Dew Points of Ternary Ethane + Water + Methanol: Measurement and

Energy & Fuels 2000, 14, 877-882

877

Dew Points of Ternary Ethane + Water + Methanol: Measurement and Correlation Sofıá T. Blanco,† Inmaculada Velasco,† Evelyne Rauzy,‡ and Santos Otıń*,† Departamento de Quı´mica Orga´ nica y Quı´mica Fı´sica, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain, and Laboratoire de Chimie Physique de Marseille. Faculte´ des Sciences de Luminy, Universite´ de la Mediterrane´ e, 13288 Marseille Cedex 9, France Received November 16, 1999

Experimental measurements of dew points for ternary ethane + water + methanol were carried out between 0.98 × 105 and 22.36 × 105 Pa and the temperature range from 246.90 to 283.06 K. An EOS-CR method (equation of state-chemical reticular) reproduces quite accurately the experimental data within average absolute deviation (AAD) from 0.05 to 4.12 K.

Introduction Methanol is one of the main additives used in natural gas processing and pipeline transport. This chemical is used as a hydrate inhibitor and as a secant following hydraulic tests of natural gas pipelines. In both the above applications, methanol is found with water in natural gases. To understand the influence of these two components on the vapor-liquid equilibrium of natural gases, the ternary systems composed of water and methanol and the major components of natural gas were studied. A water and methanol dew point generation experimental apparatus was built and commissioned. The experimental dew points of methane + water + methanol1 and ethane + water + methanol were then determined. The results obtained on ethane + water + methanol mixtures between 0.98 × 105 and 22.36 × 105 Pa and temperatures from 246.90 to 283.06 K are presented in this paper. The demand for reliable calculation procedures to estimate these dew points in natural gases is becoming more and more important.2 Therefore, the experimental results obtained on the ternary system were analyzed in terms of an EOS-CR method (equation of statechemical reticular), which reproduced experimental dew point data within AAD between 0.05 and 4.12 K. Experimental Section Apparatus. The experimental method used for this work is based on the generation of saturated gases with water and methanol by condensation of these compounds in a temperature-controlled condenser with continuous gas flow at specified pressures. The concentrations of water and methanol in the gas are measured at the outlet of the dew point generation apparatus, using a Karl Fischer titration3 and a gas chroma†

Universidad de Zaragoza. Universite´ de la Mediterraneé. (1) Blanco, S. T.; Velasco, I.; Rauzy, E.; Otıń, S. Fluid Phase Equilib., in press. (2) Le Noë, O.; Schieppati, L.; Viglietti, B.; Oellrich, L.; Althaus, K.; Pot, F.; Van der Meulen, L.; Kaesler, H.; Monco´, G.; Wismann, G. Int. Gas Res. Conf. (IGRC) 1985, 1, 25-34. ‡

Figure 1. Scheme of the experimental apparatus used in this work: RV, control valve; V, ball valve; HV, three-way valve; TI, temperature measurement; PI, pressure measurement; QI, Coulometric measurement; XI, volume measurement. tography analysis, respectively. By doing so, the water and methanol content reference values for the gaseous phase are obtained. The dew point values are measured by means of a chilled mirror instrument.4 The chilled mirror instrument input pressure is set using a regulator valve; when the apparatus reaches a stable value of dew temperature, both pressure and temperature are recorded. In this way, the values of temperature and pressure of the dew point curve of the mixture are obtained. Operating Procedure. The dew point pressure ranged from 0.98 × 105 to 22.36 × 105 Pa, and the temperature ranged from 246.90 to 283.06 K. Ethane was supplied by Air Liquide with the specified purity of 99.995 vol % and was used without further treatment. The dew point generation apparatus used for our experimental data generation (Figure 1) was built and tested in previous works.1,5 The gas is saturated with water and methanol vapor by flowing through a liquid mixture of these (3) International Standard ISO 10101, Natural gas-Determination of water by the Karl-Fischer method, 1993. (4) International Standard ISO 6327, Gas analysis. Determination of the water dew point of natural gas. Cooled surface condensation hygrometers, 1981. (5) Blanco, S. T.; Velasco, I.; Rauzy, E.; Otıń S. Fluid Phase Equilib. 1999, 161, 107-117.

10.1021/ef9902404 CCC: $19.00 © 2000 American Chemical Society Published on Web 06/07/2000

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Energy & Fuels, Vol. 14, No. 4, 2000

compounds in an isolated saturator held at laboratory temperature. The temperature controlled for the water and methanol condensation is achieved in a single stainless steel condenser. The instrumentation implemented to analyze the contents of water and methanol and to carry out the dew point measurements is the following: (1) Mitsubishi CA 06 Karl Fischer titrator, coupled with an Elster wet gasmeter type Gr. 00, E51, 0.2% accuracy and measuring range from 2 to 200 dm3/h; (2) HP 5890 gas chromatograph with TCD detector adjusted to maximum sensitivity, with uncertainty in the methanol content of 0.7%;6 (3) MBW dew point measuring instrument model DP3-D, with mirror cooling achieved by Peltier cooling with an automatic mirror check system and an uncertainty in the dew temperature of (0.4 K; (4) pressure transmitter with a maximum error of 0.04 × 105 Pa in the calibrated range. Prior to this study of ethane + water + methanol dew points, the performance of both analysis methods and experimental procedures was determined.1,5 Repeated analyses of water content of a standard nitrogen + water mixture prepared by Air Liquide were carried out in order to evaluate the experimental error of the analysis of water content. The measured values were equal to the standard water content within a rejecting percentage of 0.05%.7 Repeatability and reproducibility of Karl Fischer titration of this standard nitrogen + water mixture were calculated according to ISO 5725 (1986).8 The values obtained were 0.76 × 10-6 and 1.68 × 10-6 kg m-3 (n), respectively. Repeatability and reproducibility of water and methanol dew point generation were calculated according to ISO 5725 (1986)8 after repetitive measurements. The results obtained in the performance evaluation are the following: for water content, 15.96 × 10-6 and 36.32 × 10-6 kg m-3 (n), respectively, corresponding to a mean water content of 899.64 × 10-6 kg m-3 (n); for methanol content, 316.7 × 10-6 and 294.0 × 10-6 kg m-3 (n), respectively, corresponding to a mean methanol content of 12301.1 × 10-6 kg m-3 (n). Reference conditions for volume are 273.15 K and 1.01325 × 105 Pa. The test was achieved on a water and methanol dew point of 283.15 K and 5 × 105 Pa in pure nitrogen. The reliability tests results are taken as consistency criteria: the maximum acceptable standard deviation of measurements is derived from the repeatability value, and the maximum acceptable discrepancy with measurements from external laboratories is derived from the reproducibility value.

Results The water and methanol amounts in the vapor phase and the dew point data for the mixtures generated at the dew point generation system were determined, and the results of the experiments are provided in Table 1. Theory Introduction. Classical models such as UNIQUAC or NRTL yield good results for vapor-liquid equilibrium at low pressures for binary systems containing one selfassociating compound such as alcohol but are not available in high-pressure phase equilibrium calculations.9 (6) Blanco, S. T. Doctoral Thesis, Universidad de Zaragoza, Zaragoza, Spain, 1998. (7) International Standard ISO 2854, Statistical interpretation of data-Techniques of estimation and tests relating to means and variances, 1976. (8) International Standard ISO 5725, Precision of test methodsDetermination repeatibility and reproducibility for a standard test method by inter-laboratory tests, 1986. (9) Rauzy, E.; Berro, C. INPL 905267; 1987; pp 107-125.

Blanco et al.

In this work we used the vapor-liquid equilibrium model EOS-CR (equation of state-chemical reticular) derived from the excess function-equations of state model10 and founded on the zeroth approximation on the quasi-reticular model. The values for dew point temperature and composition of the vapor phase for the studied system are calculated by means of this theoretical method using the experimental pressure data. To evaluate this method for the prediction of the dew points of the ternary system in the temperature and pressure studied ranges, a comparison between experimental and calculated values was carried out. The results are quite good with values of AAD from 0.05 to 4.12 K. Description of the VLE Model. To represent the vapor-liquid equilibrium of mixtures containing one self-associating component, a model founded on the zeroth approximation of Guggenheim’s reticular model was selected. The model satisfies two important conditions: (1) The Helmholtz energies of pure components are calculated by an equation of state. (2) The excess functions are obtained at constant packing fraction, η. That is to say the value of the packing fraction, η, for each component of the mixture is the value corresponding to the pure component. This assumption leads to

η)

b bi ) v vi

i ) 1, ..., p

(1)

The equation of state used in this model is the translated Peng-Robinson cubic equation of state of the form11,12

P)

a(T) RT vj - b h vj (vj + γb h)

(2)

where P and T are the system pressure and temperature, R is the gas constant, vj is a translated molar volume called the pseudovolume, and b h is the pseudocovolume; it is calculated as follows for each component of the mixture:

b h ) 0.045572

RTc Pc

(3)

Here Tc and Pc are the component critical temperature and pressure, respectively. The parameter “a” in eq 2 is the attractive parameter and is only a function of the temperature. The equations used for its calculation are those proposed by Carrier (1989)13 and Carrier et al. (1988).14 (10) Peńeloux, A.; Abdoul, W.; Rauzy, E. Fluid Phase Equilib. 1989, 47, 115-132. (11) Peńeloux, A.; Rauzy, E.; Fre´ze, R. Fluid Phase Equilib. 1982, 8, 7-23. (12) Rauzy, E. The`se d’Etat-Sciences, Universite´ Aix-Marseille II, Marseille, France, 1982. (13) Carrier, B. The`se de Docteur en Sciences, Universite´ AixMarseille III, Marseille, France, 1989. (14) Carrier, B.; Rogalski, M.; Peńeloux, A. Ind. Eng. Chem. Res. 1988, 27, 1714-1721.

Dew Points of Ternary Ethane + Water + Methanol

Energy & Fuels, Vol. 14, No. 4, 2000 879

Table 1. Experimental Dew Point Temperatures and Pressures for Ternary Mixtures {(1 - y1 - y2) Ethane + y1 Water + y2 Methanol} T/K

P/105 Pa

T/K

P/105 Pa

T/K

P/105 Pa

T/K

P/105 Pa

247.66 249.07 249.89 251.05 252.57

1.59 1.82 1.96 2.48 2.95

255.05 257.79 259.71 261.73 262.94

3.83 4.99 5.96 7.02 7.98

y1 ) 0.00006; y2 ) 0.0023 264.26 8.91 265.65 9.99 266.81 11.00 267.80 11.94 268.76 12.86

269.83 270.49 270.88 271.43 272.21

14.06 14.91 15.43 16.00 16.99

272.85 273.03

17.92 19.10

248.37 249.62 252.22 256.98

1.07 1.23 1.94 2.93

259.48 262.22 264.08 265.74

3.94 4.92 6.03 6.94

y1 ) 0.00007; y2 ) 0.0031 267.24 7.92 269.34 8.91 271.65 11.07 272.24 11.49

272.95 273.48 274.69 275.69

12.07 12.97 14.00 15.04

276.05 277.00 277.54

15.95 17.06 17.89

250.28 254.40 257.21 260.83

1.32 2.08 2.83 3.97

264.32 267.72 269.05 271.34

5.08 6.63 7.83 9.53

y1 ) 0.00010; y2 ) 0.0040 272.34 10.50 272.61 11.01 274.89 13.25

276.40 277.60 278.80

14.77 16.47 18.03

279.16 280.38 280.66

18.67 20.06 21.53

249.27 250.16 256.07 260.16 263.19

1.04 1.11 2.01 2.98 3.94

265.64 267.44 267.76 268.28

4.96 5.94 6.16 6.48

y1 ) 0.00014; y2 ) 0.0041 269.09 6.95 270.28 7.86 270.62 8.06 271.78 9.03

272.84 274.49 274.64 276.58

10.00 11.63 11.81 13.53

278.70 280.04 280.35 281.85

15.87 17.56 18.06 19.70

249.46 252.93 256.07 258.25

2.17 3.02 4.05 4.95

260.46 262.00 263.18 264.76

6.10 7.02 7.92 9.11

y1 ) 0.00020; y2 ) 0.0012 265.79 9.94 266.89 11.05 267.84 12.04 268.47 12.79

269.30 270.06 270.64 271.50

13.84 14.79 15.62 16.89

272.25 272.66 273.08 273.47

18.10 18.82 19.59 20.08

253.60 256.96 260.73 263.07

2.15 3.11 4.11 5.08

265.24 265.99 267.75 268.94

6.29 6.99 8.05 9.02

y1 ) 0.00029; y2 ) 0.0020 270.14 10.04 271.21 10.97 272.21 12.08 273.24 13.04

274.30 275.12 276.12 276.25

14.04 14.91 16.16 17.05

277.12 277.81

17.96 19.03

249.99 249.72 254.73 258.12

1.09 1.23 2.08 2.88

261.43 263.86 265.82 267.63

3.99 4.91 5.98 7.04

y1 ) 0.00034; y2 ) 0.0023 269.31 8.97 271.36 9.55 273.06 10.96 274.39 12.25

275.97 277.95 278.17 279.12

14.03 15.57 17.10 18.44

280.10 280.48

19.92 22.36

250.79 257.71 261.61 264.10

1.09 2.07 3.06 3.93

266.94 268.94 270.90 272.15

5.03 6.02 7.06 7.87

y1 ) 0.00037; y2 ) 0.0027 273.75 8.98 275.10 9.97 276.08 10.87 277.13 11.96

277.80 278.71 279.80 280.48

12.81 13.79 14.99 16.19

281.11 281.65 282.85

17.08 18.06 19.75

246.90 248.51 251.35 255.41

0.98 1.19 1.53 2.19

257.45 258.93 262.13 263.37

2.70 3.04 4.12 5.00

y1 ) 0.00031; y2 ) 0.0022 265.42 5.83 267.06 6.81 268.83 7.88 270.36 8.89

271.62 272.67 273.74 274.04

9.87 10.83 11.97 12.24

274.60 275.56 276.10 276.63

12.74 13.70 14.73 15.33

250.59 253.90 255.15 257.50 261.56

0.98 1.33 1.51 1.86 2.86

265.29 267.75 269.69 271.71

4.03 4.97 5.84 6.96

y1 ) 0.00040; y2 ) 0.0033 273.37 7.96 274.33 8.64 274.97 9.03 276.31 10.09

277.31 277.62 277.82 278.44

11.06 11.46 11.57 11.89

278.70 279.50 280.52 280.77

12.16 12.88 13.97 14.21

251.38 255.82 260.13 261.80 263.83

0.98 1.47 2.09 2.43 2.97

267.16 269.83 270.18 271.70 273.55

3.87 4.96 5.13 5.92 6.81

y1 ) 0.00047; y2 ) 0.0035 273.79 7.00 275.24 7.74 276.74 8.79 277.22 9.16 277.89 9.69

277.96 278.01 278.33 279.14 280.05

9.75 9.79 10.10 10.81 11.74

281.63 281.75

13.07 13.77

258.18 260.60 263.48 263.97

1.18 1.49 1.93 1.98

266.80 268.65 270.34 271.74

2.59 3.07 3.55 3.99

y1 ) 0.00067; y2 ) 0.0052 273.56 4.61 274.69 4.99 276.37 5.62 277.05 5.98

278.73 280.20 280.24 280.32

6.89 7.61 7.82 7.95

281.68 282.09

8.91 9.10

250.93 253.40 255.74 256.04

1.01 1.25 1.52 1.55

257.82 258.29 259.59 261.59

1.77 1.85 2.10 2.40

y1 ) 0.00091; y2 ) 0.0025 263.11 2.73 264.20 3.01 265.53 3.31 266.44 3.60

267.48 268.37 269.32 270.09

3.91 4.18 4.51 4.80

270.82 271.71 272.30 273.16

5.10 5.40 5.70 6.03

T/K

P/105 Pa

880


Blanco et al.

Table 1 (Continued) T/K

P/105 Pa

T/K

P/105 Pa

T/K

P/105 Pa

T/K

P/105 Pa

253.91 257.04 260.06 262.08

1.00 1.29 1.62 1.91

264.04 265.48 266.89 268.15

2.24 2.52 2.80 3.11

y1 ) 0.00100; y2 ) 0.0028 269.04 3.33 270.20 3.63 271.21 3.91 272.18 3.97

273.06 273.90 274.80 275.43

4.51 4.82 5.11 5.40

276.23 277.00

5.71 6.06

259.82 261.85 264.33

1.03 1.20 1.44

266.32 268.32 270.47

1.70 1.97 2.31

y1 ) 0.00171; y2 ) 0.0033 272.09 2.61 273.51 2.91 274.78 3.20

276.04 277.14 278.09

3.51 3.80 4.09

279.17 280.15 281.05

4.43 4.72 5.05

263.87 266.35 268.21 270.41

1.00 1.21 1.39 1.63

271.79 273.17 274.52

1.81 2.00 2.21

y1 ) 0.00258; y2 ) 0.0036 275.75 2.41 277.09 2.65 278.02 2.83

278.84 279.70 280.66

3.01 3.20 3.43

281.50 282.20 283.06

3.64 3.82 4.05

T/K

The molar Helmholtz energy of a mixture, A, may be written as follows:

xiai Q(η) + AEres i)1 bi p

A ) Aid - RT ln(1 - η) -

∑

(4)

Q′(η) )

Q′(η) dη η

∫0η

η 1 + γη

γ ) 2(x2 + 1)

(5) (6)

The value used for the parameter γ is characteristic of the equation of state, which in this case is the translated Peng-Robinson cubic equation of state.11,12 The residual excess Helmholtz energy, AEres, can be separated into two terms, as shown in eq 7, where the

AEres

)

AEfis

+

E Aqui

) E(T, x) Q(η)

E(T, x) ) 1

p

[

∑ i)1

Kij )

p

∑ j)1

q i xi [

(8)

The physical interactions between different compounds are represented by the physical term, AEfis, using the eq 8,15 while the molecular associations are described by the chemical term, AEqui. For its calculation the CREE model (chimique reticulaire equation d’etat) is used. It is a continuous association model defined by Rauzy and Berro.9,16 (15) Hocq, H. The`se en Sciences, Universite´ de Droit, d’Economie et des Sciences d’Aix-Marseille III, Marseille, France, 1984. (16) Rauzy, E.; Berro, C. International symposium of supercritical fluids; Perrut, M., Ed.; 1988; pp 153-160.

p

qjxjKij] +

∑ i)1

p

q i xi [

qj1/3xjLji1/3]] ∑ j)1

E1ij + E2ij Lij ) E2ij - E1ij Lij ) -Lji 2

(9)

(10)

p

qm )

∑ qkxk

qk ) δkbk

(11)

k)1

Here the subscripts i and j are referred to the components i and j of the mixture with p components, qi is the molecular surface of the component i, and it is assumed that qi/qj ) (bi/bj)δ, δ being an adjustable parameter. Kij and Lij are two binary interaction parameters between components i and j, which depend on the terms of the interchange energy, E1ij and E2ij, calculated using a group contribution method as follows:15

E1ij ) -

1

N N

∑ ∑(Rik - Rjk)(Ril - Rjl)A1kl(T)

2k)1l)1

(7)

physical part, AEfis, is written by means of a formalism which enables one to separate the composition and packing fraction variables:

AEfis

For the first term on the right-hand side of eq 8 the following equations were used:15

2qm

Here Aid is the ideal mixture molar Helmholtz energy, ai is the attractive parameter of the i component of a translated Peng-Robinson cubic equation of state,11,12 bi is the component i covolume, AEres is the residual excess Helmholtz energy (explained in another section), and Q(η) is expressed as follows:

Q(η) )

P/105 Pa

A1kl ) 1A0kl E2ij ) -

1

() T0

0 1Bkl

T

(12)

N N

∑ ∑(Rik - Rjk)(Ril - Rjl)A2kl(T)

2k)1l)1

A2kl

)

0 2Akl

() T0 T

0 2Bkl

(13)

Here 1A0kl, 1B0kl, 2A0kl, and 2B0kl are group interaction parameters. In this work, new values for 2A0kl and 2B0kl group interaction parameters for the binary interchange energy E2ij between ethane and water are obtained using dew point experimental results from the literature.17 The values for these parameters used for comparison calculations in this work are presented in Table 2. (17) Reamer, H. H.; Olds, R. H.; Sage, B. H.; Lacey, W. N. Ind. Eng. Chem. 1943, 35, 790-793.

Dew Points of Ternary Ethane + Water + Methanol Table 2. Values of the Group Interaction Parameters, A0kl, 1B0kl, 2A0kl, and 2B0kl, Used in This Work binary

0 6 1Akl/10 J m-3

0 6 1Bkl/10 J m-3

0 6 2Akl/10 J m-3

Energy & Fuels, Vol. 14, No. 4, 2000 881 1

0 6 2Bkl/10 J m-3

ethane + water 1288.28715 -1.559515 5946.637a 0.390a ethane + methanol 285.62115 -0.304015 239.98515 1.846215 a

This work.

Figure 4. Comparison between experimental dew points curves (symbols) and values calculated with the EOS-CR method (lines) for the system {(1 - y1 - y2) ethane + y1 water + y2 methanol}: 9, y1 ) 0.00031, y2 ) 0.0022; 0, y1 ) 0.00040, y2 ) 0.0033; b, y1 ) 0.00047, y2 ) 0.0035; O, y1 ) 0.00067, y2 ) 0.0052.




The chemical contribution to the residual molar excess Helmholtz energy of a mixture, AEqui, is based on the self-association model of Rauzy and Berro.9,16 Comparison with Experiment and Discussion. The experimental dew point data and that calculated with the EOS-CR (equation of state-chemical reticular) method are represented in Figures 2-5. As it can be seen in Figures 2-5, an increase of water and methanol contents of the system mixtures shows a displacement of the dew point curves to higher values of dew temperatures and pressures. After comparison of the experimental and calculated dew point curves in Figures 2-5, it can be concluded that the EOS-CR (equation of state-chemical reticular) method used in this work reproduces quite satisfactorily the experimental dew point data. Values of AAD obtained for each dew point curve are presented in Table 3. It should be noted that the EOS-CR method tends to overestimate the dew point temperatures. The EOS-

Table 3. Values of AAD and Experimental Ranges of Dew Temperatures and Pressures for Ternary Mixtures {(1 - y1 - y2) Ethane + y1 Water + y2 Methanol} y1

y2

T range/K

P range/105 Pa

AAD/K

0.000 06 0.000 07 0.000 10 0.000 14 0.000 20 0.000 29 0.000 34 0.000 37 0.000 31 0.000 40 0.000 47 0.000 67 0.000 91 0.001 00 0.001 71 0.002 58

0.0023 0.0031 0.0040 0.0041 0.0012 0.0020 0.0023 0.0027 0.0022 0.0033 0.0035 0.0052 0.0025 0.0028 0.0033 0.0036

247.66-273.03 248.37-277.54 250.28-280.66 249.27-281.85 249.46-273.47 253.60-277.81 249.99-280.48 250.79-282.85 246.90-276.63 250.59-280.77 251.38-281.75 258.18-282.09 250.93-273.16 253.91-277.00 259.82-281.05 263.87-283.06

1.59-19.10 1.07-17.89 1.32-21.53 1.04-19.70 2.17-20.08 2.15-19.03 1.09-22.36 1.09-19.75 0.98-15.33 0.98-14.21 0.98-13.77 1.18-9.10 1.01-6.03 1.00-6.06 1.03-5.05 1.00-4.05

2.88 3.00 4.12 3.07 1.59 2.38 2.41 1.64 1.87 2.22 1.24 0.92 2.28 0.17 0.25 0.05

CR method could not be used to calculate several dew points for the system studied, because the EOS-CR method was not able to obtain the right molar fraction of water and methanol in the vapor phase. These points were at the lowest pressure corresponding to the mixtures with the extreme experimental water and methanol amounts. These points constitute a small part of the experimental dew point data obtained in this work and can be ignored. For most of the studied dew

882


points, the experimental and calculated values for molar fractions of water and methanol in the vapor phase were exactly the same.

Blanco et al.

curve we used the deviation

AAD ) Acknowledgment. The authors acknowledge the financial and technical support of Enaga´s, SA, during the experimental part of this work.

N

∑(Tiexp - Tical) N i)1

where N is the number of dew points which constitute a dew point curve.

Appendix For comparison between calculated and experimental dew point temperatures for each studied dew point

1

EF9902404

Dew Points of Ternary Ethane + Water + Methanol: Measurement and

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