Dew Points of Quaternary Methane + Carbon Dioxide + Water +

Experimental measurements of dew points for 14 methane + carbon dioxide + water + methanol mixtures at pressures between 1.0 × 105 and 59.1 × 105 Pa...
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Ind. Eng. Chem. Res. 2004, 43, 662-668

Dew Points of Quaternary Methane + Carbon Dioxide + Water + Methanol Mixtures. Measurement and Correlation C. Jarne,† S. T. Blanco,† J. Ferna´ ndez,† 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, and Laboratoire de Chimie Physique de Marseille, Faculte´ des Sciences de Luminy, Universite´ de la Me´ diterrane´ e, 13.288 Marseille Cedex 9, France

Experimental measurements of dew points for 14 methane + carbon dioxide + water + methanol mixtures at pressures between 1.0 × 105 and 59.1 × 105 Pa in the temperature range from 241.6 to 288.8 K were made. The experimental results obtained on the quaternary systems were analyzed in terms of a predictive EF-EOS (excess function-equation of state) method, which reproduced experimental dew-point temperature data within an AAD (absolute average deviation) of between 0.0 and 1.9 K. 1. Introduction To investigate the influence of carbon dioxide, water, methanol, and heavy hydrocarbons in natural gases on the VLE (vapor-liquid equilibrium) of natural gas within the usual pressure and temperature conditions of natural gas transport by pipeline, we first studied the systems with the lowest number of components, i.e., the carbon dioxide + water and carbon dioxide + water + methanol systems,1 and their mixtures with the major components of natural gas, which are methane and ethane. Given that experimental dew-point data for these systems were not found in the literature within the temperature and pressure ranges of interest, dew points were determined, and the results obtained for the methane + carbon dioxide + water + methanol system are presented here. The aims of the present work were to obtain experimental data on the methane + carbon dioxide + water + methanol dew points within the usual pressure and temperature conditions of natural gas pipelines and to achieve a theoretical model that allowed for adequate predicts of the experimental results obtained. The compositions of methane + carbon dioxide gaseous mixtures (Table 1) were chosen to cover a broad methane/carbon dioxide composition range. The presence of liquid methane + carbon dioxide was avoided. Consequently, the measured dew points of the studied systems are on the right-hand side, in the pressure-temperature diagram, of the dew-point curves of methane + carbon dioxide mixtures. The water dew-point-generation experimental apparatus used in this work was built and commissioned in previous works.2,3 The results of measurements on 14 methane + carbon dioxide + water + methanol mixtures at pressures between 1.0 × 105 and 59.1 × 105 Pa and temperatures from 241.6 to 288.8 K are presented here. The experimental results obtained on the quaternary mixtures were analyzed in terms of an EF-EOS (excess function-equation of state) method that reproduced the experimental dew-point temperature data within an * 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. ‡ Universite´ de la Me´diterrane´e.

Table 1. Composition of Methane or Methane + Carbon Dioxide Mixtures (mol %) and Relative Accuracy Specified by the Supplier component

gas 1

gas 2

carbon dioxide methane

20 ( 1 80 ( 1

70 ( 1 30 ( 1

absolute average deviation (AAD) of between 0.0 and 1.9 K. The good agreement obtained between the experimental and calculated values serves as validation of the predictive model. 2. Experimental Procedure The experimental dew points range from 1.0 × 105 to 59.1 × 105 Pa at temperatures from 241.6 and 288.8 K. The apparatus used for our experimental data collection was thoroughly described in previous works.2,3 In this apparatus, the dew points of pure gaseous compounds and their mixtures can be determined, and mixtures composed of water or water + methanol and pure gaseous compounds or their mixtures can be generated and their dew points determined. For the latter, the experimental method used is based on the generation of saturated gases with water or with water and methanol by the condensation of these compounds in a temperature-controlled condenser with continuous gas flow at specified pressures. In this work, the two methane + carbon dioxide mixtures, gas 1 and gas 2, were saturated with water and methanol at different conditions of pressure and temperature. The methane + carbon dioxide mixtures, whose compositions and accuracies are listed in Table 1, were prepared by Abello´ Linde according to the gravimetric method.4 A scheme of the experimental apparatus used in this work can be seen in Figure 1. After controlled expansion (RV1), the gas is saturated with water and methanol vapor by making the gas flow through an isolated saturator containing a liquid mixture of water and methanol at laboratory temperature (TI1). The temperature of condensation of water and methanol is then achieved in a stainless steel condenser that is 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 concentration of water in the gas is measured at the

10.1021/ie030628t CCC: $27.50 © 2004 American Chemical Society Published on Web 12/17/2003

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Figure 1. Scheme of the experimental apparatus used in this work: RV, control valve; V, ball valve; HV, three-way valve; TI, temperature measurement; PI, pressure measurement; QI, coulometric measurement; XI, volume measurement.

outlet of the condenser, using Karl Fischer titration, following the standard method5 at atmospheric pressure. The concentration of methanol is determined by gas chromatography analysis. In this way, the reference values for the contents of water and methanol in the gaseous phase of the generated VLE are obtained. The dew-point values of the methane + carbon dioxide + water + methanol mixtures generated are measured by means of a chilled mirror instrument. The input pressure (PI6) of the gas to the chilled mirror instrument is set using a regulator valve (RV2). When the apparatus reaches a stable value of dew temperature (TI6), both pressure and temperature are recorded. In this way, the values of the temperature and pressure of the dew-point curve of the mixture are obtained. The following instrumentation is used to analyze the contents of water and methanol and to carry out the dew-point measurements: a Mitsubishi CA 06 Karl Fischer titrator, coupled with an Elster wet gasmeter type Gr. 00, E51, with 0.2% accuracy; an HP 5890 gas chromatograph fit with a Haysep Q column and a thermal conductivity detector; an MBW dew point instrument, model DP3-D-HP-K2, in which the cooling of the mirror is achieved by a cascaded-elements Peltier device and the dew-point mirror temperature is optoelectronically controlled; and a pressure transmitter with a maximum error of 0.1% in the calibrated range. Prior to the study of methane + carbon dioxide + water + methanol dew points, the precision of both analytical methods and experimental procedures was determined. The uncertainty in the dew-point measurements, given by the supplier of the MBW dew point instrument, is (0.2 K for dew-point temperatures between 228.2 and 273.2 K. To obtain the precision of the water content analysis, repeated analyses of the 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 rejection percentage of 0.05%.6 Repeatability and reproducibility of Karl

Fischer titration of this standard nitrogen + water mixture were calculated according to ISO 5725 (1986).7 The values obtained expressed as water molar fractions were 9 × 10-7 and 2.1 × 10-6, respectively. To obtain the relative precision of the methanol content analysis, repeated analyses of the 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 dewpoint generation, repeated generations of nitrogen + water + methanol mixtures were carried out, and the water and methanol contents and dew-point curve were measured. The results obtained in the performance evaluation are the following: For the water content, the repeatability and reproducibility were 0.000 02 and 0.000 04 molar fractions, respectively, corresponding to a mean water molar fraction of 0.001 12. For the methanol content, the repeatability and reproducibility were 0.0002 and 0.0002 molar fractions, respectively, corresponding to a mean methanol molar fraction of 0.0086. For the dew-point pressure, the relative average deviation was 4.2%. For the dew-point temperature, the absolute average deviation was 0.4 K. The test was performed on a water and methanol dew point of 283.15 K and 5 × 105 Pa in pure nitrogen. The reliability test results are taken as consistency criteria: The maximum acceptable standard deviation of measurements is derived from the repeatability value, and the maximum acceptable discrepancy with measurements from external laboratories is derived from the reproducibility value. 3. Results The water and methanol molar fractions for methane + carbon dioxide + water + methanol mixtures generated at the dew-point-generation system, as well as the

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Table 2. Experimental Contents of Water and Methanol and Dew-Point Temperatures and Pressures for Methane + Carbon Dioxide + x j water+ x j methanol Systems T (K)

P (105 Pa)

T (K)

P (105 Pa)

T (K)

P (105 Pa)

T (K)

P (105 Pa)

T (K)

P (105 Pa)

T (K)

P (105 Pa)

gas 1, xjwater ) 0.000 19, xjmethanol ) 0.0018 246.9 1.9 281.2 30.2 251.8 2.9 282.1 32.7 255.6 4.0 282.7 34.3 258.4 5.0 283.3 36.4 261.5 6.3 284.1 38.9 264.5 8.0 284.7 41.2 267.5 10.1 285.1 43.0 269.7 12.0 285.5 44.7 272.0 14.1 286.0 46.9 273.3 16.0 286.3 48.6 274.8 18.0 286.7 50.7 276.2 20.2 287.0 52.5 277.6 22.4 287.3 54.1 278.5 24.3 287.7 56.8 279.7 26.6 288.0 59.1 280.7 29.0

gas 1, xjwater ) 0.000 26, xjmethanol ) 0.0012 243.2 1.2 280.6 24.2 248.7 1.9 282.1 27.5 255.9 3.4 283.2 30.3 262.9 6.0 283.6 31.4 267.1 8.3 284.3 33.4 268.9 9.7 284.9 35.4 270.8 11.2 285.5 37.2 274.1 14.5 286.2 39.2 275.2 15.6 286.8 41.2 276.8 17.8 287.4 43.1 278.1 19.8 287.7 43.8 278.8 21.0

gas 2, xjwater ) 0.000 29, xjmethanol ) 0.0079 254.2 1.1 279.0 6.1 261.7 1.9 280.9 6.9 266.3 2.6 283.2 8.0 269.4 3.1 285.2 9.2 272.4 3.8 286.7 10.2 274.7 4.5 288.6 11.5 277.1 5.3

gas 1, xjwater ) 0.000 22, xjmethanol ) 0.0023 241.6 1.1 279.6 22.2 243.0 1.3 280.8 24.3 247.2 1.8 282.0 26.6 251.9 2.6 282.9 28.6 256.4 3.7 283.8 30.8 262.1 5.8 284.6 33.0 265.2 7.3 285.4 35.3 268.0 9.1 285.8 36.4 270.0 10.5 286.4 38.5 271.5 11.8 286.9 40.1 273.5 13.8 287.3 41.8 275.8 16.5 287.8 43.8 277.1 18.2 288.3 46.3 278.2 19.8

gas 1, xjwater ) 0.000 27, xjmethanol ) 0.0016 252.2 1.9 278.5 15.0 257.8 3.0 280.0 17.1 261.4 4.1 281.6 19.2 264.7 5.3 282.7 20.9 267.1 6.3 283.9 23.0 268.3 7.0 284.9 24.8 270.1 8.0 286.1 27.3 271.7 9.0 286.9 29.1 273.5 10.4 287.3 30.2 274.6 11.2 287.9 31.4 276.8 13.2

gas 2, xjwater ) 0.000 43, xjmethanol ) 0.0023 248.0 1.1 280.2 15.5 249.4 1.3 280.9 16.2 258.0 2.6 282.4 18.4 262.4 3.7 283.4 20.0 266.1 5.0 284.2 21.3 268.9 6.4 285.0 23.0 272.0 8.1 285.9 24.8 274.0 9.4 286.6 26.7 275.6 10.7 287.2 28.2 277.3 12.2 288.2 31.3 278.7 13.6

gas 1, xjwater ) 0.000 33, xjmethanol ) 0.0028 244.5 1.1 280.2 16.8 248.6 1.5 281.4 18.6 258.3 3.2 282.7 20.4 261.8 4.3 283.8 22.4 267.1 6.4 284.8 24.1 268.9 7.3 285.6 25.5 272.4 9.5 286.2 26.6 275.1 11.5 287.0 28.3 277.4 13.8 288.1 30.9 278.7 15.2

gas 1, xjwater ) 0.000 36, xjmethanol ) 0.0029 251.3 1.1 280.3 9.2 258.5 1.9 281.6 10.0 265.2 3.1 282.8 11.0 268.3 3.9 284.0 11.9 273.3 5.6 285.2 13.0 275.4 6.5 286.2 13.9 277.6 7.5 287.5 15.1 278.1 7.9 288.0 15.9

gas 2, xjwater ) 0.000 60, xjmethanol ) 0.0031 250.4 1.1 281.6 11.8 254.9 1.6 282.8 12.9 259.3 2.2 284.4 14.5 265.0 3.4 285.7 15.9 269.0 4.6 287.0 18.0 272.5 6.0 287.7 19.3 274.8 7.1 288.3 20.5 277.8 9.0

gas 1, xjwater ) 0.000 49, xjmethanol ) 0.0053 251.6 1.1 280.1 9.0 252.9 1.2 281.3 9.7 257.1 1.7 282.7 10.5 261.7 2.4 283.7 11.2 266.0 3.4 284.9 12.3 268.9 4.2 286.3 13.4 272.9 5.5 287.1 14.1 276.2 6.9 287.9 14.9 277.9 7.7 288.5 15.6

gas 2, xjwater ) 0.000 22, xjmethanol ) 0.0038 245.5 1.2 281.5 16.9 250.3 1.7 283.9 20.7 262.0 3.9 285.0 22.5 267.9 6.1 285.7 24.0 272.2 8.5 286.2 24.9 274.8 10.2 287.2 27.3 277.2 12.2 287.8 28.3 279.3 14.3 288.3 30.2 280.2 15.3 288.8 31.8

gas 2, xjwater ) 0.001 05, xjmethanol ) 0.0045 255.9 1.0 282.2 7.4 259.4 1.4 284.7 8.7 270.7 3.3 286.1 9.5 274.7 4.4 287.5 10.5 280.2 6.4 288.4 11.2

gas 1, xjwater ) 0.000 16, xjmethanol ) 0.0008 243.2 1.3 279.0 25.3 247.7 1.9 279.9 27.3 252.9 2.9 280.7 29.0 256.6 4.0 281.7 31.3 258.5 4.7 282.2 33.0 261.1 5.9 282.9 34.8 264.8 7.9 283.8 37.5 267.1 9.6 284.2 39.3 269.6 11.6 284.7 41.1 271.5 13.6 285.2 42.8 272.8 15.2 286.0 45.7 274.2 17.2 286.3 47.4 275.5 19.0 286.8 49.6 276.8 21.2 287.6 53.6 278.1 23.3

gas 2, xjwater ) 0.000 20, xjmethanol ) 0.0051 248.2 1.0 279.1 10.3 254.6 1.7 280.8 11.6 259.3 2.5 282.4 13.0 266.7 4.3 285.2 16.2 270.0 5.4 286.2 17.4 273.7 7.0 287.2 18.9 276.4 8.4 288.2 20.3

corresponding dew-point curves, were determined, and the results of experiments are collected in Table 2. As can be seen in Table 2, for methane + carbon dioxide + water + methanol mixtures with similar water concentrations, as in the case of gas 1 + 0.000 26 water molar fraction + 0.0012 methanol molar fraction

and gas 1 + 0.000 27 water molar fraction + 0.0016 methanol molar fraction, for a given value of pressure, an increase in the amount of methanol in the mixture leads to an increase in the dew temperature. For quaternary mixtures with similar contents of methanol, for instance, gas 1 + 0.000 27 water molar

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fraction + 0.0016 methanol molar fraction and gas 1 + 0.000 19 water molar fraction + 0.0018 methanol molar fraction, for a given value of pressure, an increase in the water content in the mixture leads to an increase in the dew temperature. On the other hand, we have calculated the dew-point curves of gases 1 and 2 using the Peng-Robinson cubic equation of state, and it can be seen that the dew-point curve of gas 2 is on the right-hand side of the dew-point curve of gas 1 in the pressure-temperature diagram. This behavior is in accordance with the composition of the gaseous mixtures; the content of the heaviest component in the mixtures, carbon dioxide, is higher in gas 2 than in gas 1. However, if we consider the mixtures gas 1 + 0.000 49 water molar fraction + 0.0053 methanol molar fraction and gas 2 + 0.000 20 water molar fraction + 0.0051 methanol molar fraction, we observe that, for a given pressure, the value of the dew temperature for the second quaternary mixture is lower than that for the first one. Therefore, it seems that the values of the dew temperature and pressure of the quaternary mixtures studied are more sensitive to the water and methanol contents than to the compositions of gases 1 and 2. 4. Theory 4.1. Introduction. Classical models such as UNIQUAC8 or DISQUAC9 allow for the prediction of vaporliquid equilibrium at low pressures for systems that contain a polar compound. In this work, the ranges of dew temperature and pressure studied are within the usual temperature and pressure ranges of natural gas transmission through pipelines, which means low temperatures at high pressures. For this reason, the above-mentioned theoretical models are not suitable for the present work.10 Instead, we use the EF-EOS method, which is derived from the excess function-equation of state model and based on the zeroth approximation of the quasi-reticular model.11 To evaluate the theoretical model used in this paper for the prediction of the dew points of the quaternary system of interest in the temperature and pressure ranges studied, a comparison between experimental and calculated values of the dew-point temperature was carried out. The values of the dew-point temperature for the studied systems were calculated by means of the EF-EOS method11 using the experimental values of pressure and composition obtained in the present work. 4.2. Description of the Excess Function-Equation of State (EF-EOS) Model. To represent the vapor-liquid equilibrium in the mixtures, a model based on the zeroth approximation of Guggenheim’s reticular model was selected. This model was chosen because it allows for the adequate prediction of the dew points of all of the mixtures of current interest in the temperature and pressure ranges examined. 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, where the latter is described by v0/v, with v0 being the molar close-packed volume and v the molar volume. It is assumed that it is possible to define a “covolume” b, proportional to v0, that enables the evaluation of the packing fraction by the ratio η ) b/v. The packing fractions for the pure components and for the mixture are assumed to be the same.

Regarding the EOS used in the EF-EOS model, note that thermodynamic properties of carbon dioxide, such as saturated density, are often represented by cubic equations of state with poor accuracy, especially near the critical point. Therefore, rather than attempting to improve these equations, we used an accurate equation of state for this component, namely, the IUPAC equation.12 For methane, water, and methanol we used the translated Peng-Robinson cubic equation of state13,14 of the form

P)

a(T) RT vj - b h vj (vj + γb h)

(1)

The values of the parameters a and b h depend on the component as follows: For methane, the equations proposed by Rauzy14 were used for the calculation of a, and those proposed by Pe´neloux et al.13 and Rauzy14 were used for the calculation of b h . For water and methanol, the calculation of the attractive parameter, a, was done using the equations of Carrier15 and Carrier h , the equations used were et al.16 For the covolume, b those of Pe´neloux et al.13 and Rauzy.14 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

(2)

i

The residual excess Helmholtz energy, AEres, can be written by means of a formalism that enables the separation of the composition and packing fraction variables

AEres ) E(T,x) Q(η)

(3)

For the first term on the right-hand side of eq 3, we used different expressions depending on the binary interaction in the mixture that we were studying. In particular, for carbon dioxide + water or methanol and for water + methanol,17 we used

E(T,x) )

1

p

p

∑∑ 2i)1j)1

qiqjxixj Eij(T) qm

(4)

For carbon dioxide + water binary interactions, Eij was calculated using the equation17

Eij ) R - βT ln(T) + λT

(5)

with R ) -5018.172, β ) 13.645, and λ ) 102.580 as adjustable parameters. For carbon dioxide + methanol and water + methanol binary interactions, Eij was calculated17 using

Eij ) E0ij

( ) T0 T

r

(6)

In eq 6, E0ij is the interaction energy at the temperature of reference, T 0, and r is a parameter adjusted from experimental data. The values used in this paper for E0ij and r are listed in Table 3.

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Table 3. Values of E0ij and r Used in This Work (Eq 6) E0ij

binary system H2O + CH3OH CO2 + CH3OH

(J cm)

Table 4. Values of the Group Interaction Parameters 0 0 0 0 1Akl, 1Bkl, 2Akl, and 2Bkl Used in This Work (Eqs 13 and 15)

r

0 0 0 0 1Akl 1Bkl 2Akl 2Bkl binary system (106 J m-3) (106 J m-3) (106 J m-3) (106 J m-3)

-3.068 -1.319

253.20 673.15

For carbon dioxide + methane, we used eq 4,18 with Eij calculated by means of a group contribution method as

Eij ) -

1

H2O + CH4 1279.54019 CH3OH + CH4 53.127a a

-0.72619 3.719a

6234.78521 1378.558a

1.47621 -0.832a

This work.

N N

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

(7)

For methane + water or methanol,19 the expression used for E(T,x) was

E(T,x) )

1

p

[

2qm

p

p

p

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

(8)

with

E1ij + E2ij Kij ) 2

(9)

Lij ) E2ij - E1ij

(10)

Lij ) -Lji

(11)

In the above expressions, E1ij is the interchange energy between components i and j in a binary mixture where the molar fraction of j tends to zero, and E2ij is the interchange energy in a binary mixture of i and j where the molar fraction of i tends to zero. E1ij and E2ij were calculated using a group contribution method as follows19

E1ij ) -

1

Figure 2. Comparison between dew-point curves measured experimentally (symbols) and calculated with the EF-EOS method (lines) for gas 1 + xjwater + xjmethanol systems: (b) xjwater ) 0.000 19, xjmethanol ) 0.0018; (O) xjwater ) 0.000 22, xjmethanol ) 0.0023; (9) xjwater ) 0.000 33, xjmethanol ) 0.0028; (0) xjwater ) 0.000 49, xjmethanol ) 0.0053.

N N

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

(12)

with

A1kl ) 1A0kl

( )

0 1Bkl

0

T T

(13)

and with

E2ij ) -

1

N N

(Rik - Rjk)(Ril - Rjl)A2kl(T) ∑ ∑ 2k)1l)1

A2kl ) 2A0kl

( )

(14)

interaction parameters used in this paper for comparison calculations are presented in Table 4.

0 2Bkl

0

T T

Figure 3. Comparison between dew-point curves measured experimentally (symbols) and calculated with the EF-EOS method (lines) for gas 1 + xjwater + xjmethanol systems: (b) xjwater ) 0.000 16, xjmethanol ) 0.0008; (O) xjwater ) 0.000 26, xjmethanol ) 0.0012; (9) xjwater ) 0.000 27, xjmethanol ) 0.0016; (0) xjwater ) 0.000 36, xjmethanol ) 0.0029.

(15)

The superscripts 1 and 2 for A1kl and A2kl have the same meaning as previously explained for E1ij and E2ij.1A0kl, 1 B0kl, 2A0kl, and 2B0kl are group interaction parameters. In this work, these parameters for the interchange energies between methane and methanol were calculated using the experimental results from the literature on the vapor-liquid equilibrium of methane + methanol.20 The parameters for the interchange energies between methane and water were taken from the literature19 or calculated in a previous work.21 The values for group

5. Conclusions In this work, the dew points of the quaternary methane + carbon dioxide + water + methanol system have been studied. The experimental dew-point data and the dew points calculated with the EF-EOS method are represented in Figures 2-5. For the investigated mixtures (Figures 2-5), it can be concluded that, for a given pressure value, the dewpoint temperature increases when the amount of water and methanol also increases. The increase is greater for

Ind. Eng. Chem. Res., Vol. 43, No. 2, 2004 667 Table 5. Experimental Contents of Water and Methanol for Methane + Carbon Dioxide + x j water + x j methanol Systems, Experimental Ranges of Dew-Point Temperatures and Pressures for Methane + Carbon Dioxide + x j water + x j methanol Systems, and Values of AAD for the Dew-Point Curves

Figure 4. Comparison between dew-point curves measured experimentally (symbols) and calculated with the EF-EOS method (lines) for gas 2 + xjwater + xjmethanol systems: (b) xjwater ) 0.000 22, xjmethanol ) 0.0038; (O) xjwater ) 0.000 20, xjmethanol ) 0.0051; (9) xjwater ) 0.000 29, xjmethanol ) 0.0079.

methane + carbon dioxide mixture

xjwater

xjmethanol

T range (K)

P range (105 Pa)

AAD (K)

gas 1 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

0.000 19 0.000 22 0.000 33 0.000 49 0.000 16 0.000 26 0.000 27 0.000 36 0.000 22 0.000 20 0.000 29 0.000 43 0.000 60 0.001 05

0.0018 0.0023 0.0028 0.0053 0.0008 0.0012 0.0016 0.0029 0.0038 0.0051 0.0079 0.0023 0.0031 0.0045

246.9-288.0 241.6-288.3 244.5-288.1 251.6-288.5 243.2-287.6 243.2-287.7 252.2-287.9 251.3-288.0 245.5-288.8 248.2-288.2 254.2-288.6 248.0-288.2 250.4-288.3 255.9-288.4

1.9-59.1 1.1-46.3 1.1-30.9 1.1-15.6 1.3-53.6 1.2-43.8 1.9-31.4 1.1-15.9 1.2-31.8 1.0-20.3 1.1-11.5 1.1-31.3 1.1-20.5 1.0-11.2

1.2 1.9 1.1 1.1 1.4 0.0 1.2 0.2 0.0 0.8 1.3 0.5 1.0 1.0

function-equation of state (EF-EOS) model in this work and in previous efforts,22-26 this model should prove very useful in predicting the hydrocarbon, water, and water + methanol dew points of real natural gases with high contents of carbon dioxide, due to the lack of experimental data for binary mixtures of all components of the so-called natural gas C6+ fraction. Acknowledgment

Figure 5. Comparison between dew-point curves measured experimentally (symbols) and calculated with the EF-EOS method (lines) for gas 2 + xjwater + xjmethanol systems: (b) xjwater ) 0.000 43, xjmethanol ) 0.0023; (O) xjwater ) 0.000 60, xjmethanol ) 0.0031; (9) xjwater ) 0.001 05, xjmethanol ) 0.0045.

high values of pressure than for low values. It seems that the values of the dew temperature and pressure are more sensitive to the water and methanol contents than to the composition of methane + carbon dioxide in the mixtures. The AAD values obtained for each dew-point curve are presented in Table 5. Comparing the experimental and calculated values of the dew-point temperature, it can be concluded that the theoretical methods used in this work adequately reproduce the experimental dewpoint data. The EF-EOS model predicts the dew-point temperature within an AAD of between 0.0 and 1.9 for methane + carbon dioxide + water + methanol mixtures. No influence of the water and methanol contents or of the temperature and pressure was found for the obtained deviation values. In previous works, good results were obtained with this model for the prediction of dew points of synthetic natural gas (SNG), SNG + water mixtures, and SNG + water + methanol mixtures with low and high concentrations of carbon dioxide.22 Because of the excess function-equation of state (EF-EOS) model uses a group contribution method for those systems, the calculation of binary interaction parameters from binary experimental data is not necessary. Considering this and the adequate results obtained with the excess

This work is part of a research project (2FD97-2078) financially supported by the Science and Technology Ministry of Spain and by FEDER funds. The authors also acknowledge the technical support of ENAGAS, S.A., during the experimental part of this work Appendix A For comparison between calculated and experimental dew-point temperatures, for each studied dew-point curve, we used the deviation

AAD )

1

N

cal |Texp ∑ n - Tn | Nn)1

where N is the number of dew points constituting the dew-point curve. Notation Roman Characters 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) b h ) pseudocovolume (m3 mol-1) Eij ) terms of the interchange energy (J m-3) E1ij, E2ij ) terms of the interchange energy between methane and water or methanol (J m-3) Kij, Lij ) binary interaction parameters for methane and water or methanol (J m-3) N ) number of groups in a solution; for calculating AAD, number of dew points constituting a dew-point curve

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p ) number of components in the mixture P ) pressure (Pa) q ) molecular surface area (m2); qi ) δibi, where δi is an adjustable parameter Q ) integral of Q′(η)/η between 0 and η Q′ ) packing fraction function r ) adjustable parameter in the EF-EOS model R ) gas constant (8.314 J mol-1 K-1) T ) temperature (K) T 0 ) reference temperature (298.15 K) v ) molar volume (m3 mol-1) v0 ) molar close-packed volume (m3 mol-1) vj ) molar pseudovolume (m3 mol-1) x ) molar fraction xjwater ) experimental mean value of water molar fraction xjmethanol ) experimental mean value of methanol molar fraction Greek Letters R ) adjustable parameter in the EF-EOS model Rik ) surface area fraction of group k in molecule i β ) adjustable parameter in the EF-EOS model γ ) constant in the translated PR EOS η ) packing fraction λ ) adjustable parameter in the EF-EOS model Ψ ) function of the packing fraction Superscripts and Subscripts cal ) calculated exp ) experimental E ) excess property id ) ideal solution property i, j ) component i, j k, l ) group k, l m ) referring to a mean molecular value n ) point of a dew-point curve in the calculation of AAD res ) residual

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Received for review July 28, 2003 Revised manuscript received October 17, 2003 Accepted October 30, 2003 IE030628T