Dew-Point Curves of Natural Gas. Measurement and Modeling

Ind. Eng. Chem. Res. 2006, 45, 5179-5184

5179

Dew-Point Curves of Natural Gas. Measurement and Modeling S. Avila,† A. Benito,† C. Berro,‡ S. T. Blanco,§ S. Otıń,§ and I. Velasco*,§ Gas Engineering and Technology, Enaga´ s, S.A., 50.080 Zaragoza, Spain, Laboratoire de Chimie Physique, Faculte´ des Sciences de Luminy, UniVersite´ de la Me´ diterrane´ e, 13288 Marseille Cedex 9, France, and Departamento de Quı´mica Orga´ nica y Quı´mica Fı´sica, Facultad de Ciencias, UniVersidad de Zaragoza, 50.009 Zaragoza, Spain

To achieve a reliable method to calculate the hydrocarbon dew point for natural gases in transmission, samples of natural gas were taken at the inlet of the Magreb-Europe pipeline in Spain. The composition up to the C12 fraction of each natural gas sample was determined by gas chromatography, and the dew-point curve was measured using a chilled mirror dew-point analyzer. In this work, we present the experimental measurements of dew points for six samples of natural gas between 1.1 × 105 Pa and 78.4 × 105 Pa in the temperature range from 235.2 to 277.9 K. The experimental results obtained were analyzed in terms of a predictive excess function-equation of state (EF-EOS) method based on the zeroth-approximation of Guggenheim’s reticular model. Because the EF-EOS model uses a group contribution model, the availability of every binary experimental data corresponding to every binary interaction in the mixture is not necessary. Considering this and the good results obtained in previous studies, we concluded that the EF-EOS model could be used for proper prediction of the hydrocarbon, water, and water + methanol dew-points of real natural gases, even though binary experimental data for all components of the so-called C6+ fraction are not available. In this work, the capability of this theoretical model for the prediction of hydrocarbon dew points of the studied samples of natural gas is demonstrated within the studied temperature and pressure ranges. In fact, the model reproduces experimental dew-point temperature data within average absolute deviation between 0.4 and 3.0 K when two components are used for characterizing the composition of each heavy fraction of the samples of natural gas and from 1.6 to 2.3 K when all analyzed components are considered for each fraction. 1. Introduction Liquids in natural gas and especially the hydrocarbon dew point have been an issue for many years,1 and they are still the main topic in gas quality today. Moreover, they count for a major part in the new context of interoperability2 among all European transmission networks. The aim of our work is to investigate all of the hydrocarbon dew-point questions for a natural gas with an extremely asymmetric composition as is the case of the natural gas transported through the Magreb-Europe pipeline. These questions are the implementation of an analysis procedure of the heavy fraction of the natural gas, the determination of an adequate characterization of the analyzed heavy fraction, and the performance of a reliable theoretical model for the prediction of the hydrocarbon dew point of natural gases with different kinds of compositions. To study these questions, samples of natural gas were taken at the inlet of the Magreb-Europe pipeline in Spain. It is important to remark that the studied systems are not synthetic mixtures such as those of previous works,3-7 which were constituted by nitrogen, carbon dioxide, and n-alkanes with n e 8. The samples studied in this work contain nitrogen, carbon dioxide, and alkanes of any kind (that is, not only linear) with the number of carbon atoms g 12. We have found in the literature8-13 works related to the hydrocarbon dew point in natural gas, but they do not study all of the questions, as is the case of our work. Among them, we have found theoretical models for hydrocarbon dew-point prediction, for example, that of Wang et al.,12 which has not * Corresponding author. Fax: +34 976 761 202. Tel.: +34 976 761 197. E-mail: [email protected]. † Enaga ´ s, S.A. ‡ Universite ´ de la Me´diterraneé. § Universidad de Zaragoza.

been tested for natural gas systems, or that of Voulgaris et al.,13 which is made for restricted compositions of natural gas and not applicable for any kind of composition of natural gas. The composition up to the C12 fraction of each natural gas sample was determined by gas chromatography, and the dewpoint curve was measured using a chilled mirror dew-point analyzer. In this work, we present the experimental measurements of dew points for six samples of natural gas between 1.1 × 105 Pa and 78.4 × 105 Pa in the temperature range from 235.2 to 277.9 K. The experimental results obtained were analyzed in terms of an excess function-equation of state (EF-EOS),14 which reproduces experimental dew-point temperature data with an average absolute deviation (AAD) between 0.4 and 3.0 K when the compositions of two components are used for characterizing each heavy fraction of the samples of natural gas and from 1.6 to 2.3 K when all analyzed components are considered in each fraction. 2. Experimental Procedure The following instrumentation is used to analyze the compositions of the samples of natural gas and to carry out the dewpoint measurements. (i) A gas chromatographic system consists of an HP 6890 gas chromatograph with a thermal conductivity detector and two packed columns for the analysis of the inert gases and hydrocarbons up to C3 and a flame-ionization detector and a capillary column for hydrocarbon analysis from C4 to C12. Two gas sampling valves (10 and 6 ports) and one column isolation valve (6 ports), all automatically controlled, are installed in a thermostatically controlled heated compartment. Separation of oxygen, nitrogen, and methane is achieved on a molecular sieve 13X column (45/60 mesh, 3 ft). Carbon dioxide, ethane, and propane are separated on a Porapack N

10.1021/ie058083l CCC: $33.50 © 2006 American Chemical Society Published on Web 06/07/2006

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Ind. Eng. Chem. Res., Vol. 45, No. 14, 2006

Table 1. Compositions of Samples of Natural Gas (mol %) and Values of Uncertainty (%) component nitrogen carbon dioxide methane ethane propane i-butane n-butane i-pentane n-pentane cyclopentane 3-methylpentane n-hexane C6 fraction methylcyclopentane benzene cyclohexane y-heptane n-heptane C7 fraction methylcyclohexane toluene y-octane n-octane C8 fraction p-xylene y-nonane n-nonane C9 fraction y-C10 n-decane C10 fraction n-undecane C11 fraction n-dodecane C12 fraction

sample 1 5.693 0.205 82.770 7.901 2.137 0.344 0.529 0.124 0.138

sample 2 5.612 0.199 83.426 7.675 1.989 0.298 0.453 0.098 0.110

sample 3 4.377 0.670 83.351 8.828 2.038 0.229 0.330 0.055 0.055

0.035567 0.082906

0.029926 0.069857

0.012437 0.030888

0.009313 0.038465

0.008754 0.036738

0.003369 0.015185

0.002263 0.011958

0.001989 0.010561

0.000798 0.004295

0.000479 0.002549

0.000378 0.002085

0.000190 0.000918

0.000091 0.000467 0.000019 0.000031 0.000009 0.000009

0.000073 0.000362 0.000014 0.000030 0.000004 0.000004

0.000044 0.000143 0.000013 0.000019 0.000006 0.000006

column (80/100 mesh, 10 ft). The hydrocarbon separation is obtained on a 50 m × 0.2 mm i.d. fused-silica capillary column (PONA) coated with a 0.5 µm film of cross-linked methylsilicone gum. (ii) A MBW dew-point instrument model DP3-D-HP-K2 was used, in which the cooling of the mirror is achieved by cascaded Peltier elements and the dew-point mirror temperature is controlled opto-electronically. The uncertainty, given by the supplier, on the dew temperature is better than (0.1 K. (iii) A pressure transmitter with a maximum error of 0.1% in the calibrated range was used. Table 1 shows the composition of the samples of natural gas. The values of uncertainty in Table 1 were obtained according to ISO 6974-2:2001.15 Each value of the composition, named Cn fraction in Table 1, is the sum of the compositions of hydrocarbons which appear in the chromatogram between the Cn-1 and Cn linear alkanes, the latest included. y alkane refers to the sum of the contents of nonidentified components for each fraction. The dew-point values for the studied samples are measured by means of the 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 dew-point temperature value, both pressure and temperature are recorded. Prior to this study of natural gas dew points, the accuracy of the hydrocarbon dew-point measurement was determined; the vapor-liquid equilibrium curves of both ethane, with a specified purity of 99.995%, and propane, with specified purity of 99.95%, were measured and compared with literature.16,17 The results obtained were the following: (i) For the ethane vapor-liquid equilibrium curve, in the pressure range from 1.8 × 105 to 29.4 × 105 Pa and temperature between 195.3 and 282.0 K, the relative average deviation of

sample 4

sample 5

sample 6

uncertainty

2.224 1.047 84.033 9.333 2.396 0.338 0.421 0.080 0.060 0.003 0.023 0.015 0.041 0.0004 0.0034 0.0002 0.0102 0.0041 0.0183 0.00147 0.00057 0.00257 0.00104 0.00565 0.00013 0.00104 0.00023 0.00140 0.000244 0.000052 0.000296 0.000012 0.000012 0.000006 0.000006

3.45 0.615 83.965 8.654 2.265 0.353 0.446 0.088 0.075 0.004 0.028 0.021 0.053 0.0021 0.0051 0.0021 0.0100 0.0065 0.0258 0.00217 0.00079 0.00396 0.00170 0.00862 0.00019 0.00169 0.00038 0.00226 0.000390 0.000076 0.000466 0.000016 0.000016 0.000009 0.000009

3.048 1.201 82.816 8.934 2.831 0.341 0.661 0.057 0.056 0.003 0.019 0.016 0.038 0.0008 0.0020 0.0008 0.0048 0.0029 0.0113 0.00130 0.00037 0.00225 0.00090 0.00482 0.00008 0.00079 0.00015 0.00102 0.000197 0.000049 0.000246 0.000009 0.000009 0.000003 0.000003

2 2 0.3 2 2 5 5 5 5 5 5 5 5 5 5 5 5 5 5 13 13 13 13 13 22 22 22 22 45 45 45 45 45 65 65

the pressure values was 0.3% and the AAD of the temperature values was 0.1 K. (ii) For the propane vapor-liquid equilibrium curve, in the pressure range from 1.0 × 105 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 AAD of the temperature values was 0.2 K. 3. Results The dew-point temperatures and pressures for the studied samples are shown in Table 2. In this table, for each sample, the dew point corresponding to the maximum value of the dew temperature is the cricondentherm. It can be seen that the highest value of temperatures of cricondentherms for the studied samples corresponds to sample 1 (277.9 K at 21.3 × 105 Pa). Regarding the relationship between the composition of a natural gas and its risk of condensation, Voulgaris18 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 vapor-liquid equilibrium 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. From Tables 1 and 2, we can see that the experimental temperature of cricondentherms does not decrease as the concentration of methane, ethane, or carbon dioxide of the corresponding samples increases or as the concentration of nitrogen or hydrocarbons with more than two carbon atoms of the corresponding samples decreases. We observe, however, that experimental temperatures of cricondentherms of the samples increase as the sum of the analyzed contents of hydrocarbons

Ind. Eng. Chem. Res., Vol. 45, No. 14, 2006 5181 Table 2. Experimental Dew-Point Temperatures and Pressures for the Studied Samples of Natural Gas T (K)

P (105 Pa)

T (K)

243.2 251.5 257.1 259.6 262.3 264.7 265.9 268.0 268.8 269.6 271.0

2.2 2.6 3.9 4.7 5.9 7.3 8.0 9.7 10.6 11.2 12.9

271.8 272.8 273.3 274.0 274.6 275.2 275.5 275.8 276.2 276.5 276.8

236.9 247.8 251.9 257.1 260.4 263.7 265.0 266.9 268.2 269.4

1.1 2.4 3.4 5.4 7.2 9.4 10.4 12.5 14.2 16.1

240.0 246.6 251.1 252.8 254.0 256.1 257.4 258.9

P (105 Pa)

T (K)

P (105 Pa)

T (K)

P (105 Pa)

Sample 1 14.1 277.0 15.6 277.2 16.5 277.4 17.7 277.6 18.9 277.7 20.4 277.8 21.3 277.9 22.3 277.8 23.4 277.7 24.8 277.5 26.0 277.4

27.2 28.5 29.7 31.4 33.3 35.2 36.8 38.7 41.1 42.4 44.0

277.2 277.0 276.7 276.3 275.7 275.0 274.3 273.8

45.4 46.8 48.5 50.9 53.9 56.9 59.5 61.6

270.3 271.3 272.1 272.6 273.2 273.7 274.0 274.4 274.5 274.6

Sample 2 17.4 274.7 19.5 274.7 21.7 274.6 23.0 274.4 24.8 274.2 27.2 273.9 29.2 273.4 30.9 273.0 32.3 272.6 33.7 272.0

35.5 37.6 39.8 42.0 44.0 45.8 48.8 50.2 52.2 54.6

271.3 270.7 270.2 269.3 268.4 267.0 266.0 264.6 263.2 260.8

56.8 58.8 60.2 62.5 64.8 67.9 69.6 72.3 74.3 78.4

2.1 3.6 5.6 6.7 7.5 9.3 10.6 13.0

260.0 261.0 261.5 262.0 262.3 262.6 262.8 263.0

Sample 3 15.2 263.0 17.4 262.9 19.2 262.9 21.6 262.8 23.5 262.5 25.4 262.1 27.0 261.7 29.1 261.2

31.3 33.5 35.4 37.1 39.7 41.6 43.5 45.1

260.7 259.6 258.9 258.3 258.0

47.5 50.3 51.8 54.2 56.0

238.7 244.3 248.3 252.0 254.2 256.7 258.5

1.5 2.6 3.7 5.2 6.5 8.3 10.1

260.3 261.5 262.8 263.4 264.3 264.9 265.4

Sample 4 12.2 265.7 14.1 265.9 16.6 266.0 18.0 266.0 20.9 265.6 23.3 264.9 25.8 264.4

27.7 29.9 32.5 35.3 38.0 40.8 42.9

264.0 263.4 262.9 262.6 263.1 262.6

45.0 47.9 50.1 52.6 54.9 57.1

236.5 243.8 251.1 254.3 257.0 258.9 261.1 262.7 264.3 265.6 266.5

1.1 2.0 3.6 4.7 6.1 7.2 8.7 10.3 12.0 13.8 14.7

267.8 268.5 269.2 269.8 270.2 270.6 270.9 271.0 271.1 271.1 271.0

Sample 5 18.0 270.6 19.4 270.1 21.3 269.7 23.5 269.2 25.1 268.8 27.1 268.1 29.4 267.7 31.4 266.8 33.5 35.1 37.4

235.2 246.2 250.9 254.8 257.1 259.4 261.3 262.6

1.1 2.7 4.2 6.0 7.4 9.1 11.2 12.8

263.7 265.0 265.9 266.6 267.3 267.8 268.4 268.7

Sample 6 14.4 268.9 16.6 269.1 18.5 269.2 20.3 269.2 22.1 269.1 24.1 268.9 26.4 268.7 28.5 268.4

268.1 267.8 267.4 266.9 266.6 266.5

47.3 49.6 51.7 53.6 55.4 58.2

40.1 42.9 45.3 47.7 49.6 52.3 54.0 56.4

30.5 32.6 34.6 37.0 39.5 41.3 43.1 45.3

heavier than n-pentane increases. Sample 6 seems to be an exception to this behavior. The observed behavior in this work would not be in contradiction to Voulgaris’18 conclusions, given that the author literally refers to the condensation risk of natural gas. It is necessary to take into account the high sensitivity of the dew temperature for a given pressure to traces of heavy hydrocarbons in natural gas.19 As a consequence, for a given pressure, when

the temperature reaches the value of the dew temperature, the traces of heavy hydrocarbons condense, which does not mean significant quantities of liquids. The temperature should reach lower values than the dew temperature to have a real risk of condensation. 4. Theory Introduction. Equations of state such as the Peng-Robinson EOS20 yield good results in calculation of the dew points of natural gases. Instead of this EOS, we use the EF-EOS method, which is derived from the EF-EOS model14 and based on the zeroth order approximation of the quasi-reticular model. Because of the EF-EOS model uses a group contribution model, the availability of every binary experimental data corresponding to every binary interaction in the mixture is not necessary. Considering this and the good results obtained in previous studies,3-7 we concluded that EF-EOS model could be used for the proper prediction of hydrocarbon, water, and water + methanol dew points of real natural gases, even though binary experimental data for all components of the so-called C6+ fraction are not available. The aim of this work is demonstrating the capability of this theoretical model for the prediction of hydrocarbon dew points of natural gas. To evaluate the theoretical model used in this paper for the prediction of the dew points of samples in the studied temperature and pressure ranges, a comparison between experimental and calculated values of the dew-point temperature was carried out. The values of the dew temperature of the vapor phase for the investigated systems are calculated by means of the EFEOS method14 using the experimental values for pressure and composition obtained in the present work. Referring to composition, each heavy fraction of samples is characterized considering either two components (a linear alkane and a nonlinear alkane) or all analyzed components. Description of the EF-EOS Model. To represent the vaporliquid 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 EOS. (2) The EFs 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 being the molar volume. The EOS used in the EF-EOS model is the translated PengRobinson cubic EOS21 for components different from carbon dioxide and the IUPAC equation22 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 equations of state especially near of the critical point. The IUPAC equation22 is easy to use given its polynomial form, even if the parameters used are numerous.

z)1+

F i)9 j)6

( )( )

∑∑cij

Fc i)0 j)0

Tc T

j

-1

F

Fc

i

-1

(1)

The translated Peng-Robinson cubic EOS22 is of the form

P)

a(T) RT Vj - bh Vj(Vj + γbh)

(2)

The values of the parameters a and bh depend on the components as follows. (i) For nitrogen and hydrocarbons with less than six carbon atoms, the following equation is used for the covolume, bh.21

5182


bh ) 0.045 572

RTc Pc

(3)

The attractive parameter a as a function of the temperature, T, is calculated using various equations taken from Peńeloux et al.21 (ii) For hydrocarbons with more than five carbon atoms, the covolume, bh, is calculated by means of a group contribution method.23 The attractive parameter, a, is obtained using the equations proposed by Coniglio et al.23 and Carrier et al.24 The EF 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 ) A - RT ln(1 - η) id

xi

Ψi(η) + ∑ i)1 b

Table 3. Values of the Group Interaction Parameters, Akl0, Used in Equation 9 for the EF-EOS Model binary

Akl0 (106 J m-3)

CO2 + N2 CO2 + CH4 CO2 + -CH3 CO2 + -CH2CO2 + -CH|

28.2787 253.27827 442.31426 442.31426 328.30326

and

qk ) δkbk Eij1 + Eij2 2

(14)

Lij ) Eij2 - Eij1

(15)

Lij ) -Lji

(16)

Kij ) AEres

(4)

i

AEres,

The residual excess Helmholtz energy, can be written by means of a formalism which enables the composition and packing fraction variables to be separated:

AEres ) E(T, x) Q(η)

(5)

The interchange energies, Eij1 and Eij2, are calculated using a group contribution method as follows:28

where Q(η) is expressed as21

Q(η) )

Eij1 ) -

∫0η(1 +1 γη) dη

(6)

1

N

N

∑∑(Rik - Rjk)(Ril - Rjl)Akl1(T)

2k)1 l)1

where the value of the parameter γ 20 when the IUPAC equation is used. If the translated Peng-Robinson cubic EOS is used the value for parameter γ is 2(x2 + 1). The first term on the right-hand side of eq 5 is expressed as follows. (i) For carbon dioxide + alkane or nitrogen binaries, the equations proposed by Berro et al.26 are used.

Eij ) -

1

N

p

p

∑∑

∑∑(Rik - Rjk)(Ril - Rjl)Akl(T)

2k)1 l)1

T0 T

r ) β1(lhyd)1.5 + β2lhyd

(8)

r

2qm

p

p

(10)

p

qixi[∑qjxjKij] + ∑qixi[∑qj1/3xjLji1/3]] ∑ i)1 j)1 i)1 j)1

(11)

with

∑qkxk

(18)

N

∑∑(Rik - Rjk)(Ril - Rjl)Akl2(T)

2k)1 l)1

(19)

0

() T0 T

0

2Bkl

(20)

where 1Akl0, 1Bkl0, 2Akl0, and 2Bkl0 are group interaction parameters. The values for the group interaction parameters for interchange energies are the same as in previous works.3-6

In this work the dew points for six samples of natural gas have been studied. The experimental dew-point curves and calculated values using the EF-EOS method are represented in Figures 1-3. It can be seen that the calculated temperatures of cricondentherms of the samples increase as the sum of the analyzed contents of hydrocarbons heavier than n-pentane increases (Table 1). The experimental temperature of cricondentherm for sample 6 does not follow this trend; however, the calculated temperature does. Hence, there is probably experimental error in the data of sample 6. Values of AAD are calculated using eq 21 and listed for each dew-point curve in Table 4.

AAD )

p

k)1

0

1Bkl

5. Discussion and Conclusions

[

qm )

() T0 T

(9)

The values for the group interaction parameters Akl0 used in this work are presented in Table 3. (ii) For alkane + alkane or nitrogen binaries, the equations proposed by Hocq28 are used: p

N

Akl ) 2Akl

with

1

1

2

[]

E(T, x) )

Eij2 ) -

0

(7)

N

Akl ) Akl0[1 + exp(R1lhyd + R2)]

Akl ) 1Akl 1

with

qiqjxixj Eij(T) 2 i)1 j)1 qm 1

(17)

with

is25

E(T, x) )

(13)

1

N

∑|Tnexp - Tncalc|

Nn)1

(21)

(12) As explained previously, the calculated values for dew tem-

Ind. Eng. Chem. Res., Vol. 45, No. 14, 2006 5183 Table 4. Experimental Ranges of Dew Temperatures and Pressures for the Samples of Natural Gas and Values of AAD(1)a and of AAD(2)b for the Measured Dew-Point Curves sample

T range (K)

P range (105 Pa)

AAD(1) (K)

AAD(2) (K)

1 2 3 4 5 6

243.2-277.9 236.9-274.7 240.0-263.0 238.7-266.0 236.5-271.1 235.2-269.2

2.2-61.6 1.1-78.4 2.1-56.0 1.5-57.1 1.1-56.4 1.1-58.2

1.3 0.5 0.4 2.5 3.0 2.9

1.6 1.9 2.3

a Two components are used for characterizing the composition of each heavy fraction. b All analyzed components are considered in each fraction.

Figure 1. Comparison between measured dew-point curves (symbols), (b) sample 1 and (O) sample 6, and those calculated using the EF-EOS method; two components are used for characterizing each heavy fraction (curve), and all components are considered in each fraction for sample 6 (dotted curve).



peratures with the theoretical model are obtained using the experimental values of pressure and composition obtained in this work. As it can be concluded from the values of AAD(1) and AAD(2) in Table 4, the EF-EOS predicts adequately the hydrocarbon dew point of natural gas, in the studied ranges of temperature

and pressure. Regarding samples 4-6, we can say that the predictions of the theoretical model improve when all the analyzed components of the heavy fractions of natural gas are used for the calculation. In this work we have succeed in addressing the three questions related to the hydrocarbon dew point pointed out in the introduction, because the values of AAD obtained in this work are similar to those of our previous works for synthetic mixtures.3-7 Moreover, we have demonstrated that the EF-EOS method, because of the group contribution model, can be used for natural gases with different kinds of composition. This is true even for a highly asymmetric composition as is the case of the natural gas imported from Algeria, which has been studied in this work, within the investigated temperature and pressures ranges. Because of the EF-EOS model uses a group contribution model, the calculation of the binary interaction parameter from binary experimental data is not necessary. Considering this property and the good results obtained with this model both in this work and in the previous ones,3-7,27 the model could be very suitable to predict, besides hydrocarbon dew points, water and water + methanol dew points of real natural gases, although binary experimental data for all components of the so-called C6+ fraction are not available. Nomenclature a ) EOS attractive energy parameter (Pa m6 mol-2) A ) molar Helmholtz energy (J mol-1) Akl ) group interaction parameter between groups k and l (J m-3) AAD ) absolute average deviation (K) b ) covolume; EOS size parameter (m3 mol-1) bh ) pseudo-covolume (m3 mol-1) cij ) parameters of the accurate EOS, the IUPAC equation Eij1, Eij2 ) terms of the interchange energy between alkane and alkane and between nitrogen and alkane (J m-3) 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)

5184


z ) compressibility factor Greek Symbols Rlk ) surface area fraction of group k in molecule l β1, β2 ) adjusted parameters in the EF-EOS model γ ) constant of the translated Peng-Robinson cubic EOS 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) Ψ ) function of the packing fraction ω ) acentric factor Subscripts c ) critical value 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 The authors from University of Zaragoza acknowledge that the experimental work of this paper was made possible by Enaga´s, S.A. Literature Cited (1) Bergman, D. F.; Teck, M. R.; Katz, D. L. Retrograde condensation in natural gas pipelines; American Gas Association: VA, 1975. (2) GTE Interoperability Report, 20/06/2001. (3) Avila, S.; Blanco, S. T.; Velasco, I.; Rauzy, E.; Otıń, S. Thermodynamic Properties of Synthetic Natural Gases. Part 1. Dew Point Curves of Synthetic Natural Gases and their Mixtures with Water and Methanol. Measurement and Correlation. Ind. Eng. Chem. Res. 2002, 15, 3714-3721. (4) Avila, S.; Blanco, S. T.; Velasco, I.; Rauzy, E.; Otıń, S. Thermodynamic Properties of Synthetic Natural Gases. Part 2. Dew Point Curves of Synthetic Natural Gases and their Mixtures with Water and Methanol. Measurement and Correlation. Energy Fuels 2002, 16 (4), 928-934. (5) Avila, S.; Blanco, S. T.; Velasco, I.; Rauzy, E.; Otıń, S. Thermodynamic Properties of Synthetic Natural Gases. Part 3. Dew Point Curves of Synthetic Natural Gases and their Mixtures with Water. Measurement and Correlation. Energy Fuels 2003, 17 (2), 338-343. (6) Avila, S.; Blanco, S. T.; Velasco, I.; Rauzy, E.; Otıń, S. Thermodynamic Properties of Synthetic Natural Gases. Part 4. Dew Point Curves of Synthetic Natural Gases and their Mixtures with Water. Measurement and Correlation. Fluid Phase Equilib. 2002, 202, 399-412. (7) Jarne, C.; Avila, S.; Blanco, S. T.; Rauzy, E.; Otıń, S.; Velasco, I. Thermodynamic Properties of Synthetic Natural Gases. Part 5. Dew Point Curves of Synthetic Natural Gases and their Mixtures with Water and Methanol. Measurement and Correlation. Ind. Eng. Chem. Res. 2004, 43, 662. (8) Renfrow, J. Characterization of heavy components in natural gas and natural liquids (extended analysis). Proc. Int. Sch. Hydrocarbon Meas. 1998, 73, 15-18.

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ReceiVed for reView November 16, 2005 ReVised manuscript receiVed April 28, 2006 Accepted May 10, 2006 IE058083L

Dew-Point Curves of Natural Gas. Measurement and Modeling

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