Dew Points of Binary Propane or n-butane + ... - ACS Publications

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Ind. Eng. Chem. Res. 2006, 45, 3974-3980

GENERAL RESEARCH Dew Points of Binary Propane or n-butane + Carbon Dioxide, Ternary Propane or n-butane + Carbon Dioxide + Water, and Quaternary Propane or n-butane + Carbon Dioxide + Water + Methanol Mixtures: Measurement and Modeling L. Gil,† S. Avila,‡ P. Garcıá-Gime´ nez,† S. T. Blanco,† C. Berro,§ S. Otin,† and I. Velasco*,† Departamento de Quı´mica Orga´ nica y Quı´mica Fı´sica, Facultad de Ciencias, UniVersidad de Zaragoza, 50.009sZaragoza, 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, 13.288sMarseille Cedex 9, France

Dew points have been measured for binary propane or n-butane + carbon dioxide mixtures at pressures from 1.2 × 105 to 34.9 × 105 Pa and temperatures from 192.6 to 274.8 K, four ternary propane or n-butane + carbon dioxide + water mixtures from 1.1 × 105 to 20.7 × 105 Pa and temperatures from 247.5 to 289.0 K, and eight quaternary propane or n-butane + carbon dioxide + water + methanol mixtures from 1.1 × 105 to 21.8 × 105 Pa and temperatures from 249.8 to 289.9 K. The results are analyzed in terms of a predictive EF-EOS excess-function equation of state method based on the zeroth-approximation of Guggenheim’s reticular model. This method has been chosen because it can be used to adequately predict the dew points of all the mixtures of our interest in the dew temperature and pressure ranges. In fact, the model reproduces the experimental dew-point temperature data within an AAD (absolute average deviation) of 1.6 and 1.3 K for the binary systems, between 0.1 and 2.5 K for the ternary systems, and between 0.0 and 5.1 K for the quaternary systems. The experimental results obtained for ternary propane or n-butane + carbon dioxide + water mixtures at pressure values higher than 5 × 105 Pa were also compared to a predictive EOS (equation of state) model. It reproduced experimental dew-point temperature data within AAD between 0.0 and 5.5 K. 1. Introduction To investigate the influence of carbon dioxide, water, methanol, and heavy hydrocarbons on the vapor-liquid equilibrium (VLE) of natural gas within the usual pressure and temperature conditions of natural gas transported by pipeline, we have previously studied the following systems: carbon dioxide + water and carbon dioxide + water + methanol,1 methane + carbon dioxide + water,2 ethane + carbon dioxide + water,2 methane + carbon dioxide + water + methanol,3 ethane + carbon dioxide + water +methanol,4 and two synthetic natural gases (SNG), with high contents of carbon dioxide, and their mixtures with water and with water and methanol.5 Dewpoint data for binary propane or n-butane + carbon dioxide, ternary propane or n-butane + carbon dioxide + water, and quaternary propane or n-butane + carbon dioxide + water + methanol are reported in the present work. We have found in the bibliography some dew-point data for propane + carbon dioxide6-10 and for n-butane + carbon dioxide,7,10-12 but not for the ternary and quaternary systems studied in this work. In addition, we have developed a theoretical model for dew-point prediction. The experimental apparatus used in this work for water and water + methanol dew-point generation, and for hydrocarbon, * Corresponding author. Fax: +34 976 761 202. Tel.: +34 976 761 197. E-mail: [email protected]. † Universidad de Zaragoza. ‡ ENAGAS. § Universite ´ de la Me´diterraneé.

water, and water + methanol dew-point determination, was built and tested in previous studies.13,14 The results for propane or n-butane + carbon dioxide mixtures at pressures from 1.2 × 105 to 34.9 × 105 Pa and temperatures from 192.6 to 274.8 K, four propane or n-butane + carbon dioxide + water mixtures from 1.1 × 105 to 20.7 × 105 Pa and temperatures from 247.5 to 289.0 K, and eight propane or n-butane + carbon dioxide + water + methanol mixtures from 1.1 × 105 to 21.8 × 105 Pa and temperatures from 249.8 to 289.9 K are presented here. The experimental results obtained for studied mixtures were analyzed in terms of a predictive EF-EOS excess-function equation of state method based on the zero-order approximation of Guggenheim’s reticular model, which reproduces the experimental dew-point temperature data within an absolute average deviation (AAD) of 1.6 and 1.3 K for dry systems, between 0.1 and 2.5 K for the systems with water, and between 0.0 and 5.1 K for the systems with water and methanol. The experimental results obtained for propane or n-butane + carbon dioxide + water mixtures at pressure values higher than 5 × 105 Pa were also compared to a predictive EOS equation of state model. It reproduced experimental dew-point temperature data with an AAD e 5.5 K. 2. Experimental Section The experimental method used in this work is based on the generation of gases saturated with water or with water and methanol by condensation of water or water + methanol, respectively, in a temperature-controlled condenser with continuous gas flow at specified pressures.

10.1021/ie058068g CCC: $33.50 © 2006 American Chemical Society Published on Web 05/03/2006

Ind. Eng. Chem. Res., Vol. 45, No. 11, 2006 3975

Figure 1. Schematic diagram 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 ) water content analyzer; and XI ) volume measurement. Table 1. Composition of Propane + Carbon Dioxide and n-butane + Carbon Dioxide Mixtures and Relative Accuracy Specified by the Supplier component

Gas 1

propane n-butane carbon dioxide

5 ( 1% 95 ( 1%

Gas 2 1 ( 1% 99 ( 1%

A schematic diagram of the experimental apparatus is shown in Figure 1. The gas supply bottles which contain the propane or n-butane + carbon dioxide mixture (Table 1) were prepared by weight by Abello-Linde.15 After controlled expansion (RV1), the gas from the bottle was saturated with water or water + methanol vapor by flowing the gas through a saturator containing liquid water or a liquid mixture of water and methanol at laboratory temperature (TI1). The temperature of condensation of water or water + methanol was then achieved in a stainless steel condenser, which was located in a thermostatic bath set at the desired temperature of condensation (TI2). This temperature (TI2) is lower than the temperature in the saturator (TI1). The values for the water and methanol contents in the gas phase of the generated VLE are obtained at the outlet of the condenser using Karl Fischer titration16 for water content and using gas chromatographic analysis for methanol content. The dew-point values for the mixtures were measured by means of a chilled-mirror instrument. The input pressure (PI6) of the gas in the chilled-mirror instrument was set using a regulator valve (RV2). When the apparatus reached a stable dewpoint temperature (TI6), both the pressure and temperature were recorded. In the case of the dry mixtures (propane or n-butane + carbon dioxide), the gas was directly sent to the chilled-mirror instrument from the bottle supply, which was connected to the regulator valve (RV2). The following instrumentation is used in the experimental apparatus: a Mitsubishi CA 06 Karl Fischer titrator, coupled with an Elster wet gas meter type Gr. 00, E51 to measure the water content (0.2% accuracy); an HP 5890 gas chromatograph fitted with a Haysep Q column and a thermal conductivity detector to measure the methanol content; and an MBW dewpoint instrument (model DP3-D-HP-K2) to measure the dewpoint temperatures. The cooling of the mirror is achieved by a cascaded-element Peltier cooling unit, and the dew-point mirror

temperature is optoelectronically controlled; a pressure transmitter is used to measure the dew-point pressures (maximum error of 0.1%). Prior to this study of propane or n-butane + carbon dioxide, propane or n-butane + carbon dioxide + water, and propane or n-butane + carbon dioxide + water + methanol dew points, the precision of the experimental procedure 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%, were measured and compared with literature.17,18 The results obtained were the following: (i) For the ethane vapor-liquid equilibrium curve, on 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 pressure values was 0.3% and the absolute average deviation of temperature values was 0.1 K. (ii) For the propane vapor-liquid equilibrium curve, on 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 absolute average deviation of temperature values was 0.2 K. To evaluate the precision of the analysis of water content, repeated analyses 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%.19 The relative average deviation was of 0.8% for a mean value of water content of 59.0 × 10-6 kg m-3 (n). To obtain the relative precision of the analysis of methanol content, repeated analyses 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 0.7%. To evaluate the precision of water and methanol dew-point generation, repeated generations 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:

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Ind. Eng. Chem. Res., Vol. 45, No. 11, 2006

Table 2. Experimental Dew Point Temperatures and Pressures for Gas 1 and Gas 2 T/K

P/105 Pa

T/K

198.3 205.1 211.6 222.8 225.1 229.3 233.4 236.3

1.2 3.2 4.3 6.7 7.4 8.6 9.9 11.0

244.4 244.9 246.0 246.2 248.9 249.7 252.7 253.8

P/105 Pa

T/K

P/105 Pa

255.4 256.2 259.2 262.5 268.2 270.6 272.2 274.8

20.7 21.2 23.4 25.6 29.7 31.7 32.8 34.9

Gas 1 13.9 14.5 14.7 15.1 17.3 17.1 18.9 19.5 Gas 2 192.6 199.5 202.6 207.9 209.8 215.2 222.6 223.5

1.3 1.7 2.8 2.5 3.4 4.5 6.3 6.6

226.9 228.6 232.2 234.5 237.4 239.6 242.1 246.4

7.6 8.0 9.2 10.0 11.0 12.5 13.9 15.6

250.3 255.3 258.5 261.4 263.7 270.5 274.5

18.0 19.8 22.6 24.4 26.2 31.7 34.9

Table 3. Experimental Contents of Water and Dew-Point Temperatures and Pressures for Gas 1 + Water (xjwater) and for Gas 2 + Water (xjwater) T/K

P/105 Pa

T/K

P/105 Pa

T/K

P/105 Pa

1.1 1.3 2.2 3.6

Gas 1: xjwater ) 0.001 08 273.3 6.2 277.1 8.4 280.7 10.9 282.4 12.5

256.9 265.9 271.6

1.1 2.2 3.2

Gas 1: xjwater ) 0.001 68 277.1 4.6 279.8 5.6 284.5 7.9

287.5 289.0

9.6 10.6

252.9 259.8 266.1 270.1

1.1 2.0 3.5 4.9

Gas 2: xjwater ) 0.000 73 276.3 7.9 279.2 10.0 281.2 11.7 283.5 13.8

285.2 287.0 288.3

16.0 18.4 20.7

257.9 266.0 271.5

1.2 2.1 3.2

Gas 2: xjwater ) 0.001 37 274.9 4.1 278.0 5.1 281.5 6.6

284.8 288.2

8.2 10.4

247.5 254.2 260.4 266.5

284.5 286.7 287.4 288.7

14.9 17.3 18.9 20.7

(i) For water content, the relative average deviation was 9.3% for a mean water content of 34.3 × 10-6 kg m-3 (n). (ii) For methanol content, the relative average deviation was 3.1% for a mean methanol content of 2 719.0 × 10-6 kg m-3 (n). (iii) For dew-point pressure, the relative average deviation was 4.2% on a range from 3.7 × 105 to 80.8 × 105 Pa. (iv) 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 1.013 25 × 105 Pa. The test was achieved on a water and methanol dew point of 283.15 K and 80 × 105 Pa in pure methane. 3. Results The values of dew temperatures and pressures for Gas 1 and Gas 2 (Table 1) are collected in Table 2. The water and methanol mole fractions and the dew-point temperatures and pressures for the ternary and quaternary systems are collected in Tables 3 and 4, respectively. The compositions of Gas 1 and Gas 2 were selected to avoid hydrates in the apparatus during the experimental study of Gas 1 or Gas 2 + water. The experimental dew points for ternary and quaternary systems range from 1.1 × 105 to 21.8 × 105 Pa at temperatures from 247.5 to 289.9 K

Table 4. Experimental Contents of Water and Methanol and Dew-Point Temperatures and Pressures for Gas 1 + Water (xjwater) + Methanol (xjmethanol) and for Gas 2 + Water (xjwater) + Methanol (xjmethanol) Systems T/K

P/105 Pa

T/K

P/105 Pa

T/K

P/105 Pa

250.8 262.9 266.7 272.2 275.9

Gas 1: xjwater ) 0.000 52; xjmethanol ) 0.003 1 1.1 278.0 8.9 286.1 2.9 281.8 11.9 286.6 3.8 283.0 13.1 287.3 5.6 283.9 14.1 288.4 7.5 285.2 15.5

16.8 17.4 18.6 20.2

249.8 261.5 269.5 277.4

Gas 1: xjwater ) 0.000 28; xjmethanol ) 0.005 1 1.1 280.7 10.8 288.3 2.6 285.5 16.0 288.8 4.7 286.4 17.4 289.9 8.4

19.2 19.8 20.6

257.4 263.8 267.8 270.8

Gas 1: xjwater ) 0.000 71; xjmethanol ) 0.004 8 1.1 275.4 4.3 284.4 1.9 278.4 5.4 286.0 2.5 280.0 6.0 287.3 3.1 283.6 7.7 288.2

8.2 9.1 9.9 10.5

257.3 263.1 269.4

Gas 1: xjwater ) 0.000 37; xjmethanol ) 0.008 2 1.1 274.5 3.7 285.4 1.8 279.0 4.8 288.8 2.8 282.3 6.3 289.5

7.8 9.7 10.2

250.4 258.6 266.6 272.3

Gas 2: xjwater ) 0.000 59; xjmethanol ) 0.003 1 1.1 277.8 9.2 285.5 2.2 280.4 11.2 287.0 3.9 282.7 13.7 288.4 6.0 284.1 15.4

254.5 264.6 266.1 268.6 271.9

Gas 2: xjwater ) 0.000 41; xjmethanol ) 0.005 1 1.8 273.0 6.7 284.1 3.9 274.0 7.2 284.5 4.1 277.6 9.3 286.6 4.9 279.7 10.7 287.8 6.2 282.2 12.9 288.7

252.9 255.6 261.2 265.7

Gas 2: xjwater ) 0.000 66; xjmethanol ) 0.003 8 1.1 274.2 5.7 284.7 1.3 277.1 6.8 287.0 2.0 281.2 9.0 288.8 3.0

260.9 267.5 271.1


8.8 10.1 10.3

259.7 265.3 270.9


8.9 10.6 11.3

17.1 19.5 21.8

14.8 16.5 17.8 20.3 21.8 11.4 14.0 16.0

to avoid the presence of liquid propane, butane, or carbon dioxide in the apparatus. For the binary and ternary systems, results in Tables 2 and 3 respectively, if dew-point temperatures and pressures fell within solid-vapor equilibrium conditions, the dew points measured would be metastable liquid-vapor equilibria. Regarding the relationship between the composition of a natural gas and its dew-point curve,20 we notice that the hydrocarbon component in Gas 2, n-butane, is heavier than that in Gas 1, propane, which would have as a consequence the increase of dew temperature for a given pressure.20 However, the higher content of carbon dioxide in Gas 2 (99%) than in Gas 1 (95%) would lead to a decrease of dew temperature for a given pressure.20 Because of the two opposite effects, the measured dew-point curves for these dry gases 1 and 2 (Table 2) are practically the same. The experimental dew-point data found in the literature for Gas 16,7 and for Gas 27 are in good agreement with the data presented in this work. When looking at our dew-point data for these systems and those from


literature8-12 for slightly different compositions, we can see an adequate tendency indicating good agreement. On the other hand, from Gas 1 and Gas 1 + water dew-point curves and from Gas 2 and Gas 2 + water dew-point curves (Tables 2 and 3), it can be seen that an increase of water content in the mixtures leads to higher dew temperatures for a given pressure (such as Gas 1 and Gas 1 + 0.001 08 water mole fraction and Gas 1 + 0.001 68 water mole fraction). In the case of similar values of water content, analogous dew-point curves are found. Such is the case of Gas 1 + 0.001 68 water mole fraction and Gas 2 + 0.001 37 water mole fraction (Table 3). This seems to indicate that the water dew-point temperature and pressure depend on the amount of water in the mixture but not on the composition of the gas without water. Similar conclusions were found in the literature.5,21-23 When comparing the results from Gas 1 + water and Gas 2 + water (Table 3) with the results of Gas 1 + water + methanol and Gas 2 + water + methanol (Table 4) with similar water contents, we found that the presence of methanol in the mixtures leads to a displacement of the dew-point curves to higher values of dew-point temperature and pressure. Such is the case of Gas 2 + 0.000 73 water mole fraction (Table 3) and Gas 2 + 0.000 78 water mole fraction + 0.005 1 methanol mole fraction (Table 4) or Gas1 + 0.000 71 water mole fraction + 0.004 8 methanol mole fraction (Table 4); for a given pressure, the difference between the dew-temperature values of the mixtures with and without methanol are up to 7 K. As shown in Table 4 for Gas 1 + water + methanol and Gas 2 + water + methanol mixtures with similar water mole fractions (such as Gas 1 + 0.000 37 water mole fraction + 0.008 2 methanol mole fraction and Gas 2 + 0.000 41 water mole fraction + 0.005 1 methanol mole fraction), increasing the methanol mole fraction in the mixture leads to an increase of the dew-point temperature at a given pressure. For the quaternary mixtures with similar methanol mole fractions (such as Gas 1 + 0.000 28 water mole fraction + 0.005 1 methanol mole fraction and Gas 2 + 0.000 78 water mole fraction + 0.005 1 methanol mole fraction), the dew-point temperature at a given pressure increases as the water content increases. 4. Theory Introduction. As mentioned earlier, this work is part of a program of research investigating the influence of carbon dioxide, water, methanol, and heavy compounds of natural gases on the VLE of natural gas. Therefore, the ranges of dew temperature and pressure are studied within the typical ranges for natural gas transmission through pipelines, which means temperatures from 249 to 288 K and pressures up to 10 MPa. Given that classical models such as UNIQUAC,24 DISQUAC,25 or modified UNIFAC26 allow the prediction of vapor-liquid equilibria at low pressures for systems which contain polar compounds, they are not suitable for the present work. Instead, we use two models in this work: the EF-EOS model, which is based on the zeroth order approximation of Guggenheim’s quasireticular model, and the classical EOS model, which is based on a modified Peng-Robinson EOS. A comparison between the experimental and calculated dewpoint temperatures was carried out. The values of dew temperature for the systems investigated were calculated by means of the EF-EOS method27 using the experimental values of pressure and composition obtained in the present work. The experimental dew-point temperatures obtained for Gas 1 or Gas 2 + water at pressure values higher than 5 × 105 Pa were also compared to

a classical EOS model. The EF-EOS model and the EOS model have been used and thoroughly described in previous works.1,3 Description of the Excess-Function Equation of State (EFEOS) Model. The EF-EOS model has been chosen because it can be used to adequately predict the dew points of all the mixtures of present interest in the temperature and pressure ranges. Regarding the EOS used in the EF-EOS model, we have used for carbon dioxide an accurate equation of state, the IUPAC equation.28 For propane, n-butane, water, and methanol, the translated Peng-Robinson cubic equation of state is used.27,29 The excess function of the EF-EOS model is the residual excess Helmholtz energy, AEref, which contributes to the molar Helmholtz energy of mixture, A, as follows

xi

p

A ) A - RT ln(1 - η) id

Ψi(η) + AEres ∑ i)1 b

(1)

i

where Aid is the ideal mixture molar Helmholtz energy, bi is the molar covolume for component i, Ψi(η) is a function of the packing fraction, and xi is the molar fraction for component i in the mixture. The residual excess Helmholtz energy, AEres, is a function in which composition x and packing fraction η are separated variables

AEres(T,x,η) ) E(T,x)

∫0η (Q′(η)/η) dη

(2)

where Q′(η) is a function of the packing fraction. For the first factor on the right-hand side of eq 2, different equations are used depending on the binary interaction which is present in the mixture. For binary interactions between carbon dioxide and water, carbon dioxide and methanol, carbon dioxide and propane, carbon dioxide and n-butane, and water and methanol, we used30

E(T,x) )

1

p

p

∑∑ 2 i)1 j)1

qiqjxixj Eij(T) qm

(3)

where the subscripts i and j referred to the components i and j of the mixture with p components, qj is the molecular surface of the component i, qm is the mean molecular surface, and Eij is the interaction energy between i and j. Equations for calculating Eij are taken from the literature.30 The binary interactions between propane and water, n-butane and water, propane and methanol, and n-butane and methanol were calculated using31

E(T,x) )

1 2qm

p

[

∑ i)1

p

∑ j)1

qixi[

p

qjxjKij] +

∑ i)1

p

qixi[

qj1/3xjLji1/3]] ∑ j)1

(4)

where Kij and Lij are binary interaction parameters calculated using the following equations

E1ij + E2ij Kij ) 2

(5)

Lij ) E2ij - E1ij

(6)

Lij ) -Lji

(7)

E1ij and E2ij are calculated using a group contribution method as follows31

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E1ij ) -

1

N

N

∑∑(Rik - Rjk)(Ril - Rjl)A1kl(T) 2k)1 l)1

(8)

with

A1kl E2ij ) -

1

N

)

0 1Akl

() T0 T

Bkl0

1

(9)

N

∑∑(Rik - Rjk)(Ril - Rjl)A2kl(T)

2k)1 l)1

(10)

with

A2kl ) 2A0kl

() 0

T T

Bkl0

2

(11)

and 2A0kl, 2B0kl are group interaction parameters at the reference temperature T0. The parameters for interchange energies between propane and water, n-butane and water, propane and methanol, and n-butane and methanol were taken from previous studies.5 Description of the Equation of State (EOS) Model. The EOS model used in this work is based on a modified PengRobinson EOS in order to obtain a good description of the vapor pressure of ice and liquid water.32 This equation, which was developed by the European Gas Research Group (GERG), allows for predicting adequately the water dew-point curve in the usual temperature and pressure range of importance for natural gas pipelines. It is written as

Figure 2. Comparison of measured dew points (b) and calculated values using the EF-EOS method (curves) for Gas 1, and comparison of measured dew points (symbols) and calculated values using the EF-EOS method (curves) and the EOS model (dotted curves) for {Gas 1 + xjwater} systems: (2), xjwater ) 0.001 08; (4), xjwater ) 0.001 68.

0 0 1Akl, 1Bkl,

P)

a RT V - b V2 + 2bV - b2

(12)

Figure 3. Comparison of measured dew points (b) and calculated values using the EF-EOS method (curves) for Gas 2, and comparison of measured dew points (symbols) and calculated values using the EF-EOS method (curves) and the EOS model (dotted curves) for {Gas 2 + xjwater} systems: (2), xjwater ) 0.000 73; (4), xjwater ) 0.001 37.

with

b(T) ) b(Tc)

(13)

a(T) ) a(Tc)R(Tr,ω)

(14)

R1/2 ) 1 + κ(1 - Tr1/2)

(15)

κ ) 0.374 640 + 1.542 26ω - 0.269 92ω2

(16)

and

where

and

where ω is the acentric factor of the component. The modification of the Peng-Robinson equation is made using for water the following equation,32

Figure 4. Comparison of measured dew points (symbols) and calculated values using the EF-EOS method (curves) for {Gas 1 + xjwater + xjmethanol} systems: (b), xjwater ) 0.000 52, xjmethanol ) 0.003 1; (O), xjwater ) 0.000 28, xjmethanol ) 0.005 1; (2), xjwater ) 0.000 71, xjmethanol ) 0.004 8; (4), xjwater ) 0.000 37, xjmethanol ) 0.008 2.

R1/2 ) A0 + A1(1 - Tr1/2) + A2(1 - Tr1/2)2 + A3(1 - Tr1/2)4 (17)

listed for each dew-point curve in Table 5.

where different values for coefficients A0, A1, A2, and A3 are used for T > 273.15 K and for T < 273.15 K.

AAD )

5. Conclusions The measured dew-point curves and calculated values using the EF-EOS method and the EOS model are presented in Figures 2-5. Values of the AAD are calculated using eq 18 and are

1

N

calc |Texp ∑ n - Tn | Nn)1

(18)

where N is the number of measured dew points that constitute an experimental dew-point curve and T is the dew temperature. The EF-EOS method predicts the dew temperature within AAD e 1.6 K for the binary systems, e2.5 K for the ternary


and FEDER funds. The authors also acknowledge the technical support of ENAGAS, S. A. Nomenclature

Figure 5. Comparison of measured dew points (symbols) and calculated values using the EF-EOS method (curves) for {Gas 2 + xjwater + xjmethanol} systems: (b), xjwater ) 0.000 59, xjmethanol ) 0.003 1; (O), xjwater ) 0.000 41, xjmethanol ) 0.005 1; (2), xjwater ) 0.000 66, xjmethanol ) 0.003 8; (4), xjwater ) 0.000 43, xjmethanol ) 0.008 7; (9), xjwater ) 0.000 78, xjmethanol ) 0.005 1. Table 5. Water Contents for Gas 1 + Water (xjwater) and Gas 2 + Water (xjwater) Systems and Water and Methanol Contents for Gas 1 + Water (xjwater) + Methanol (xjmethanol) and Gas 2 + Water (xjwater) + Methanol (xjmethanol) Systems, As Well As Experimental Ranges of Dew Temperatures and Pressures and Values of AAD1 (EF-EOS Model) and of AAD2 (EOS model) for the Measured Dew-Point Curves mixture gas 1 gas 1 gas 1 gas 1 gas 1 gas 1 gas 1 gas 2 gas 2 gas 2 gas 2 gas 2 gas 2 gas 2 gas 2

xjwater 0.001 08 0.001 68 0.000 52 0.000 28 0.000 71 0.000 37 0.000 73 0.001 37 0.000 59 0.000 41 0.000 66 0.000 43 0.000 78

xjmethanol

0.003 1 0.005 1 0.004 8 0.008 2

0.003 1 0.005 1 0.003 8 0.008 7 0.005 1

T range (K)

P range (105 Pa)

198.3 to 274.8 247.5 to 288.7 256.9 to 289.0 250.8 to 288.4 249.8 to 289.9 257.4 to 288.2 257.3 to 289.5 192.6 to 274.5 252.9 to 288.3 257.9 to 288.2 250.4 to 288.4 254.5 to 288.7 252.9 to 288.8 260.9 to 289.5 259.7 to 288.4

1.2 to 34.9 1.1 to 20.7 1.1 to 10.6 1.1 to 20.2 1.1 to 20.6 1.1 to 10.5 1.1 to 10.2 1.3 to 34.9 1.1 to 20.7 1.2 to 10.4 1.1 to 21.8 1.8 to 21.8 1.1 to 16.0 1.6 to 10.3 1.4 to 11.3

AAD1 AAD2 (K) (K) 1.6 1.5 0.1 3.2 0.0 3.7 3.9 1.3 2.5 2.0 0.3 3.4 3.2 2.1 5.1

0.0 1.7

a ) equation of state 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; equation of state size parameter (m3 mol-1) Eij ) interchange energy (J m-3) E1ij, E2ij ) interchange energy between propane or n-butane and water or methanol (J m-3) Kji, Lij ) binary interaction parameters for propane or n-butane + water and propane or n-butane + methanol (J m-3) 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); qi ) δibi with δi an adjustable parameter and bi the covolume for component i Q′ ) a packing fraction function R ) gas constant (8.314 J mol-1 K-1) T ) temperature (K) T0 ) reference temperature (298.15 K) V ) molar volume (m3 mol-1) x ) mole fraction xjwater ) experimental mean value of water mole fraction xjmethanol ) experimental mean value of methanol mole fraction Greek Letters

5.5 4.1

systems, and e5.1 K for the quaternary systems. The AAD values are e5.5 for the ternary systems analyzed in terms of the EOS model. No influence of temperature and pressure is found for the values of deviations. The results obtained in this paper using the EF-EOS method and the EOS model validate both models for the prediction of water dew points of the investigated systems, as well as validating the EF-EOS model for the prediction of dew points of propane or n-butane + carbon dioxide mixtures and for water + methanol dew points of the studied systems. Because the EF-EOS model uses a group contribution model, the availability of binary experimental data corresponding to every binary interaction in the mixture is not necessary. In view of this feature and the results obtained with this model in this work and previous studies,1-5,13,14,33-36 the EF-EOS model could be used to predict reliable dew points for hydrocarbons, water, and water + methanol in real natural gases, even though binary experimental data for all components of the so-called C6+ fraction are not available. Acknowledgment This work is part of research project 2FD97-2078 financially supported by the Science and Technology Ministry of Spain

Rik ) surface area fraction of group k in molecule i η ) packing fraction Ψ ) function of the packing fraction ω ) acentric factor Superscripts and Subscripts c ) critical value calc ) calculated exp ) experimental E ) excess property id ) ideal solution property i, j ) referring to components i, j k, l ) referring to groups k, l m ) referring to a mean molecular value n ) referring to a point of a dew-point curve in the calculation of AAD res ) residual Literature Cited (1) Jarne, C.; Blanco, S. T.; Artal, M.; Rauzy, E.; Otin, S.; Velasco I. Dew points of binary carbon dioxide + water and ternary carbon dioxide + water + methanol mixtures. Measurement and modelling. Fluid Phase Equilib. 2004, 216, 85-93. (2) Jarne, C.; Blanco, S. T.; Gallardo, M. A.; Rauzy, E.; Otin, S.; Velasco I. Dew points of ternary methane (or ethane) + carbon dioxide + water mixtures: Measurement and correlation. Energy Fuels 2004, 18, 396-404. (3) Jarne, C.; Blanco, S. T.; Fernandez, J.; Rauzy, E.; Otin, S.; Velasco I. Dew points of quaternary methane + carbon dioxide + water + methanol mixtures. Measurement and correlation. Ind. Eng. Chem. Res. 2004, 43, 662-668. (4) Jarne, C.; Blanco, S. T.; Avila, S.; Berro, C.; Otin, S.; Velasco I. Dew points of quaternary ethane + carbon dioxide + water + methanol mixtures. Measurement and modelling. Can. J. Chem. 2005, 83, 220-226.

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ReceiVed for reView August 1, 2005 ReVised manuscript receiVed January 4, 2006 Accepted March 29, 2006 IE058068G

Dew Points of Binary Propane or n-butane + ... - ACS Publications

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