Ind. Eng. Chem. Res. 2004, 43, 209-217
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Thermodynamic Properties of Synthetic Natural Gases. 5. Dew Point Curves of Synthetic Natural Gases and Their Mixtures with Water and with Water and Methanol: Measurement and Correlation C. Jarne,† S. Avila,‡ S. T. Blanco,† E. Rauzy,§ S. Otı´n,† and I. Velasco*,† Departamento de Quı´mica Orga´ nica y Quı´mica Fı´sica. Facultad de Ciencias. Universidad de Zaragoza, 50.009 - Zaragoza, Spain, Technology, Environment and Construction Direction, ENAGAS, S. A., Spain, and Laboratoire de Chimie Physique de Marseille, Faculte´ des Sciences de Luminy, Universite´ de la Me´ diterrane´ e, 13.288 - Marseille Cedex 9, France
Dew points for two synthetic natural gas (SNG) mixtures between 1.2 × 105 and 81.8 × 105 Pa in the temperature range from 213.6 to 261.4 K, four SNG + water mixtures between 1.1 × 105 and 41.0 × 105 Pa and temperatures from 244.7 to 288.1 K, and four SNG + water + methanol mixtures between 1.1 × 105 and 20.7 × 105 Pa and temperatures from 247.6 to 288.6 K were experimentally determined. The experimental results obtained on the multicomponent systems were analyzed in terms of a predictive excess function-equation of state (EF-EOS) method, which reproduced experimental dew point temperature data with absolute average deviation (AAD) between 0.9 and 3.1 K for the dry systems, from 0.0 to 1.6 K for the systems with water, and from 0.0 to 3.0 K for the systems with water and methanol. The experimental results obtained for synthetic natural gas (SNG) + water mixtures at pressure values higher than 5 × 105 Pa were also compared to a predictive equation of state (EOS) model. It reproduced experimental dew point temperature data within AAD between 1.8 and 5.3 K. 1. Introduction Following our systematic study of the influence of water, methanol, and heavy hydrocarbons of natural gases on the vapor-liquid equilibrium of natural gas,1-4 we report in this paper the experimental results of a similar examination of the vapor-liquid equilibrium of two SNGs, with high contents of carbon dioxide, and their mixtures with water and with water and methanol. The purposes of the present work were to obtain experimental data to study the influence of the presence of carbon dioxide on dew points of SNG, SNG + water, and SNG + water + methanol mixtures, and to achieve a theoretical model that allows one to predict adequately the experimental results obtained. The dew temperature and pressure ranges studied here are within the usual pressure and temperature conditions of natural gas transport by pipeline. The study of gases with a higher carbon dioxide content than the usual ones in natural gases is justified because there are natural gases such as those from Lacq (France), St. Faust Meillon (France), or Kapuni (New Zealand), with high carbon dioxide contents; also because carbon dioxide is found as a remains after having been used to extract hydrocarbons from exhausted natural gas fields. The experimental apparatus used in this work for water and water + methanol dew point generation, and hydrocarbon, water, and water + methanol dew point * To whom correspondence should be addressed. Tel.: +34 976 761 197. Fax: +34 976 761 202. E-mail: curra@ posta.unizar.es. † Universidad de Zaragoza. ‡ Technology, Environment and Construction Direction, ENAGAS. § Universite´ de la Me´diterrane´e.
determination was built and commissioned in a previous work.5 The results on the two SNGs mixtures between 1.2 × 105 and 81.8 × 105 Pa in the temperature range from 213.6 to 261.4 K, four SNG + water mixtures between 1.1 × 105 and 41.0 × 105 Pa and temperatures from 244.7 to 288.1 K, and four SNG + water + methanol mixtures between 1.1 × 105 and 20.7 × 105 Pa and temperatures from 247.6 to 288.6 K are presented here. The experimental results obtained on the multicomponent systems were analyzed using a predictive EFEOS method, which reproduced experimental dew point temperature data within AADs between 0.9 and 3.1 K for the dry systems, from 0.0 to 1.6 K for the systems with water, and from 0.0 to 3.0 K for the systems with water and methanol. The experimental results obtained on the SNG + water mixtures were also compared to a classical EOS model, which reproduced experimental dew point temperature data within an AAD between 1.8 and 5.3 K. The good agreement obtained between experimental and calculated values serves as validation of both predictive models. 2. Experimental Procedures The experimental dew points range from 1.1 × 105 to 81.8 × 105 Pa at temperatures from 213.6 and 288.6 K. The two SNGs used in this work were prepared according to the gravimetric method (International Standard ISO 6142: 1981),6 by Abello´-Linde. The compositions of these SNGs and their accuracy specified by the supplier are listed in Table 1. The apparatus used was described in a previous work.5 In this apparatus, the hydrocarbon, water, and water + methanol dew point can be determined and the water and water + methanol dew point can be generated. For the latter, the experimental method used is
10.1021/ie030121i CCC: $27.50 © 2004 American Chemical Society Published on Web 12/10/2003
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Ind. Eng. Chem. Res., Vol. 43, No. 1, 2004
Table 1. Composition of Synthetic Natural Gases (% mol) and Relative Accuracy Specified by the Supplier nitrogen CO2 methane ethane propane i-butane n-butane i-pentane n-pentane n-hexane
gas 1
gas 2
1.559 ( 1% 25.908 ( 1% 69.114 ( 0.2% 2.620 ( 1% 0.423 ( 2% 0.105 ( 2% 0.104 ( 2% 0.034 ( 2% 0.023 ( 2% 0.110 ( 2%
0.772 ( 2% 1.700 ( 1% 84.446 ( 0.2% 8.683 ( 1% 3.297 ( 1% 0.293 ( 2% 0.589 ( 2% 0.084 ( 2% 0.086 ( 2% 0.050 ( 2%
based on the generation of saturated gases with water or with water and methanol by condensation of these compounds in a temperature-controlled condenser with continuous gas flow at specified pressures. After controlled expansion, the gas is saturated with water or with water and methanol vapor by making it flow through an isolated saturator containing water or a liquid mixture of water and methanol at laboratory temperature. The condensation temperature of water or water and methanol is then achieved in a stainless steel condenser, which is located in a thermostatic bath set at the desired equilibrium temperature. The concentration of water in the gas is measured at the outlet of the dew point generation system, using a Karl Fischer titration, according to the standard method7 at atmospheric pressure. The concentration of methanol is determined by gas chromatography analysis. By doing so, the reference values for the contents of water and methanol in the gaseous phase are obtained. The dew point values of the SNGs, of SNG + water and of SNG + water + methanol mixtures are measured by means of a chilled mirror instrument. The input pressure of the gas to the chilled mirror instrument is set using a regulator valve. When the apparatus reaches a stable value of dew temperature, both pressure and temperature are recorded. The following instrumentation is used to analyze the contents of water and methanol and to carry out the dew point measurements: Mitsubishi CA 06 Karl Fischer titrator, coupled with an Elster wet gasmeter type Gr. 00, E51, 0.2% accuracy. HP 5890 gas chromatograph fit up with a Haysep Q column and thermal conductivity detector. MBW Dew Point instrument, model DP3-D-HP-K2. The cooling of the mirror is achieved by a cascaded Peltier elements, and the dew point mirror temperature is optoelectronically controlled. The uncertainty on the dew temperature is better than ( 0.1 K. A pressure transmitter with a maximum error of 0.1% in the calibrated range. Prior to the study of SNG, SNG + water, and SNG + water + methanol dew points, the precision of both analytical methods and experimental procedures was determined.2,4 3. Results The values of dew temperature and pressure for gas 1 and gas 2 were measured, and their values are presented in Table 2. The water and methanol contents for SNG + water and SNG + water + methanol generated mixtures at the dew point generation system, and their dew point curves were determined, and the results of experiments are collected in Table 2.
As can be seen in Table 2, the values of dew temperature and pressure of gas 2 are higher than those of gas 1; because of it, the risk of condensation of gas 2 is higher than that of gas 1. In fact, gas 2 could condense at usual values of temperature and pressure in natural gas transport by pipeline, whereas gas 1 could not condense. Regarding the relationship between the composition of a natural gas and its risk of condensation, Voulgaris8 concluded that an increase in the concentration of methane, ethane, or carbon dioxide in a natural gas leads to an increase of the solubility of heavy hydrocarbons in the vapor phase of the ELV of this natural gas, and as consequence, a decrease in the risk of condensation for a given pressure value. Increasing the concentration of nitrogen or hydrocarbons with more than two carbon atoms in the studied natural gas had the opposite effect.8 For gas 1 and gas 2, the value of the sum of concentrations of nitrogen, methane, ethane, and carbon dioxide are only lightly higher in gas 1 than in gas 2. This fact would balance the two opposite effects of the composition in the condensation risk, but because the concentration of hydrocarbons with more than two carbon atoms is higher in gas 2 (4.399%) than in gas 1 (0.799%), the measured dew temperature and pressure of gas 2 are higher than those of gas 1. The difference between the experimental temperature values for the cricondentherm, of the corresponding dew point curves, is nine degrees. On the other hand, from SNG + water and SNG + water + methanol dew point curves (Table 2), it can be seen that an increase of the contents of water or water + methanol in the mixtures of the studied systems leads to a displacement of the dew point curves to higher values of dew temperature and pressure. In case of SNG + water mixtures with similar values of water content, analogous values of dew temperature and pressures are found for the corresponding dew point curves. This seems to indicate that the water dew point depends on the amount of water in the mixture, but not on the composition of SNG. Similar conclusions were found in the literature.9-11 As can be seen in Table 2, for gas 2 + 324 × 10-6 kg m-3(n) water and gas 2 + 386.6 × 10-6 kg m-3(n) water + 6351.4 × 10-6 kg m-3(n) methanol, for a given pressure value, the difference between the dew temperature values of the mixture with methanol and without methanol is up to 10 degrees. Then, it can be concluded that for a given amount of water in the mixture, the dew temperature increases when the amount of methanol in the mixture also increases. 4. Theory Introduction. Equations of state such as the SantisBreedveld-Prausnitz EOS,12 the Nakamura-Breedveld-Prausnitz EOS,13 the Peng-Robinson EOS,14 and the Robinson-Peng-Ng EOS15 yield good results in calculation of the water dew points of natural gases at higher temperatures than the temperature of the natural gas pipeline network. Instead of these, we use two models: one is the EF-EOS method, which is derived from the EF-EOS model16 and based on the zeroth order approximation of the quasireticular model. This model has been chosen because it allows one to predict adequately the dew points of the whole studied mixtures in the dew temperature and pressure ranges. The second model is an EOS based on a modified PengRobinson EOS.3,4 This equation allows predicting adequately the water dew point curve in the usual
Ind. Eng. Chem. Res., Vol. 43, No. 1, 2004 211 Table 2. Experimental Contents of Water and Methanol for {SNG + Gjwater} Mixtures and for {SNG + Gjwater + Gjmethanol} Mixtures and Dew Points Temperatures and Pressures for SNG, {SNG + Gjwater} Mixtures, and {SNG + Gjwater + Gmethanol} Mixtures gas 1
gas 1 with Fwater ) 277.9 × 10-6 kg m-3(n)
gas 1
T/K
P/105 Pa
T/K
P/105 Pa
T/K
P/105 Pa
213.6 216.2 216.4 217.0 217.5 218.6 219.5 221.1 222.0 222.7 224.5 226.6 228.5 229.3 231.5 232.6 233.4 235.1 235.6 236.7 237.8 238.4 239.4 240.4 241.3 242.1 243.2 244.1 245.1 245.8 246.7 247.4
1.2 1.2 1.2 1.2 1.3 1.3 1.4 1.6 1.7 1.8 2.1 2.5 2.9 3.1 3.8 4.1 4.4 5.0 5.2 5.8 6.3 6.7 7.2 7.9 8.5 9.2 10.1 11.0 12.0 12.9 14.2 15.2
248.9 249.5 249.8 250.1 250.5 250.7 251.1 251.3 251.5 251.7 251.9 252.0 252.1 252.2 252.2 252.2 252.2 252.2 252.2 252.0 251.9 251.6 251.3 251.0 250.7 250.2 249.5 248.8 248.1 247.6 246.4
18.0 19.4 20.2 20.9 22.2 23.0 24.2 25.3 26.4 27.6 28.8 30.4 31.4 32.5 33.7 34.0 35.3 36.8 38.3 39.6 40.8 43.0 45.0 46.3 47.9 50.0 52.0 54.2 56.1 58.3 60.2
246.1 252.6 256.8 260.1 264.8 266.9 268.7 270.6 272.9 274.4 276.0 277.0 278.9 279.9 281.6 282.6 283.3 284.0 285.0 286.2 286.9 287.8 288.1
1.1 2.1 3.0 4.1 6.0 7.9 9.0 10.5 12.4 14.1 15.9 17.2 19.8 21.4 24.6 26.6 28.1 29.5 32.4 35.1 37.1 40.0 40.9
gas 1 Fjwater ) 1392.1 × 10-6 kg m-3(n)
gas 1 with Fjwater ) 183.5 × 10-6 kg m-3(n) and Fjmethanol ) 6523.8 × 10-6 kg m-3(n)
gas 1 with Fwater ) 337.6 × 10-6 kg m-3(n) and Fjmethanol ) 4804.1 × 10-6 kg m-3(n)
T/K
P/105 Pa
T/K
P/105 Pa
T/K
P/105 Pa
261.3 265.2 268.4 270.8 272.8 274.6 272.6 277.9
1.5 2.0 2.6 3.1 3.5 4.0 4.5 5.0
248.1 250.0 255.3 264.5 268.1 272.6 276.7 280.2 281.9 283.4 285.5 287.3 288.6
1.1 1.3 1.9 3.8 4.9 6.8 8.9 11.5 13.0 14.6 16.7 18.7 20.5
249.0 252.8 259.3 265.3 269.3 271.9 274.3 275.4 277.3 279.9 282.1 283.2 284.1 285.7 287.4 288.2
1.2 1.6 2.5 4.0 5.3 6.4 7.8 8.4 9.6 11.7 13.7 14.7 15.6 17.3 19.7 20.7
gas 2
gas 2 with Fjwater ) 324.8 × 10-6 kg m-3(n)
gas 2
TK
P/105 Pa
T/K
P/105 Pa
T/K
P/105 Pa
217.9 219.6 222.6 228.1 232.1 235.9 238.7 240.7 242.5 244.4 247.1
1.2 1.4 2.1 3.1 4.1 5.3 6.4 7.3 8.6 9.8 11.8
259.9 259.1 258.1 256.5 255.9 254.2 253.5 252.4 251.4 234.0 234.8
62.4 65.1 67.6 69.8 71.9 75.4 75.9 77.7 77.8 79.2 79.3
244.7 247.9 251.4 255.4 259.1 261.1 263.8 266.2 268.3 269.6 270.5
1.1 1.5 2.0 3.0 4.0 5.0 6.0 7.0 9.1 10.2 11.1
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Ind. Eng. Chem. Res., Vol. 43, No. 1, 2004
Table 2 (Continued) gas 2
gas 2 with Fjwater ) 324.8 × 10-6 kg m-3(n)
gas 2
T/K
P/105 Pa
T/K
P/105 Pa
T/K
P/105 Pa
247.5 249.2 250.4 252.3 253.5 254.7 256.4 258.0 258.5 259.5 260.1 260.8 261.1 261.4 260.8
12.1 13.6 14.8 17.5 19.1 21.9 25.2 28.9 30.5 34.0 37.5 41.8 45.2 51.0 57.3
250.3 236.2 247.3 238.2 239.6 241.7 245.3 243.0 242.3 244.5
79.4 80.0 80.7 81.0 81.3 81.3 81.3 81.7 81.8 81.8
271.6 272.5 274.6 276.1 277.5 279.0 280.0 281.4 282.4 283.3 284.5 285.1 286.3 287.1 288.0
12.0 12.9 15.3 17.3 19.1 21.1 23.1 25.4 27.2 29.1 31.7 33.1 36.1 38.5 41.0
gas 2 Fjwater ) 1244.5 10-6 kg m-3(n)
gas 2 Fjwater ) 386.6 × 10-6 kg m-3(n) and Fjmethanol ) 6351.4 × 10-6 kg m-3(n)
gas 2 Fjwater ) 707.4 × 10-6 kg m-3(n) and Fmethanol ) 3429.4 × 10-6 kg m-3(n)
T/K
P/105 Pa
T/K
P/105 Pa
T/K
P/105 Pa
256.9 261.6 264.0 269.0 272.0 273.9 275.8 277.3 278.1
1.1 1.6 2.0 2.9 3.6 4.0 4.6 5.0 5.3
247.6 253.9 257.3 261.2 265.0 267.9 270.3 272.8 274.5 276.3 277.9 279.2 280.5 281.5 282.6 283.9 285.0 285.5 286.5 287.3 288.2
1.1 1.8 2.3 3.1 4.1 5.0 6.0 7.1 8.0 9.0 10.1 11.1 12.1 13.0 13.9 15.1 16.3 17.0 18.2 19.1 20.2
248.7 250.8 256.7 261.0 266.6 271.9 273.1 276.2 278.0 288.0 280.7 281.8 283.2 284.5 286.2 287.1 288.1
1.1 1.3 2.1 2.9 4.4 6.5 7.2 8.9 10.1 11.8 12.3 13.3 14.6 15.9 18.0 19.3 20.6
temperature and pressure range of importance for natural gas pipelines. To evaluate the theoretical models used in this paper for the prediction of the dew points of the multicomponent systems in the studied temperature and pressure ranges, a comparison between experimental and calculated values of dew point temperature was carried out. The values of dew temperature of the vapor phase for the investigated systems are calculated by means of the EF-EOS method16 and the EOS model3,4 using the experimental values of pressure and composition obtained in the present work. Description of the EF-EOS Model. To represent the vapor-liquid equilibrium in the mixtures, a model based on the zeroth order approximation of Guggenheim’s reticular theory 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 defined at constant packing fraction, η ) b/v, b being the covolume that can be identified as the molar close-packed volume and v the molar volume. The EOS used in the EF-EOS model is the translated Peng-Robinson cubic EOS17 for components different from carbon dioxide and the IUPAC equation18 for
carbon dioxide. The reason for this choice is that thermodynamic properties of carbon dioxide such as saturated density are often poorly represented by cubic EOS especially near of the critical point. The IUPAC equation18 is easy to use given its polynomial form, even if the parameters used are numerous.
z)1+
F i)9 j)6
( )( )
∑∑cij
Fci)0j)0
Tc T
j
-1
F
Fc
i
-1
(1)
The translated Peng-Robinson cubic equation of state17 is of the form:
P)
a(T) RT vj - b h vj (vj + γb h)
(2)
The values of the parameters a and b h depend on the component as follows. For nitrogen and hydrocarbons with less than six carbon atoms the following equation is used for the covolume, b h :17
RTc b h ) 0.045572 Pc
(3)
Ind. Eng. Chem. Res., Vol. 43, No. 1, 2004 213
The attractive parameter a as a function of the temperature, T, is calculated using various equations taken from Pe´neloux et al..17 For hydrocarbons with more than five carbon atoms, the covolume, b h , is calculated by means of a group contribution method.19 The attractive parameter, a, is obtained using the equations proposed by Coniglio et al.19 and Carrier et al.20 For water and methanol, eq 3 is used for the calculation of the covolume, b h ,17 and the equations proposed by Carrier et al.20 for the attractive parameter, a. The excess function of the EF-EOS model is the residual excess Helmholtz energy, AEres, which contributes to the molar Helmholtz energy of a mixture, A, as follows: p
A ) Aid - RT ln(1 - η) -
xi
Ψi (η) + AEres ∑ i)1b
(4)
Table 3. Values of the Group Interaction Parameters, A0kl, Used in eq 9 for the EF-EOS Model
a
This work.
For alkane + alkane or water or methanol and nitrogen + alkane or water or methanol binaries, the equations proposed by Hocq29 are used:
i
The residual excess Helmholtz energy, AEres, can be written by means of a formalism that enables to separate the composition and packing fraction variables:
AEres ) E(T, x)Q(η)
E(T, x) )
p
1 2qm
∑ i)1
[
p
qixi[
∑ j)1
p
qjxjKij] +
(5)
(12)
qk ) δkbk
(7)
1
∑ ∑(Rik - Rjk)(Ril - Rjl)Akl(T)
[]
T0 Akl ) A0kl[1 + exp(R1lhyd + R2)] T
Lij ) E2ij - E1ij
(15)
Lij ) -Lji
(16)
N N
∑ ∑(Rik - Rjk)(Ril - Rjl)A1kl(T)
(17)
( )
(18)
2k)1l)1
with
N N
2k)1 /)1
(14)
The interchange energies, E1ij and E2ij, are calculated using a group contribution method as follows:29
p
∑∑
(13)
E1ij + E2ij 2
Kij )
E1ij )
qiqjxixj 1 Eij(T) E (T,x) ) 2i)1j)1 qm Eij )
∑ qkxk k)1
and
(6)
where the value of the parameter γ is21 20 when the IUPAC equation is used. If the translated PengRobinson cubic equation of state is used the value for parameter γ is 2(x2 + 1). The first factor on the right-hand side of eq 5 is expressed as follows. For carbon dioxide + water or methanol and for water + methanol binaries using the equations taken from Rauzy et al.22 For carbon dioxide + alkane or nitrogen binaries, the equations proposed by Berro et al.23 are used.
1
(11)
p
qm )
∫0η(1 +1 γη)dη
p
1/3 q1/3 ∑ j xjLji ]] j)1
with
where Q(η) is expressed as:17
Q(η) )
∑ i)1
p
q i xi [
A1kl
(8) E2ij )
r
(9)
1
)
0 1Akl
T0 T
0
1Bkl
N N
(Rik - Rjk)(Ril - Rjl)A2kl(T) ∑ ∑ 2k)1l)1
(19)
with
with
r ) β1(lhyd)1.5 + β2lhyd
(10)
The values of these parameters used in later calculations in this work are presented in Table 3. The value for the interchange energy, A0kl, between carbon dioxide and nitrogen is obtained in this work using the experimental results of vapor-liquid equilibrium for carbon dioxide + nitrogen from literature.25-28
( )
T0 A2kl ) 2A0kl T
0
2Bkl
(20)
where 1A0kl, 1B0kl, 2A0kl, and 2B0kl are group interaction parameters. In this work, these parameters for interchange energies between methanol and nitrogen or propane or butane or i-butane or pentane or i-pentane or hexane are calculated using experimental results from literature of vapor-liquid equilibrium (Table 4).
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Ind. Eng. Chem. Res., Vol. 43, No. 1, 2004
Table 4. References Corresponding to the Experimental Data from Literature Used to Calculate the Values for the Group Interaction Parameters, 1A0kl, 1B0kl, 2A0kl, and 2B0kl, for Methanol + Nitrogen or Alkane Binaries binary
refs
methanol + nitrogen methanol + propane methanol + butane methanol + i-butane methanol + pentane methanol + i-pentane methanol + hexane
Bruner et al.,30 Weber et al.,31 Zeck et al.32 Galivel-Solastiouk et al.,33 Kretschmer and Wiebe,34 Leu et al.35 Kretschmer and Wiebe,34 Leu and Robinson,36 Leu and Robinson37 Leu and Robinson38 Thomas et al.,39 Wilsak et al.40 Budantseva et al.,41 Ogorodnikov et al.42 Choi et al.,43, Ferguson,44 Goral et al.,45 Hongo et al.46, Hwang and Robinson,47 Iguchi,48 Liu et al.,49 Oracz and Warycha,50 Wolff and Hoeppel51
Table 5. Values of the Group Interaction Parameters, 1A0kl, 1B0kl, 2A0kl, 2B0kl for Interchange Energies between Methanol and Nitrogen or Alkane, Used in eqs 18 and 20 for the EF-EOS Model 0 6 1Akl/10
binary CH3OH + N2 CH3OH + CH4 CH3OH + C2H6 CH3OH + C3H8 CH3OH + n-C4H10 CH3OH + i-C4H10 CH3OH + n-C5H12 CH3OH + i-C5H12 CH3OH + n-C6H14 a
0 6 1Bkl/10
J m-3
J m-3
0 6 2Akl/10
J m-3
723.407a
-1.459a
1819.963a
53.12752 264.04653 545.787a 637.105a 652.693a 709.691a 803.051a 855.564a
3.71952 0.78353 -1.276a -1.904a -1.671a -1.918a -5.958a -1.844a
1378.55852 1272.67253 1183.705a 1106.423a 955.446a 991.033a 803.051a 897.089a
0 6 2Bkl/10
J m-3
-0.482a -0.83252 -0.93153 -0.699a -0.677a -1.369a -0.610a -5.958a -0.263a
This work.
Table 6. Values of Binary Interaction Coefficients, kij,0 and kij,1, for Carbon Dioxide + Nitrogen or Water or Alkane, for the EOS Modela N2
H2O
CH4
C2H6
C3H8
-0.0170
0.1840
0.0919
0.1322
0.1241
i-C4H10
n-C4H10
i-C5H12
n-C5H12
n-C6H14
0.1333
0.1219
0.1222
0.1100
kij,0 0.1200 kij,1 0.2360
a
Refs 3 and 4.
The values for the group interaction parameters for interchange energies between methanol and nitrogen or alkane are presented in Table 5. The group interaction parameters for the other interchange energies are the same as in previous works.1-4 Description of the Equation of State (EOS) Model. The EOS model used in this work is based on a modified Peng-Robinson EOS to obtain a good description of vapor pressure of ice and liquid water.3,4 The equation of state used is the Peng-Robinson cubic equation of state of the form:
P)
RT a ) v - b v2 + 2bv - b2
(21)
The binary interaction coefficients, kij, used for the calculation of attractive parameter, a, in eq 21 are temperature dependent for CO2 + H2O, CH4 + H2O, and C2H6 + H2O binaries. The following temperaturedependent equation has to be used:3,4
kij(T) ) kij,0 + kij,1
T - 1] [273.15
(22)
Values for the binary interaction parameters kij,0 and kij,1 used in this work for carbon dioxide + nitrogen or water or alkane are collected in Table 6. These coefficients for the other binary interactions are the same as in previous works.3,4 5. Discussion In this work, the influence of water, methanol, carbon dioxide, and the usual components of natural gas on vapor-liquid equilibrium of natural gases has been studied.
Figure 1. Comparison between experimental dew points (symbol) and calculated with the EF-EOS method (line) for the systems: (O) gas 1, and (b) gas 2.
The experimental dew point data and the dew points calculated with the EF-EOS method and with the EOS model are represented in Figures 1-3. Values of the AAD obtained for each dew point curve are presented in Table 7. Comparing the experimental and calculated values of the dew point temperature, it can be concluded that both theoretical methods used in this work predict quite adequately the experimental dew point data. The EF-EOS model predicts the dew temperature within AAD of 0.9 K for gas 1 and 3.1 K for gas 2. The
Ind. Eng. Chem. Res., Vol. 43, No. 1, 2004 215 Table 7. Experimental Contents of Water and Methanol for {SNG + Gjwater} Mixtures and for {SNG + Gjwater + Gjmethanol} Mixtures, Experimental Ranges of Dew Temperatures and Pressures for SNGs, for {SNG + Gjwater} Mixtures, and for {SNG + Gjwater + Gjmethanol} Mixtures, and Values of AAD1 (EF-EOS Model) and of AAD2 (EOS Model) for the Measured Dew Point Curves SNG mixture gas 1 gas 2 gas 1 gas 1 gas 2 gas 2 gas 1 gas 1 gas 2 gas 2
Fjwater/10-6 kg m-3(n)
277.9 1392.1 324.8 1244.5 183.5 337.6 386.6 707.4
Fjmethanol/10-6 kg m-3(n)
T range/K
P range/105 Pa
AAD/K
6523.8 4804.1 6351.4 3429.4
213.6-252.2 217.9-261.4 246.1-288.1 261.3-277.9 244.7-288.0 256.9-278.1 248.1-288.6 249.0-288.2 247.6-288.2 248.7-288.1
1.2-60.2 1.2-81.8 1.1-40.9 1.5-5.0 1.1-41.0 1.1-5.3 1.1-20.5 1.2-20.7 1.1-20.2 1.1-20.6
0.9 3.1 1.6 0.4 0.4 0.0 0.0 2.4 1.5 3.0
Figure 2. Comparison between experimental dew points (symbol) and calculated with the EF-EOS method (line) and with the EOS model (dotted line) for the systems: (b) gas 1 + 277.9 × 10-6 kg m-3(n) water; (O) gas 1 + 1392.1 × 10-6 kg m-3(n) water; (2) gas 1 + 183.5 × 10-6 kg m-3(n) water + 6523.8 × 10-6 kg m-3 methanol; (4) gas 1 + 337.6 × 10-6 kg m-3(n) water + 4804.1 × 10-6 kg m-3(n) methanol.
AAD/K
5.3 1.8
Figure 3. Comparison between experimental dew points (symbol) and calculated with the EF-EOS method (line) and with the EOS model (dotted line) for the systems: (b) gas 2 + 324.8 × 10-6 kg m-3(n) water; (O) gas 2 + 1244.5 × 10-6 kg m-3 water; (2) gas 2 + 386.6 × 10-6 kg m-3(n) water + 6351.4 10-6 kg m-3(n) methanol; (4) gas 2 + 707.4 × 10-6 kg m-3(n) water + 3429.4 × 10-6 kg m-3(n) methanol.
6. Conclusions high value of AAD for gas 2 can be due to the asymmetry of this SNG, given that the contents of hydrocarbons with more than two carbon atoms are higher for gas 2 than for gas 1. No influence of pressure and temperature is found for the values of deviations. The values of AAD for SNG + water mixtures are from 0.0 to 1.6 K. The greatest deviation occurs for the mixture with the lowest water content. This can be due to the increasing experimental error in the water content analysis when the water contents decrease. No influence of pressure and temperature is found for the values of deviations. For the systems with water and methanol, the values of AAD are between 0.0 and 3.0 K, and no influence of water and methanol content or of temperature and pressure is found. The experimental results obtained for SNG + water mixtures at pressure values higher than 5 × 105 Pa were also analyzed by means of an EOS model; it reproduced experimental dew point temperature data within AAD between 1.8 and 5.3 K. No influence of water content or of temperature and pressure is found for the values of deviations. This model calculates systematically lower values of dew temperature than those experimentally obtained.
The good results obtained in this paper using the EFEOS method validate this model for the prediction of hydrocarbon, water, and water + methanol dew points of the investigated systems. It can be concluded that the introduction of a group contribution method, as it is used in the EF-EOS model, does not impair the predictions with respect to the EOS methods with interaction parameters obtained from binary experimental data. It makes the EF-EOS model very useful to predict hydrocarbon, water, and/ or water + methanol dew point of real natural gases with high contents of carbon dioxide, provided that not always binary experimental data for all components of the so-called C6+ fraction are available. Nomenclature a ) equation of state attractive energy parameter (Pa m6 mol-2) A) molar Helmholtz energy (J mol-1) A ) coefficients in EOS model Akl ) group interaction parameter between groups k and l (J m-3) AAD ) absolute average deviation (K)
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b ) covolume; equation of state size parameter (m3 mol-1) b h ) pseudo covolume (m3 mol-1) cij ) parameters of the accurate equation of state, the IUPAC equation E1ij, E2ij ) terms of the interchange energy between alkane and alkane or water or methanol and between nitrogen and alkane or water or methanol (J m-3) kij ) binary interaction coefficients in EOS model Kij, Lij ) binary interaction parameters (J m-3) lhyd ) parameter related to the chain-length of the hydrocarbons N ) number of groups in a solution N ) for calculating AAD, number of dew points which constitute a dew point curve p ) number of components in the mixture P ) pressure (Pa) q ) molecular surface (m2) Q ) integral of Q′/η between 0 and η R ) gas constant (8.314 J mol-1 K-1) r ) adjusted parameter T ) temperature (K) T0 ) reference temperature (298.15 K) v ) molar volume (m3 mol-1) vj ) molar pseudo-volume (m3 mol-1) z ) compressibilty factor Greek letters R1, R2 ) adjusted parameters in EF-EOS model Rik ) surface area fraction of group k in molecule I β1, β2 ) adjusted parameters in EF-EOS model γ ) constant of the translated Peng-Robinson cubic equation of state δ ) adjustable parameter, proportionality coefficient between the surface measure, q, and the covolume, v η ) packing fraction F ) mass of carbon dioxide per unit of volume (g cm-3) Fjwater ) experimental mean value of water content (10-6 kg m-3(n)) Fjmethanol ) experimental mean value of methanol content (10-6 kg m-3(n)) Ψ ) function of the packing fraction ω ) acentric factor Subscripts c ) critical value eb ) value at normal vaporization temperature i,j ) referring to components i,j k,l ) referring to groups k,l n ) referring to a point of a dew point curve in the calculation of AAD N ) number of dew points which constitute a dew point curve res ) residual Superscripts cal ) calculated exp ) experimental E ) excess property id ) ideal solution property
Acknowledgment This work is part of a research project 2FD97-2078 financially supported by Science and Technology Ministry of Spain, and FEDER funds. The authors also
acknowledge the technical support of ENAGAS, S. A. during the experimental part of this work. Appendix For comparison between calculated and experimental dew point temperatures for each studied dew point curve we use the deviation
AAD )
1
N
cal |Texp ∑ n - Tn | Nn)1
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Received for review February 11, 2003 Revised manuscript received October 6, 2003 Accepted October 15, 2003 IE030121I
