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Thermodynamic Properties of Synthetic Natural Gases. 2. Dew Point Curves of Synthetic Natural Gases and Their Mixtures with Water and Methanol. Measurement and Correlation Susana Avila,† Sofı´a T. Blanco,‡ Inmaculada Velasco,‡ Evelyne Rauzy,§ and Santos Otı´n*,‡ Departamento de Innovacio´ n Tecnolo´ gica, ENAGAS, S. A., Spain, Departamento de Quı´mica Orga´ nica y Quı´mica Fı´sica, Facultad de Ciencias, Universidad de Zaragoza, 50.009 Zaragoza, Spain, and Laboratoire de Chimie Physique de Marseille, Faculte´ des Sciences de Luminy, Universite´ de la Mediterrane´ e, 13.288 Marseille, Cedex 9, France Received December 4, 2001. Revised Manuscript Received April 6, 2002
Experimental measurements of dew points for four synthetic natural gases (SNG) and seven SNG + water + methanol mixtures were carried out between (1.4 and 77.7) × 105 Pa and the temperature range from 199.9 to 284.1 K. An EOS-CR method (equation of state-chemical reticular) reproduces quite accurately the experimental dew point temperature data within average absolute deviation (AAD) from 0.7 to 2.7 K.
Introduction Methanol is one of the main additives used in natural gas processing and pipeline transport. This chemical is used for hydrate inhibition 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, a water and methanol dew point generation apparatus was built and commissioned and the systems composed by the major components of natural gas and water and methanol; methane + water + methanol,1 ethane + water + methanol,2 and propane + water + methanol3 were studied. Afterward, synthetic natural gases (SNG) and their mixtures with water and methanol were studied in this work and in a previous paper.4 The compositions of the SNG studied in this work are the same as those of the natural gases supplied in Spain as liquefied natural gases. In a previous work,4 SNG mixtures similar to those supplied through both European and Magreb gas pipeline networks and their mixtures with water and methanol were studied. For the LNG compositions, similar to those of SNG studied in this work, the condensation risk in transmission * Corresponding author. Tel.: +34 976 761 199. Fax: +34 976 761 202. E-mail address:
[email protected]. † Departamento de Innovacio ´ n Tecnolo´gica. ‡ Departamento de Quı´mica Orga ´ nica y Quı´mica Fı´sica. § Laboratoire de Chimie Physique de Marseille. (1) Blanco, S. T.; Velasco, I.; Rauzy, E.; Otı´n, S. Can. J. Chem. 2000, 78, 1587-1593. (2) Blanco, S. T.; Velasco, I.; Rauzy, E.; Otı´n, S. Energy Fuels 2000, 14, 877-882. (3) Blanco, S. T.; Velasco, I.; Rauzy, E.; Otı´n, S. J. Chem. Eng. Jpn. 2001, 34, 971-978. (4) Avila, S.; Blanco, S. T.; Velasco, I.; Rauzy, E.; Otı´n, S. Proc. 2001 Int. Gas Res. Conf. (IGRC) 2001, TP-17.
through gas pipeline is mainly due to the presence of water and methanol in the mixtures. However for compositions similar to those of natural gases imported through gas pipeline, such is the case of SNG studied in a previous work,4 the condensation risk is strongly influenced by the hydrocarbon composition of the mixtures. The results obtained on four SNG between (2.3 and 77.7) × 105 Pa and temperatures from 199.9 to 240.8 K, and seven SNG + water + methanol mixtures between (1.4 and 72.2) × 105 Pa and temperatures from 236.4 to 284.1 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.5 Therefore, the experimental results obtained on the multicomponent systems were analyzed in terms of an EOS-CR method (equation of state-chemical reticular), which reproduced experimental dew point data within AAD between 1.9 and 2.7 K on dry systems, and from 0.7 to 2.3 K on systems with water and methanol. 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 dew point generation apparatus used for our experimental data generation (Figure 1) was built and tested in previous works.6 The gas is saturated with water and (5) Le No¨e, 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. (6) Blanco, S. T.; Velasco, I.; Rauzy, E.; Otı´n, S. Fluid Phase Equlib. 1999, 161, 107-117.
10.1021/ef0102824 CCC: $22.00 © 2002 American Chemical Society Published on Web 06/05/2002
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Energy & Fuels, Vol. 16, No. 4, 2002 929
Figure 1. Experimental apparatus used in this work. RV: control valve. HV: three ways valve. TI: Temperature measurement. PI: pressure measurement. QI: Coulometric measurement. XI: volume measurement. V: ball valve. Table 1. Compositions of Synthetic Natural Gases (% mol) and Absolute or Relative Accuracy Specified by the Supplier nitrogen methane ethane propane i-butane n-butane i-pentane n-pentane n-hexane
gas 1
gas 2
gas 3
gas 4
0.67 ( 0.02 the rest 8.22 ( 0.17 0.90 ( 0.02 0.11 ( 0.01 0.13 ( 0.01 0.0084 ( 0.0002 0.0032 ( 0.001
0.48 ( 0.01 the rest 8.54 ( 0.17 1.68 ( 0.04 0.22 ( 0.01 0.29 ( 0.01 0.0182 ( 0.0004 0.0084 ( 0.0002
0.862 ( 2% the rest 9.832 ( 1% 2.388 ( 1% 0.183 ( 2% 0.231 ( 2% 0.0139 ( 2% 0.0063 ( 2%
0.410 ( 0.04 the rest 2.510 ( 0.05 0.213 ( 0.005 0.184 ( 0.004 0.197 ( 0.004 0.0096 ( 0.0002 0.0100 ( 0.0002 0.0010 ( 0.0001
methanol vapor by flowing through a liquid mixture of these compounds in an isolated saturator held at laboratory temperature. Thereafter, the gas is cooled in a stainless steel condenser, which is located in a thermostat bath set at the desired equilibrium temperature. The water and methanol contents of the gas that leaves the condenser are measured using a Karl Fischer titration7 and a gas chromatography 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.8 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 (1.4 to 77.7) × 105 Pa and the temperature range between 199.9 and 284.1 K. The synthetic natural gases used in this work were prepared according to the gravimetric method (International Standard ISO 6142:1981),9 by Air-Liquide and (7) Natural Gas-Determination of Water by the Karl-Fischer method. International Standard ISO 10101; International Organization of Standardization: Geneva, Switzerland, 1993. (8) Gas Analysis. Determination of the Water Dew Point of Natural Gas. Cooled Surface Condensation Hygrometers. International Standard ISO 6327; International Organization of Standardization: Geneva, Switzerland, 1981. (9) Analyse des gaz - Pre´paration des me´langes de gaz pour e´talonnage. Me´thodes ponde´rales. International Standard ISO 6142; International Organization of Standardization: Geneva, Switzerland, 1981.
Abello´-Linde. The compositions of the four SNG mixtures used in this work and their accuracy specified by the supplier are listed in Table 1. To analyze the contents of water and methanol and to carry out the dew point measurements the following instrumentation is used: •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. •HP 5890 Gas Chromatograph fit up with a Haysep Q column and a thermal conductivity detector. •MBW Dew Point Instrument. Mod. DP3-D-HP-K2, in which the cooling of the mirror is achieved by cascaded Peltier elements and the dew point mirror temperature is controlled optoelectronically. The uncertainty on the dew temperature is better than (0.1 K. •Pressure Transmitter with a maximum error of 0.1% in the calibrated range. Prior to this study of SNG and SNG + water + methanol dew points, the performance of both analytical methods and experimental procedures was determined. To obtain the accuracy of the dew point measurement on dry systems, the vapor-liquid equilibrium curves of both ethane, with specified purity of 99.995%, and propane, with specified purity of 99.95%, where measured and compared with literature.10,11 The results obtained were the following: (10) Goodwin, R. D.; Roder, H. M.; Starty, G. C. Thermophysical Properties of Ethane from 90 to 600 K at Pressures to 700 bar. Technical Note 684; Cryogenics Division, National Bureau of Standards: Boulder, Canada, 1976.
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Avila et al.
Table 2. Experimental Dew Points Temperatures and Pressures for Synthetic Natural Gas Mixtures T/K
P/105 Pa
T/K
P/105 Pa
T/K
Gas 1 200.3 207.3 212.9 218.1 219.6 221.7 223.7 224.7
5.4 10.2 14.7 19.6 24.5 29.7 35.7 40.4
202.9 210.6 214.6 218.5 224.7 228.9 232.1 234.0 235.5 236.4
2.9 5.1 7.0 10.0 14.9 19.9 25.5 30.1 35.1 40.2
199.9 207.4 213.8 220.1 225.2 230.1 233.1 235.5 237.7 239.3 240.2
2.3 4.5 6.3 10.3 15.0 20.0 24.6 29.6 35.5 40.3 45.4
Table 3. Experimental Dew Points Temperatures and Pressures for Multicomponent Mixtures {SNG + Gjwater + Gjmethanol}
225.5 225.6 226.4 226.9 226.6 222.4 217.5
44.4 49.5 55.8 61.1 64.7 66.7 63.7
237.4 237.7 237.4 237.1 235.3 232.4 227.9 222.2 217.6
45.0 49.0 55.0 60.5 65.2 70.4 71.2 69.4 64.0
240.8 240.8 239.6 239.4 239.4 238.4 236.7 233.8 229.2 220.4 215.8
50.0 54.5 59.5 63.4 67.7 70.5 74.5 77.4 77.7 73.6 69.6
Gas 2
Gas 3
4.7 9.5 14.3 19.7 24.7 30.2 34.7
217.7 217.8 216.8 214.9 211.6 206.0 203.4
39.5 44.9 50.9 54.7 58.4 58.3 56.1
•Ethane vapor-liquid equilibrium curve: On the pressure range from (1.8 to 29.4) × 105 Pa and temperature between 195.3 and 282.0 K, the relative average deviation of pressure values was 0.3% and the absolute average deviation of temperature values was 0.1 K. •Propane vapor-liquid equilibrium curve: On the pressure range from (1.0 to 6.2) × 105 Pa and temperature between 230.4 and 282.0 K, the relative average deviation of pressure values was 0.6% and the absolute average deviation of temperature values was 0.2 K. To evaluate the relative precision of the analysis of methanol content, repeated analysis of methanol content of a standard nitrogen + methanol mixture prepared by Air-Liquide were carried out. The result obtained expressed as the relation between the standard deviation and the mean chromatographic area value was of 0.7%. To obtain the precision of the analysis of water content, repeated analysis of water content of a standard nitrogen + water mixture prepared by Air-Liquide were carried out. The measured values were equal to the standard water content within a rejecting percentage of 0.05%.12 The relative average (11) Goodwin, R. D.; Haynes, W. M. Thermophysical Properties of Propane from 85 to 700 K at Pressures to 70 MPa. National Bureau of Standards Monograph 170; National Bureau of Standards: Boulder, Canada, 1982 (12) Statistical Interpretation of Data-Techniques of Estimation and Tests Relating to Means and Variances. International Standard ISO 2854; International Organization of Standardization: Geneva, Switzerland, 1976.
T/K
242.3 247.9 256.2 261.0 264.3 266.9 269.2 270.7
Gas 1, Fjwater ) 45.3 × 10-6 kg m-3(n), Fjmethanol ) 1782.4 × 10-6 kg m-3(n) 3.1 272.1 5.0 273.3 10.1 274.1 15.1 275.2 20.2 275.8 25.0 276.5 30.7 277.1 35.1
242.0 249.8 254.3 257.9 261.5 264.2 266.7 269.2 271.8
Gas 1, Fjwater ) 220.9 × 10-6 kg m-3(n), -6 kg m-3(n) methanol ) 1403.3 × 10 1.4 273.6 2.5 275.3 3.7 276.9 5.0 278.2 6.7 279.6 8.3 280.8 10.2 281.7 12.5 282.6 15.1
241.9 247.9 254.9 259.9 263.0 265.7 267.9
Gas 2, Fjwater ) 84.1 × 10-6 kg m-3(n), Fmethanol ) 853.6 × 10-6 kg m-3(n) 3.2 269.5 5.6 271.0 10.2 272.2 15.3 273.6 20.1 274.6 25.2 275.6 30.2 276.2
236.4 249.5 258.1 262.8 265.6 268.9 271.1 272.4
Gas 3, Fjwater ) 27.2 × 10-6 kg m-3(n), Fmethanol ) 2288.0 × 10-6 kg m-3(n) 1.7 274.3 5.0 275.2 10.0 276.2 15.0 276.9 19.7 277.5 25.0 277.9 30.0 277.6 34.8
243.3 254.0 262.5 268.1 271.4 274.2 276.4 278.2
Gas 3, Fjwater ) 30.6 × 10-6 kg m-3(n), Fjmethanol ) 3084.0 × 10-6 kg m-3(n) 2.2 279.7 5.2 281.0 10.1 281.7 15.4 282.7 20.1 282.8 25.2 283.5 30.2 284.1 35.4
244.7 253.0 260.4 265.9 269.0 271.9 274.4 276.1
Gas 4, Fjwater ) 77.4 × 10-6 kg m-3(n), Fmethanol ) 2216.1 × 10-6 kg m-3(n) 2.6 277.3 5.5 278.9 10.1 279.8 15.4 281.0 19.7 281.6 25.0 282.5 30.8 283.3 35.5
246.3 249.0 253.4 257.4 261.0 264.0 266.9 269.6 271.9
Gas 4, Fjwater ) 48.2 × 10-6 kg m-3(n), Fjmethanol ) 4485.2 × 10-6 kg m-3(n) 2.1 274.0 2.6 275.7 3.7 277.3 5.1 278.8 6.7 280.1 8.3 281.1 10.3 282.3 12.6 283.2 14.9
Gas 4 203.6 209.9 213.9 216.4 217.9 218.9 218.8
P/105 Pa
P/105 Pa
40.4 45.2 49.0 55.0 59.6 65.0 71.7
17.5 19.9 22.5 24.9 27.6 30.2 32.6 34.9
35.1 39.9 44.7 50.2 54.7 59.7 63.4
40.5 44.9 50.0 55.0 60.2 65.0 71.9
40.2 45.4 50.0 55.4 60.9 65.9 72.2
39.3 45.7 49.5 55.6 58.8 64.1 70.9
17.5 19.9 22.3 25.0 27.5 29.8 32.6 35.0
Synthetic Natural Gases
Energy & Fuels, Vol. 16, No. 4, 2002 931
Table 4. Values of the Group Interaction Parameter, 1Akl 0/106 J m-3(n), Used in This Work 1 1 2 3 4 8 9 11 17 18
2
3
0 77.97019 32.68019
0 7.70019
45.87019 2.21019 314.35019 29.40417 207.90117
97.44019 67.08019 230.35019 3154.73417 502.35817
4
8
9
11
17
18
0 7.86019 130.00019 1279.54017 161.79120
0 284.77019 1288.28717 285.62117
0 2274.28117 675.20617
0 -1027.69517
0
0 0 44.38019 0.12019 231.10019 2358.81317 383.13517
3121.34820 347.28520
Table 5. Values of the Group Interaction Parameter, 1Bkl 1 1 2 3 4 8 9 11 17 18
2
3
0/106
J
m-3(n),
Used in This Work
4
8
9
11
17
18
-1.79320 0.94020
117 2.34017 0.04017 -0.72617 2.39020
117 -0.95017 -1.56017 -0.30417
117 -1.11517 -0.08917
117 0.13117
117
117 0.92017 0.73017
117 1.84017
-3.65017 18.68017 -0.91017 -4.79517 -0.02717
1.08017 -0.33017 0.85017 -1.25717 0.68417
117 -3.77017 -22.97017 0.74017 -1.24817 0.47517
117
Table 6. Values of the Group Interaction Parameter, 2Akl 0/106 J m-3(n), Used in This Work 1 1 2 3 4 8 9 11 17 18
2
3
0 77.97019 32.68019
0 7.70019
0
45.87019 2.21019 314.35019 153213.17217 198.10617
97.44019 67.08019 230.35019 104763.14117 642.07217
4
8
9
11
17
18
0 7.86019 130.00019 4279.21223 1761.99520
0 284.77019 5946.63720 239.98517
0 8712.37520 486.89017
0 7538.73717
0
0 44.38019 0.12019 231.10019 120420.4317 468.87717
5553.58220 324.94620
Table 7. Values of the Group Interaction Parameter, 2Bkl 1 1 2 3 4 8 9 11 17 18
2
3
4
0/106
J
m-3(n),
Used in This Work
8
9
11
17
18
117 2.34017 0.04017 5.53721 -11.60520
117 -0.95017 0.39020 1.84617
117 7.14020 0.57817
117 -1.85017
117
117 0.92017 0.73017
117 1.84017
-3.65017 18.68017 -0.91017 0.06517 0.15417
1.08017 -0.33017 0.85017 1.22917 1.47617
117 -3.77017 -22.97017 0.74017 0.58917 1.67617
117
1.28320 1.18620
deviation was of 0.8% for a mean value of water content of 59.0 × 10-6 kg m-3(n). To evaluate the precision of water and methanol dew point generation, repeated generation of methane + water + methanol were carried out, and the water and methanol content and the dew point curve were measured. The results obtained in the performance evaluation are the following: •For water content, the relative average deviation was of 9.3% for a mean water content of 34.3 × 10-6 kg m-3(n). •For methanol content, the relative average deviation was of 3.1% for a mean methanol content of 2719.0 × 10-6 kg m-3(n). •For dew point pressure, the relative average deviation was 4.2% on a range from (3.7 to 80.8) × 105 Pa. •For dew point temperature, the absolute average deviation was 0.4 K on a range from 248.2 to 284.0 K. 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 80 × 105 Pa in pure methane. Results. The dew point data for dry mixtures were obtained and the results are given in Table 2. 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 3.
Theory Introduction. Classical models such as UNIQUAC or NRTL yield good results for vapor-liquid equilibrium at low pressures for systems containing one self-associating compound such as alcohol, but are not available in high-pressure phase equilibrium calculations.13 In this work it is used the vapor-liquid equilibrium model EOS-CR (equation of state-chemical reticular) derived from the excess function equations of the state model14 and founded on the zeroth approximation on the quasireticular model. Other simpler models, such as the Peng-Robinson EOS, calculates properly the dew point curves of the dry mixtures studied, but available experimental binary systems data are required to obtain the interaction parameters. In the EOS-CR method, (13) Rauzy, E.; Berro, C. INPL 905267 1987, 107-125. (14) Pe´neloux, A.; Abdoul, W.; Rauzy, E. Fluid Phase Equilib. 1989, 47, 115-132.
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Energy & Fuels, Vol. 16, No. 4, 2002
Figure 2. Comparison between experimental dew points curves (symbol) and calculated with the EOS-CR method (line) for the systems: (9) gas 1, (b) gas 1 + 45.3 × 10-6 kg m-3(n) water + 1782.4 × 10-6 kg m-3(n) methanol, (O) gas 1 + 220.9 × 10-6 kg m-3(n) water + 1403.3 × 10-6 kg m-3(n) methanol.
Avila et al.
Figure 5. Comparison between experimental dew points curves (symbol) and calculated with the EOS-CR method (line) for the systems: (9) gas 4, (b) gas 4 + 77.4 × 10-6 kg m-3(n) water + 2216.1 × 10-6 kg m-3(n) methanol, (O) gas 4 + 48.2 × 10-6 kg m-3(n) water + 4485.2 × 10-6 kg m-3(n) methanol. Table 8. Numbers of Groups of Each Kind for Every Component of the Studied Systems kind of group
molecule
1 2 3 4 8 9 11 17 18 sCH3 sCH2s -CH- C3H8 CH4 C2H6 N2 H2O CH3- OH |
CH4 C2H6 C3H8
Figure 3. Comparison between experimental dew points curves (symbol) and calculated with the EOS-CR method (line) for the systems: (9) gas 2, (b) gas 2 + 84.1 × 10-6 kg m-3(n) water + 853.6 × 10-6 kg m-3(n) methanol.
i-C4H10 n-C4H10 i-C5H12 n-C5H12 n-C6H14 N2 H2O CH3OH
0 0
{ 02 0 2 1 2 2 0 0 0
0 0 0 1 0 2 0.5 3 4 0 0 0
0 0 0 0 1 0 3.5 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 1
Table 9. Values of AAD and Experimental Ranges of Dew Temperatures and Pressures for Synthetic Natural Gas Mixtures
Figure 4. Comparison between experimental dew points curves (symbol) and calculated with the EOS-CR method (line) for the systems: (9) gas 3, (b) gas 3 + 27.2 × 10-6 kg m-3(n) water + 2288.0 × 10-6 kg m-3(n) methanol, (O) gas 3 + 30.6 × 10-6 kg m-3(n) water + 3084.0 × 10-6 kg m-3(n) methanol.
these are calculated by means of a group contribution method what makes it useful to predict the dew point curves of real natural gases, provided that not always binary experimental data for all the components of the so-called C6+ fraction exist. Moreover, the EOS-CR method used in this work allows studying dry mixtures and systems with water and a self-associated component, as methanol. The values for dew point temperature of the vapor phase for the studied systems are calculated by means of this theoretical method using the experimental pressure and composition data. To evaluate this method for the prediction of the dew points of the multicomponent systems in the tempera-
SNG mixture
T range/K
P range/105 Pa
AAD/K
gas 1 gas 2 gas 3 gas 4
200.3-226.9 202.9-237.7 199.9-240.8 203.4-218.9
5.4-66.7 2.9-71.2 2.3-77.7 4.7-58.4
2.1 1.9 2.7 2.3
ture and pressure studied ranges, a comparison between experimental and calculated dew point values was carried out. The results are quite good with values of AAD from 1.9 to 2.7 K on dry systems and between 0.7 and 2.3 K on systems with water and methanol. 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 corresponding value to the pure component. This assumption leads to
η)
b bi ) (i ) 1, ..., p) v vi
(1)
Synthetic Natural Gases
Energy & Fuels, Vol. 16, No. 4, 2002 933
Table 10. Values of AAD and Experimental Ranges of Dew Temperatures and Pressures for Multicomponent Mixtures {SNG + Gjwater + Gjmethanol} SNG mixture
Fjwater/10-6 kg m-3(n)
Fjmethanol/10-6 kg m-3(n)
T range/K
P range/105 Pa
AAD/K
gas 1 gas 1 gas 2 gas 3 gas 3 gas 4 gas 4
45.3 220.9 84.1 27.2 30.6 77.4 48.2
1782.4 1403.3 853.6 2288.0 3084.0 2216.1 4485.2
242.3-277.1 242.0-282.6 241.9-276.2 236.4-277.6 243.3-284.1 244.7-283.3 246.3-283.2
3.1-71.7 1.4-34.9 3.2-63.4 1.7-71.9 2.2-72.2 2.6-70.9 2.1-35.0
1.2 1.1 1.5 1.2 1.2 0.7 2.3
The molar Helmholtz energy of a mixture, A, may be written as follows:
xiai A ) A - RT ln(1 - η) Q(η) + AEres i)1 bi
For the first term on the right-hand side of eq 6, the following equations are used:17
p
∑
id
(2)
where Aid is the ideal mixture molar Helmholtz energy, ai is the attractive parameter of i component of a translated Peng-Robinson cubic equation of state,15,16 bi is the component i covolume, AEres is the residual excess Helmholtz energy (explained in other section), and Q(η) is expressed as follows:
E(T,x) )
1
p
[
2qm
p
p
p
1/3 qixi[∑qjxjKij] + ∑qixi[∑q1/3 ∑ j xjLji ]] i)1 j)1 i)1 j)1
(7) with
Kij )
Eij1 + Eij2 and Lij ) Eij2 - Eij1 Lij ) -Lji (8) 2 p
Q(η) )
∫0
η
Q′(η) dη η
(3)
where
Q′(η) )
η 1 + γη
and
γ ) 2(x2 + 1) (4)
The residual excess Helmholtz energy, AEres, can be separated into two terms, as shown in eq 5. E AEres ) AEfis + Aqui
(5)
where the physical part, AEfis, is written by means of a formalism which enables to separate the composition and packing fraction variables:
AEfis ) E(T,x)Q(η)
qm )
∑ qkxk k)1
(15) Pe´neloux, A.; Rauzy, E.; Fre´ze, R. Fluid Phase Equilib. 1982, 8, 7-23. (16) Rauzy, E. The`se d’Etat-Sciences. Universite´ Aix-Marseille II, Marseille, France, 1982. (17) Hocq, H. The`se en Sciences, Universite´ de Droit, d’Economie et des Sciences d’Aix-Marseille III, Marseille, France, 1994. (18) Rauzy, E.; Berro, C. International Symposium of Supercritical Fluids; Perrut, M., Ed.; Strasbourg, France, 1988; pp 153-160. (19) Abdoul, W. Une me´thode de contribution de groupes applicable a` la corre´lation et pre´diction des propie´te´s thermodynamique des fluides pe´troliers. The´se en Sciences. Universite´ Aix-Marseille II, Marseille, France, 1987. (20) Blanco, S. T. Curvas de rocı´o de sistemas constituidos por componentes y aditivos del gas natural. Determinacio´n experimental y prediccio´n teo´rica. Tesis en Ciencias (Quı´micas). Universidad de Zaragoza, Spain, 1998. (21) Avila, S. Curvas de rocı´o de gases naturales sinte´ticos y de sus mezclas con agua y metanol. Determinacio´n experimental y predicciones teo´ricas. Tesis en Ciencias (Quı´micas). Universidad de Zaragoza, Spain, 1999.
qk ) δkbk
(9)
where 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 supposed 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:17
Eij1 ) -
1
N
N
(Rik - Rjk)(Ril - Rjl)Akl1(T) ∑ ∑ 2 k)1 l)1 Akl1 ) 1Akl0
(6)
The physical interactions between different compounds are represented by the physical term, AEfis, using the eq 6,17 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.13,18
and
Eij2 ) -
1
N
with
() T0
0
1Bkl
(10)
T
N
∑ ∑(Rik - Rjk)(Ril - Rjl)Akl2(T)
2 k)1 l)1
Akl2 ) 2Akl0
with
() T0 T
0
2Bkl
(11)
where 1Akl0, 1Bkl0, 2Akl0, and 2Bkl0 are group interaction parameters. The values for the group interactions parameters used for comparison calculations in this work are presented in Tables 4-7. The numbers of groups, of each kind, for every component of the studied systems, are given on Table 8. 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 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 at any pressure.
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Energy & Fuels, Vol. 16, No. 4, 2002
For the SNG systems studied, the introduction of a group contribution method does not impair predictions respect to methods that use EOS with interaction parameters obtained from binary experimental data. It makes EOS-CR model very useful to predict the dew point of real natural gases, provided that, not always binary experimental data for all components of the socalled C6+ fraction exist. After comparing 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 on dry systems and on systems with water and methanol, are presented in Tables 9 and 10, respectively.
Avila et al.
Acknowledgment. The authors acknowledge the financial and technical support of Enaga´s, S. A., during the experimental part of this work. Appendix 1 For comparison between calculated and experimental dew point temperatures for each studied dew point curve we used the deviation
AAD )
1
N
∑|Tiexp - Ticalcd| N i)1
where N is the number of dew points which constitute a dew point curve. EF0102824
