into a 3.175 mm o.d. column containing 0.16 m of HayeSep® Q and 1.22 m of Chromosorb 104, both with packings of 80/100 mesh. Temperature programming was employed with the initial condition of 160◦ C and an increase of 64◦ C/min to 250◦ C. The retention times and response factors of CH4 /H2 O/EtSH for the vapor phase analysis were: 0.37/0.75/3.5 min and 2.00/2.86/1.00, respectively. The retention times and response factors of CH4 /H2 O/EtSH/TeEG for the liquid phase analysis were: 0.15/0.58/0.78/18.4 min and 2.00/2.71/1.00/0.36, respectively. The uncertainty in the analysis of the phases is estimated to be ±5%. 3. Results Measurements were made at 25, 40, 70, 100 and 130◦ C over the complete range of EtSH composition. The experimental data for the vapor–liquid equilibrium of EtSH in TeEg are presented in Table 1. Because of the hygroscopic nature of tetraethylene glycol, water was present in small amounts in both phases. 4. Data reduction and correlation The equilibrium data were correlated using the Peng–Robinson [5] equation of state. The parameters a and b of the solutes and solvent were obtained from the critical constants. The critical constants and
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Table 2 Parameters for the temperature dependent binary interaction parameter, Henry’s Law Constant, and Margules parameter
δ12 ln H2,1 A (J/mol)
α0 , β0 , γ0
α1 , β1 , γ1
0.1077 15.47 5383
−5742 −3.1173 −1.168 × 106
acentric factors of the solutes and solvent were taken from the compilation of Daubert and Danner [6]. The binary interaction parameter, δ 12 , was obtained from the experimental equilibrium data at each temperature by minimizing the following objective function: NP OBJ = Fj
(1)
j
Fj =
NC
(ln(fiL ) − ln(fiV ))2
(2)
i=1
The binary interaction parameter δ 12 appears in the mixing rule of the equation of state a12 = (a12 a22 )1/2 (1 − δ12 )
(3)
Values of δ 12 were found to have a moderate temperature dependence and could be fit by a simple relationship δ12 = α0 + α1 × T −2
(4)
The correlation parameters α 0 and α 1 are presented in Table 2 and the smoothed values of δ 12 (at each experimental temperature) are presented in Table 3. The VLE data were then calculated with the smoothed temperature-dependent form of the binary interaction parameter. These calculated results are compared with the experimental data in Fig. 1. As can be seen the Peng–Robinson equation of state with the critical constants from Daubert and Danner [6] and the smoothed binary interaction parameter satisfactorily correlated the data. The overall average absolute percent difference in the EtSH partial pressures was determined to be 6.1%, which is close to the experimental uncertainty. Table 3 Binary interaction parameters for the Peng–Robinson equation of state t (◦ C)
δ12
25 40 70 100 130
0.043 0.049 0.059 0.066 0.072
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213
Fig. 1. Vapor–liquid equilibria of ethanethiol in tetraethylene glycol.
Because the removal of ethanethiol from natural gas streams is often a process involving dilute concentrations of EtSH it was of interest to determine the Henry’s Law constants of EtSH in TeEG. In this investigation the Kritchevsky–Iliinskaya [7] equation
fˆ2 RT ln x2
= RT ln H21 + v¯2∞ (P − P1S ) + A[x12 − 1]
(5)
was used to determine these Henry’s Law constants by correlating all the VLE data over the 25–130◦ C temperature range. As discussed by Prausnitz et al. [8] the application of the Kritchevsky–Iliinskaya equation requires the evaluation of three parameters, the Henry’s Law constant, H2,1 , the partial molar volume of the solute at infinite dilution, v¯2∞ , and the Margules parameter, A. In order to minimize the number of parameters to be obtained from Eq. (5), the partial molar volume at infinite dilution was obtained from the Peng–Robinson equation of state using the smoothed values of δ 12 and the critical properties discussed earlier. In this
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Table 4 Parameters for the Kritchevsky–Iliinskaya equation t (◦ C)
H2,1 (kPa)
v¯2∞ (m3 kmol−1 )
A/RT
25 40 70 100 130
151 248 593 1231 2293
0.0701 0.0715 0.0745 0.0776 0.0813
0.592 0.635 0.694 0.726 0.742
study the temperature dependent functional forms of H2,1 and A were assumed to be lnH2,1 = β0 + 1000 A = γ0 +
β1 T
γ1 T
(6) (7)
Regression of the data using Eq. (5) yielded the four parameters, β 0 , β 1 , γ 0 and γ 1 , which are presented in Table 2. Presented in Table 4 are the H2,1 ,¯ν2∞ and A/RT at each of the temperatures investigated. The dominant term in Eq. (5) is the Henry’s Law constant and the second and third terms are small and almost cancel each other. List of symbols a parameter in the Peng–Robinson equation, Pa m6 mol−2 A Margules parameter, J mol−1 b parameter in the Peng–Robinson equation, cm3 mol−1 fˆi fugacity of component i in a mixture, kPa F residual property H2,1 Henry’s Law constant of solute 2 in solvent 1 at P1S , kPa L liquid NC number of components NP number of data points OBJ objective function pi partial pressure, yi P, kPa P total pressure, kPa S P1 vapor pressure of the solvent, kPa R gas constant, J mol−1 K−1 t Celsius temperature, ◦ C T absolute temperature, K V vapor phase v¯2∞ partial molar volume at infinite dilution, m3 kmol−1 xi mole fraction in the liquid phase yi mole fraction in the vapor phase
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Greek letters α parameter in the binary interaction parameter equation β parameter in the Henry’s Law constant equation γ parameter in the Margules parameter equation δ 12 binary interaction parameter in the Peng–Robinson equation References [1] [2] [3] [4] [5] [6]
L.F. Sokolina, A.V. Gladkii, Yu.M. Afanas’ev, N.S. Torocheshnikov, Khim. Prom. (Moscow) 47 (1971) 828. F.-Y. Jou, A.E. Mather, K.A.G. Schmidt, H.-J. Ng, J. Chem. Eng. Data 44 (1999) 833–835. F.-Y. Jou, A.E. Mather, H.-J. Ng, J. Chem. Eng. Data 45 (2000) 1096–1099. F.-Y. Jou, A.E. Mather, F.D. Otto, Can. J. Chem. Eng. 73 (1995) 140–147. D.-Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fundamentals 15 (1976) 59–64. T.E. Daubert, R. P. Danner, Physical and Thermodynamic Properties of Pure Chemicals: Data Compilation, Hemisphere, Washington, DC, 1991. [7] I. Kritchevsky, A. Iliinskaya, Acta Physicochim. URSS 20 (1945) 327–348. [8] J.M. Prausnitz, R.N. Lichtenthaler, E.G. de Azevedo, Molecular Thermodynamics of Fluid-Phase Equilibria, 3rd Edition, Prentice-Hall, Englewood Cliffs, NJ, 1999, p. 592.
Vapor–liquid equilibrium in the system ethanethiol + tetraethylene glycol F.-Y. Jou, K.A.G. Schmidt1 , A.E. Mather∗ Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2G6 Received 4 August 2000; accepted 5 December 2000
Abstract The vapor–liquid equilibrium in the system ethanethiol+tetraethylene glycol has been determined at temperatures in the range 25–130◦ C at pressures up to 1000 kPa. The experimental results were correlated by the Peng–Robinson equation of state, and interaction parameters have been obtained for this system. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Experimental method; Vapor–liquid equilibria; Equation of state; Data
1. Introduction Mercaptans (thiols) are sulfur compounds which are impurities in natural gas. Ethanethiol has an overpowering offensive odor and, while small amounts are added to natural gas and liquefied petroleum gas for safety purposes, larger quantities must be removed to meet specifications on the total sulfur content. Sokolina et al. [1] measured the solubility of ethanethiol in a number of organic solvents. In this laboratory the solubility of ethanethiol in an aqueous solution of methyldiethanolamine was measured at 40 and 70◦ C [2]; similar data were obtained in a diethanolamine solution at the same temperatures [3]. This work was undertaken to ascertain the usefulness of tetraethylene glycol for the removal of ethanethiol; measurements were extended to cover the complete range of ethanethiol concentration. 2. Experimental details The apparatus and experimental technique used in the present investigation are similar to those described by Jou et al. [4]. The equilibrium cell is mounted in an air bath. The temperature of the contents of the cell was measured by a calibrated iron–constantan thermocouple and the pressure in the cell was measured ∗
Corresponding author. Tel.: +1-780-492-3957; fax: +1-780-492-2881. E-mail address: [email protected] (A.E. Mather). 1 Present address: DB Robinson Research Ltd., Edmonton, Alberta, Canada. 0378-3812/01/$20.00 © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 ( 0 1 ) 0 0 3 9 6 - X
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Table 1 Vapor–liquid equilibrium data P (kPa)
yCH4
yH 2 O
yEtSH
xCH4
xH 2 O
xEtSH
xTeEG
t=25◦ C 200 200 207 200 200 220 63 101
0.998 0.998 0.993 0.996 0.963 0.820 – 0.3255
1.45 × 10−3 4.50 × 10−4 2.17 × 10−3 – – 2.55 × 10−3 – 1.19 × 10−3
2.35 × 10−4 1.35 × 10−3 5.07 × 10−3 3.65 × 10−3 3.73 × 10−3 0.178 1.00 0.6733
1.06 × 10−3 1.25 × 10−3 1.30 × 10−3 1.25 × 10−3 1.26 × 10−3 1.82 × 10−3 – 6.57 × 10−4
2.50 × 10−2 2.02 × 10−2 1.95 × 10−2 2.83 × 10−2 1.22 × 10−2 1.27 × 10−2 4.15 × 10−3 4.21 × 10−4
3.36 × 10−4 1.95 × 10−3 7.01 × 10−3 5.07 × 10−3 4.24 × 10−2 0.305 0.750 0.964
0.974 0.977 0.965 0.965 0.944 0.681 0.246 0.0353
t = 40◦ C 200 200 200 200 200 170 150
0.997 0.997 0.997 0.942 0.662 0.359 0.192
2.90 × 10−3 2.50 × 10−3 1.00 × 10−3 4.00 × 10−4 4.15 × 10−3 – 1.33 × 10−3
3.15 × 10−4 4.10 × 10−4 2.52 × 10−3 5.75 × 10−2 0.333 0.641 0.807
1.19 × 10−3 1.20 × 10−3 1.21 × 10−3 9.68 × 10−4 1.10 × 10−3 – 4.99 × 10−4
2.47 × 10−2 2.45 × 10−2 2.50 × 10−2 1.32 × 10−2 1.24 × 10−2 4.66 × 10−3 1.53 × 10−4
3.09 × 10−4 3.40 × 10−4 2.08 × 10−3 4.21 × 10−2 0.283 0.737 0.993
0.974 0.974 0.972 0.944 0.703 0.259 0.00630
t =70◦ C 180 220 220 220 200 200 350 320 300
0.999 0.990 0.982 0.989 0.950 0.875 0.580 0.209 0.037
6.11 × 10−4 9.54 × 10−3 1.45 × 10−2 6.36 × 10−3 9.50 × 10−3 2.70 × 10−3 2.86 × 10−3 – –
2.16 × 10−4 8.64 × 10−4 3.10 × 10−3 4.51 × 10−3 4.05 × 10−2 0.122 0.417 0.791 0.963
1.11 × 10−3 1.34 × 10−3 1.35 × 10−3 1.40 × 10−3 1.10 × 10−3 9.17 × 10−4 1.97 × 10−3 4.41 × 10−4 –
6.15 × 10−3 2.60 × 10−2 2.01 × 10−2 2.43 × 10−2 1.42 × 10−2 1.30 × 10−2 1.13 × 10−2 5.09 × 10−3 1.09 × 10−3
5.45 × 10−5 3.13 × 10−4 1.11 × 10−3 1.56 × 10−3 1.35 × 10−2 3.92 × 10−2 0.290 0.689 0.956
0.993 0.972 0.977 0.973 0.971 0.947 0.697 0.306 0.0429
0.9997 0.985 0.981 0.953 0.796 0.433 6.04 × 10−3
– 1.41 × 10−2 1.42 × 10−2 1.17 × 10−2 5.54 × 10−3 4.33 × 10−3 3.58 × 10−3
3.23 × 10−4 1.42 × 10−3 4.83 × 10−3 3.58 × 10−2 0.199 0.562 0.990
1.26 × 10−3 1.15 × 10−3 1.52 × 10−3 1.46 × 10−3 1.23 × 10−3 2.43 × 10−3 –
2.02 × 10−2 2.37 × 10−2 2.47 × 10−2 2.02 × 10−2 1.55 × 10−2 1.27 × 10−2 5.24 × 10−3
5.00 × 10−5 2.36 × 10−4 9.60 × 10−4 6.50 × 10−3 3.69 × 10−2 0.329 0.670
0.978 0.975 0.973 0.972 0.946 0.655 0.325
0.991 0.969 0.967 0.928 0.549 0.219 1.23 × 10−2 1.40 × 10−3
8.0 × 10−3 2.64 × 10−2 2.64 × 10−2 2.40 × 10−2 1.09 × 10−2 7.23 × 10−3 6.75 × 10−3 3.30 × 10−3
4.68 × 10−4 4.14 × 10−3 7.12 × 10−3 4.80 × 10−2 0.441 0.774 0.981 0.995
1.43 × 10−3 1.84 × 10−3 1.54 × 10−3 1.50 × 10−3 7.88 × 10−4 2.53 × 10−3 – –
4.09 × 10−3 1.87 × 10−2 2.46 × 10−2 2.22 × 10−2 1.26 × 10−2 1.20 × 10−2 6.26 × 10−3 4.11 × 10−4
5.05 × 10−5 5.57 × 10−4 7.43 × 10−4 5.56 × 10−3 4.96 × 10−2 0.283 0.535 0.970
0.994 0.979 0.973 0.971 0.937 0.702 0.459 0.0291
t = 100◦ C 220 220 240 240 220 600 530 t = 130◦ C 250 280 250 250 220 650 800 1000
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211
by digital Heise gauges. The thermocouple had an accuracy of ±0.1◦ C by comparison with a platinum resistance thermometer. The pressure gauges had an accuracy of ±0.1% of full scale by comparison with a dead-weight gauge. The apparatus and experimental technique were checked by determination of the critical point and the vapor pressure of propane, carbon dioxide, and hydrogen sulphide. Differences of ±0.1◦ C between the measured critical temperature and literature values and ±0.1% in vapor pressure between the measured pressures and literature values were found. The tetraethylene glycol (Chemical Abstracts Registry No. (112-60-7)) of purity 99% and the ethanethiol (75-08-1) of purity 97% were purchased from Aldrich Chemical. Methane (UHP grade) was supplied by Praxair. The ethanethiol (EtSH) was first transferred from the glass bottle in which it was supplied to a 500 ml stainless steel cylinder. This cylinder was connected to a vacuum pump, a length of 0.5 m×12.5 mm o.d. stainless steel tubing containing a 3A molecular sieve, and a second cylinder. A vacuum was drawn on the EtSH to remove air and then the first cylinder was closed. The tubing and the second cylinder were evacuated overnight. The EtSH was distilled over into the second cylinder by maintaining the first cylinder at 30◦ C with heating tape and cooling the second cylinder with an ice-water bath. The second cylinder was then disconnected from the vacuum system and attached to the manifold of the equilibrium cell. Using a hand pump, the EtSH was loaded into the evacuated equilibrium cell and the vapor pressure of EtSH measured over a range of temperatures. The tetraethylene glycol (TeEG) was purged with methane while being evacuated at a total pressure of 10 kPa at 100◦ C to remove any water. After being purged, the TeEG was stored in a 300 ml cylinder. TeEG was then tranferred into the cell by the application of pressure by methane. To maintain smooth operation of the magnetic pump, which circulates the vapor phase to the bottom of the cell, methane was added to the cell to ensure the total pressure was greater than 200 kPa. The analysis of both phases was done with a gas chromatograph equipped with a thermal conductivity detector maintained at 250◦ C. The components in the vapor phase were separated with a 2 m × 3.175 mm o.d. stainless steel column packed with Haye Sep Q and operated at 180◦ C. The liquid phase was analyzed by injection of a 3.3 l sample into a 3.175 mm o.d. column containing 0.16 m of HayeSep® Q and 1.22 m of Chromosorb 104, both with packings of 80/100 mesh. Temperature programming was employed with the initial condition of 160◦ C and an increase of 64◦ C/min to 250◦ C. The retention times and response factors of CH4 /H2 O/EtSH for the vapor phase analysis were: 0.37/0.75/3.5 min and 2.00/2.86/1.00, respectively. The retention times and response factors of CH4 /H2 O/EtSH/TeEG for the liquid phase analysis were: 0.15/0.58/0.78/18.4 min and 2.00/2.71/1.00/0.36, respectively. The uncertainty in the analysis of the phases is estimated to be ±5%. 3. Results Measurements were made at 25, 40, 70, 100 and 130◦ C over the complete range of EtSH composition. The experimental data for the vapor–liquid equilibrium of EtSH in TeEg are presented in Table 1. Because of the hygroscopic nature of tetraethylene glycol, water was present in small amounts in both phases. 4. Data reduction and correlation The equilibrium data were correlated using the Peng–Robinson [5] equation of state. The parameters a and b of the solutes and solvent were obtained from the critical constants. The critical constants and
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Table 2 Parameters for the temperature dependent binary interaction parameter, Henry’s Law Constant, and Margules parameter
δ12 ln H2,1 A (J/mol)
α0 , β0 , γ0
α1 , β1 , γ1
0.1077 15.47 5383
−5742 −3.1173 −1.168 × 106
acentric factors of the solutes and solvent were taken from the compilation of Daubert and Danner [6]. The binary interaction parameter, δ 12 , was obtained from the experimental equilibrium data at each temperature by minimizing the following objective function: NP OBJ = Fj
(1)
j
Fj =
NC
(ln(fiL ) − ln(fiV ))2
(2)
i=1
The binary interaction parameter δ 12 appears in the mixing rule of the equation of state a12 = (a12 a22 )1/2 (1 − δ12 )
(3)
Values of δ 12 were found to have a moderate temperature dependence and could be fit by a simple relationship δ12 = α0 + α1 × T −2
(4)
The correlation parameters α 0 and α 1 are presented in Table 2 and the smoothed values of δ 12 (at each experimental temperature) are presented in Table 3. The VLE data were then calculated with the smoothed temperature-dependent form of the binary interaction parameter. These calculated results are compared with the experimental data in Fig. 1. As can be seen the Peng–Robinson equation of state with the critical constants from Daubert and Danner [6] and the smoothed binary interaction parameter satisfactorily correlated the data. The overall average absolute percent difference in the EtSH partial pressures was determined to be 6.1%, which is close to the experimental uncertainty. Table 3 Binary interaction parameters for the Peng–Robinson equation of state t (◦ C)
δ12
25 40 70 100 130
0.043 0.049 0.059 0.066 0.072
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Fig. 1. Vapor–liquid equilibria of ethanethiol in tetraethylene glycol.
Because the removal of ethanethiol from natural gas streams is often a process involving dilute concentrations of EtSH it was of interest to determine the Henry’s Law constants of EtSH in TeEG. In this investigation the Kritchevsky–Iliinskaya [7] equation
fˆ2 RT ln x2
= RT ln H21 + v¯2∞ (P − P1S ) + A[x12 − 1]
(5)
was used to determine these Henry’s Law constants by correlating all the VLE data over the 25–130◦ C temperature range. As discussed by Prausnitz et al. [8] the application of the Kritchevsky–Iliinskaya equation requires the evaluation of three parameters, the Henry’s Law constant, H2,1 , the partial molar volume of the solute at infinite dilution, v¯2∞ , and the Margules parameter, A. In order to minimize the number of parameters to be obtained from Eq. (5), the partial molar volume at infinite dilution was obtained from the Peng–Robinson equation of state using the smoothed values of δ 12 and the critical properties discussed earlier. In this
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Table 4 Parameters for the Kritchevsky–Iliinskaya equation t (◦ C)
H2,1 (kPa)
v¯2∞ (m3 kmol−1 )
A/RT
25 40 70 100 130
151 248 593 1231 2293
0.0701 0.0715 0.0745 0.0776 0.0813
0.592 0.635 0.694 0.726 0.742
study the temperature dependent functional forms of H2,1 and A were assumed to be lnH2,1 = β0 + 1000 A = γ0 +
β1 T
γ1 T
(6) (7)
Regression of the data using Eq. (5) yielded the four parameters, β 0 , β 1 , γ 0 and γ 1 , which are presented in Table 2. Presented in Table 4 are the H2,1 ,¯ν2∞ and A/RT at each of the temperatures investigated. The dominant term in Eq. (5) is the Henry’s Law constant and the second and third terms are small and almost cancel each other. List of symbols a parameter in the Peng–Robinson equation, Pa m6 mol−2 A Margules parameter, J mol−1 b parameter in the Peng–Robinson equation, cm3 mol−1 fˆi fugacity of component i in a mixture, kPa F residual property H2,1 Henry’s Law constant of solute 2 in solvent 1 at P1S , kPa L liquid NC number of components NP number of data points OBJ objective function pi partial pressure, yi P, kPa P total pressure, kPa S P1 vapor pressure of the solvent, kPa R gas constant, J mol−1 K−1 t Celsius temperature, ◦ C T absolute temperature, K V vapor phase v¯2∞ partial molar volume at infinite dilution, m3 kmol−1 xi mole fraction in the liquid phase yi mole fraction in the vapor phase
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Greek letters α parameter in the binary interaction parameter equation β parameter in the Henry’s Law constant equation γ parameter in the Margules parameter equation δ 12 binary interaction parameter in the Peng–Robinson equation References [1] [2] [3] [4] [5] [6]
L.F. Sokolina, A.V. Gladkii, Yu.M. Afanas’ev, N.S. Torocheshnikov, Khim. Prom. (Moscow) 47 (1971) 828. F.-Y. Jou, A.E. Mather, K.A.G. Schmidt, H.-J. Ng, J. Chem. Eng. Data 44 (1999) 833–835. F.-Y. Jou, A.E. Mather, H.-J. Ng, J. Chem. Eng. Data 45 (2000) 1096–1099. F.-Y. Jou, A.E. Mather, F.D. Otto, Can. J. Chem. Eng. 73 (1995) 140–147. D.-Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fundamentals 15 (1976) 59–64. T.E. Daubert, R. P. Danner, Physical and Thermodynamic Properties of Pure Chemicals: Data Compilation, Hemisphere, Washington, DC, 1991. [7] I. Kritchevsky, A. Iliinskaya, Acta Physicochim. URSS 20 (1945) 327–348. [8] J.M. Prausnitz, R.N. Lichtenthaler, E.G. de Azevedo, Molecular Thermodynamics of Fluid-Phase Equilibria, 3rd Edition, Prentice-Hall, Englewood Cliffs, NJ, 1999, p. 592.