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Dew points of ternary methane+ethane+butane and quaternary methane+ethane+butane+water mixtures: measurement and correlation
Fluid Phase Equilibria 171 Ž2000. 233–242 www.elsevier.nlrlocaterfluid
Dew points of ternary methaneq ethane q butane and quaternary methaneq ethane q butaneq water mixtures: measurement and correlation Sofıa ´ T. Blanco a , Susana Avila a , Inmaculada Velasco a , Evelyne Rauzy b , Santos Otın ´ a, ) a
Departamento de Quımica Organica y Quımica Fısica, Facultad de Cienciasr Ciudad UniÕersitaria, ´ ´ ´ ´ UniÕersidad de Zaragoza, 50009 Zaragoza, Spain b Laboratoire de Chimie – Physique de Marseille, Faculte´ des Sciences de Luminy, UniÕersite´ de la Mediterranee, ´ 13288 Marseille Cedex 9, France Received 2 February 2000; accepted 2 May 2000
Abstract Dew points for ternary methaneq ethaneq butane and quaternary methaneq ethane q butaneq water mixtures were determined experimentally between 4.77 = 10 5 and 99.45 = 10 5 Pa and at temperatures from 250.92 to 288.54 K. The experimental dew point curves of the mixtures with water were reproduced quite accurately with an excess function–equation of state method, independent of the temperature and pressure ranges. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Dew point; Experimental method; Equation of state; Excess function
1. Introduction Nowadays, there are several suppliers of natural gas in Europe. One of them directly imports natural gas from Algeria through the Magreb–Europe gas pipeline. Previously, most imports were carried out as liquefied natural gas ŽLNG.. LNG contains nitrogen, methane and other light hydrocarbons, which rarely have more than six carbon atoms. The natural gas imported through the gas pipeline, however, can reach a content of heavier hydrocarbons of 0.3% and water content of 65 = 10y6 kg my3 ŽSTP 1 .. Because of this, there is a risk of condensation in pipes, undesired formation of ice or hydrates and the corrosion of the pipes or blockages during transport of LNG. )
Corresponding author. Tel.: q34-976-761199; fax: q34-976-761202. E-mail address: [email protected] ŽS. Otın ´ .. 1 STP: standard temperature and pressure Ž273.15 K, 1.01325=10 5 Pa..
0378-3812r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 Ž 0 0 . 0 0 3 6 8 - X
234
S.T. Blanco et al.r Fluid Phase Equilibria 171 (2000) 233–242
In order to know the vapour–liquid equilibrium behaviour of the Algerian natural gas, in the present work, a synthetic dry mixture of methaneq ethaneq butane is studied, whose composition is defined so that it has the same values of density, high-caloric value and higher dew temperature as the Algerian natural gas transported by the Magreb–Europe gas pipeline. Experimental dew points of one ternary methaneq ethane q butane mixture, and of various methaneq ethane q butane q water mixtures between 4.77 = 10 5 and 99.45 = 10 5 Pa and temperatures from 250.92 to 288.54 K have been measured in order to get an approximate knowledge of the experimental water dew point in Algerian natural gas, which is important for the design of dehydration units. The demand for reliable calculation procedures to estimate these dew points in natural gases is becoming more and more important. Therefore, the experimental results obtained on the quaternary system were analysed in terms of an excess function–equation of state method developed by Peneloux ´ et al. w1x, which reproduces quite well the experimental dew point curves.
2. Experimental 2.1. Gases The gas, a synthetic methaneq ethaneq butane mixture, was supplied by Air Liquide with the specified composition of Ž7 " 0.14. vol.% of ethane and Ž 3.99 " 0.08. vol.% of butane which was verified by chromatographic analysis. 2.2. Apparatus The experimental method used in this work is based on the generation of wet gases by water condensation in two temperature-controlled condensers with continuous gas flow at specified pressures. The experimental device used Žsee Fig. 1. was tested in a previous work w2x. The water concentration in the gas is measured at the outlet of the moisture-generation system using Karl Fischer
Fig. 1. Schematic representation of the experimental device for the generation of wet gases and measurement of dew point curves and water content at saturation.
S.T. Blanco et al.r Fluid Phase Equilibria 171 (2000) 233–242
235
titration, which is carried out at atmospheric pressure, according to the standard method ISO 10101r3 w3x. By doing so, a water content reference value of the gaseous phase is obtained. The dew point values are measured by means of a chilled mirror instrument. The chilled mirror-instrument input pressure is set using a regulator valve. When the apparatus reaches a stable value of dew temperature, both pressure and temperature are recorded. In this way, the value of the dew point pressure as function of temperature of the wet gas is obtained. The dew point curve of the dry mixture is obtained directly, without passing the gas through the moisture-generation system. The instrumentations used for water content and dew point measurements are the following. Ø Mitsubishi CA 06 Karl Fischer Titrator, coupled with an Elster wet gas meter Type Gr. 00, E51, 0.2% accuracy. Ø MBW dew point instrument mod. DP3-D. The cooling of the mirror is achieved by a Peltier cooling unit with automatic mirror check device. The uncertainty in the dew temperature is better than "0.4 K. Ø Pressure transmitter with a maximum error of 0.2% in the calibrated range.
Table 1 Experimental dew point temperatures and pressures for a ternary mixture methaneqethaneqbutane with 7 vol.% ethane and 4 vol.% butane T ŽK.
P Ž10 5 Pa.
T ŽK.
P Ž10 5 Pa.
T ŽK.
P Ž10 5 Pa.
T ŽK.
P Ž10 5 Pa.
253.7 254.0 254.3 254.5 254.7 255.0 255.2 255.4 255.6 255.9 256.1 256.3 256.5 256.7 256.9 257.1 257.3 257.6 257.8 258.6 259.0 259.8 260.7 261.5 262.3
12.7 12.9 13.1 13.3 13.5 13.7 13.8 14.0 14.2 14.4 14.6 14.8 15.0 15.2 15.3 15.5 15.7 15.9 16.1 17.0 17.4 18.2 19.3 20.3 21.3
263.1 263.8 264.5 265.2 265.8 266.4 266.9 267.4 268.0 268.4 268.8 269.2 269.6 270.0 270.3 270.7 270.9 271.1 271.3 271.5 271.8 271.9 272.1 272.3 272.5
22.3 23.4 24.5 25.5 26.6 27.6 28.7 29.8 30.9 31.9 33.0 34.0 35.1 36.1 37.1 38.2 39.3 40.1 41.0 41.9 42.8 43.7 44.7 45.7 46.7
272.6 272.7 272.8 272.9 273.0 273.1 273.1 273.2 273.2 273.3 273.3 273.3 273.3 273.3 273.3 273.3 273.3 273.2 273.2 273.1 273.0 272.9 272.9 272.7 272.7
47.7 48.7 49.7 50.5 51.4 52.2 53.1 54.0 55.0 55.9 56.9 57.8 58.7 59.6 60.6 61.5 62.4 63.4 64.4 65.3 66.2 67.1 68.0 69.0 69.9
272.6 272.4 272.2 272.1 271.9 271.8 271.6 271.4 271.2 270.9 270.7 270.5 270.2 269.9 269.6 269.3 268.9 268.5 268.1 267.7 267.3 266.9 266.6 266.1 265.8
70.8 71.7 72.7 73.6 74.6 75.5 76.4 77.3 78.2 79.2 80.1 80.9 81.9 82.8 83.7 84.6 85.5 86.4 87.3 88.2 89.1 90.0 90.8 91.7 92.5
236
S.T. Blanco et al.r Fluid Phase Equilibria 171 (2000) 233–242
Prior to the study of methaneq ethane q butane and methaneq ethane q butaneq water mixtures, the performance of both the analytical method and the experimental procedures used for the present work was determined w2x. Repeatability and reproducibility of the Karl Fischer titration were Table 2 Experimental dew point temperatures and pressures for quaternary mixtures Ž1y y .Žmethaneqethaneqbutane.q y water4 T ŽK.
P Ž10 5 Pa.
T ŽK.
P Ž10 5 Pa.
y s 0.00012 250.92 256.64 260.07 264.15 266.87 269.04
4.91 10.00 14.90 20.11 25.09 29.94
270.91 272.41 273.15 273.71 274.64 275.47
34.92 39.89 44.96 49.88 54.99 59.84
y s 0.00014 254.77 261.25 266.81 270.78
7.69 15.10 24.96 34.96
273.91 276.55 278.20 279.07
44.90 54.92 64.95 72.95
y s 0.00018 253.65 259.18 264.60 267.90
4.93 9.99 15.15 19.98
270.15 272.56 274.26 275.65
24.90 29.92 35.04 39.88
y s 0.00021 255.37 261.80 266.92 269.42 272.17 273.50 274.91 276.53 278.08 280.02
4.77 9.98 15.57 20.25 25.21 30.32 35.20 40.04 46.59 54.89
281.06 281.85 282.56 283.30 284.13 284.78 285.40 285.84 286.16
60.35 65.16 70.02 74.87 79.96 85.12 89.92 94.69 99.45
y s 0.00031 256.53 263.15 268.11 270.54 272.62 274.72 276.97 278.47 280.22 281.72
4.98 9.68 15.36 19.91 24.98 29.67 34.86 39.43 44.90 49.75
282.74 283.95 284.44 284.99 285.35 286.11 286.81 287.38 288.35 288.54
51.26 60.09 64.93 69.65 74.95 79.21 84.84 88.75 95.30 97.05
S.T. Blanco et al.r Fluid Phase Equilibria 171 (2000) 233–242
237
0.73 = 10y6 and 1.68 = 10y6 kg my3 ŽSTP., respectively, and of the water dew point generation in pure nitrogen, were 3.64 = 10y6 and 8.90 = 10y6 kg my3 ŽSTP., respectively. 2.3. Results The experimental dew points obtained for the methaneq ethaneq butane system are presented in Table 1. The water content in the vapour phase and the dew point curves of the mixtures generated with the moisture-generation system were also determined, and the results of the experiments are collected in Table 2.
3. Theory 3.1. Introduction Classical models as UNIQUAC or NRTL yield good results for vapour–liquid equilibrium of binary systems at low pressures, but are not suitable for high-pressure phase equilibrium calculations. In this work, an excess function–equation of state method developed by Peneloux et al. w1x is used, ´ which allows to describe high-pressure phase equilibria. This approach is found on the zeroth order approximation of Guggenheim’s regular solution model. Other simpler models, like the Peng–Robinson EOS w4x, describes properly the dew point curves of the mixtures with the lowest content of water studied. This work is part of a research that aims to study the influence of the presence of methanol, as an additive of natural gas, on the water dew point. The excess function–equation of state method used in this work includes components with self-association, like methanol. The values of dew temperature and composition of the vapour phase for the quaternary system are calculated by means of the excess function–equation of state method, using the experimental values of pressure obtained in the present work. In order to stand the ability of this method to predict the dew point curves of the quaternary system in the temperature and pressure range studied, a comparison between experimental and calculated values is made. 3.2. Description of the model The model used in the present work is characterised by the following conditions. Ž1. The pure component Helmholtz energies are calculated using equations of state. Ž2. The excess functions are defined at constant packing fraction, given by Õ 0rÕ, where Õ 0 is the molar close-packed volume and Õ the molar volume. It is assumed that it is possible to define a ‘‘covolume’’ b which is proportional to Õ 0 , which enables to evaluate the packing fraction by the ratio h s brÕ. If the packing fraction for the pure components and for the mixture is assumed to be the same, then
hs
b s Õ
bi Õi
Ž i s 1, . . . , p . .
Ž1.
S.T. Blanco et al.r Fluid Phase Equilibria 171 (2000) 233–242
238
The equation of state used in this model is the translated Peng–Robinson cubic equation of state w5,6x of the form Ps
RT
aŽ T .
y
Ž2.
ÕŽ Õqg b.
Õyb
where P and T are the system pressure and temperature, R is the gas constant, Õ is a translated molar volume, also called the pseudo molar volume, and b is the pseudo covolume. The molar Helmholtz energy of a mixture, A, may be written as follows p
A s Aid y RT ln Ž 1 y h . y
Ý is1
x i ai bi
Q Ž h . q AEres
Ž3.
where Aid is the ideal mixture molar Helmholtz energy, a i is the attractive parameter of the translated Peng–Robinson cubic equation of state for the component i w5,6x, bi is the molar covolume for the component i. AEres is the residual excess Helmholtz energy, which depends on the temperature, composition and packing fraction, and which can be written by means of a formalism which enables a separation of composition and packing fraction variables AEres s E Ž T , x . Q Ž h . .
Ž4.
For the first factor on the right hand side of Eq. Ž4., the following equations are used w7x EŽT , x . s
p
1 2 qm
p
Ý qi x i Ý q j x j K i j is1
p
q
js1
p
x j L1r3 Ý qi x i Ý q 1r3 j ji is1
Ž5.
js1
with Kijs
Ei1j q Ei2j
L i j s Ei2j y Ei1j
2
L i j s yL ji
Ž6.
p
qm s
Ý qi x i
and
q i s d i bi
Ž7.
is1
where the subscripts i and j refer to the components i and j of the mixture with p components, and qi is the molecular surface of the component i. It is supposed that Ž qi . rŽ q j . s ŽŽ bi .rŽ bj .. d , where d is an adjustable parameter. K i j and L i j are two binary interaction parameters between components i and j, which depend on the terms of the binary interchange energy, Ei1j and Ei2j , calculated using a group contribution method as follows w7x Ei1j s y Ei2j s y
1 2 1 2
N
N
Ý Ý Ž a i k y a jk .Ž a il y a jl .
A1k l
Ž T . with
A1k l s1
A0k l
ks1 ls1 N
Ý
N
Ý Ž a i k y a jk .Ž a il y a jl . A2k l Ž T . with
ks1 ls1
A2k l s2 A0k l
T0
ž / ž / T
Bk0l 1
T0 T
Bk0l 2
Ž8. Ž9.
where the subscripts k and l refer to groups k and l of the mixture with N different groups, a i k is the surface area fraction of group k in molecule i, T 0 is the reference temperature and 1 A0k l , 1 Bk0l ,
S.T. Blanco et al.r Fluid Phase Equilibria 171 (2000) 233–242
239
Table 3 Values of the group interaction parameters, 1 A0k l , 1 Bk0l , 2 A0k l and 2 Bk0l , used in this work Binary
0 1 Ak l
methaneqwater ethaneqwater butaneqwater
1279.540 w7x 1288.287 w7x 3821.641a
a
Ž10 6 J my3 .
0 1 Bk l
Ž10 6 J my3 .
y0.7259 w7x y1.5595 w7x y0.2890 a
2
A0k l Ž10 6 J my3 .
6234.785a 5946.637 a 6697.505a
2
Bk0l Ž10 6 J my3 .
1.476 a 0.390 a 0.683 a
This work.
A0k l and 2 Bk0l are group interaction parameters. In this work, new values for group interaction parameters 2 A0k l and 2 Bk0l for the binary interchange energy Ei2j between methane and water, and ethane and water are obtained using experimental dew point results available in Enagas, ´ and data from the literature w8x. New values for 1 A0k l , 1 Bk0l , 2 A0k l and 2 Bk0l necessary to calculate the terms of binary interchange energy, Ei1j and Ei2j , between butane and water, have been determined in the present work making use of vapour–liquid equilibrium data from literature w9x. The values obtained for these parameters used in later calculations of the present work are presented in Table 3. 2
4. Discussion As can be seen in Fig. 3, where the experimental and calculated dew point curves obtained for the quaternary system are represented, an increase of water content in the mixtures leads to a shift to
Fig. 2. Experimental dew point curve for the synthetic methaneqethaneqbutane mixture.
240
S.T. Blanco et al.r Fluid Phase Equilibria 171 (2000) 233–242
higher values of the water dew temperature for any value of the pressure. For instance, if the experimental curves in Figs. 2 and 3 are compared, the dew temperature of methaneq ethane q butane mixture is 273.15 K at 60 = 10 5 Pa ŽFig. 2. . If 100.79 = 10y6 kg my3 ŽSTP. Ž y s 0.00012. of water is added, the dew temperature of the mixture is displaced by approximately 2 K Ž Fig. 3. . For the same value of the pressure, the dew temperature of the mixture is 283.95 K when the water content is 248.00 = 10y6 kg my3 ŽSTP. Ž y s 0.00031. ŽFig. 3.. It was also observed that the difference in the dew temperature of the quaternary system and of the ternary system ŽFig. 3. increases as the pressure increases. Thus, the presence of water in the mixture of hydrocarbons leads to an augmentation of the risk of condensation, which is greater as the pressure increases. After comparing the experimental and calculated dew point curves in Fig. 3, it can be concluded that the excess function–equation of state method used in this work for quaternary mixtures reproduces quite accurately the dew point curves in the pressure and temperature range studied. The mean dew point temperature deviations obtained are between 0.78 and 4.08 K, and decrease when the water content increases. The greatest deviations between calculated and experimental dew point temperature are found for the mixtures with the lowest water content. This can be due to the difficulty of measuring dew point curves of these kind of mixtures or to the use of values for the interchange energy Ei1j and Ei2j between butane and water, which were calculated without using experimental dew point results. These data are not available in literature and cannot be obtained using our experimental device.
Fig. 3. Comparison between experimental dew point curves Žsymbol. and calculated with the excess function–equation of state method Žline. for the system Ž1y y .methaneqethaneqbutaneq y water4: B, y s 0.00012; I, y s 0.00014; ', y s 0.00018; D, y s 0.00021; l, y s 0.00031.
S.T. Blanco et al.r Fluid Phase Equilibria 171 (2000) 233–242
241
5. Nomenclature List of symbols a equation of state energy parameter Ž Pa m6 moly2 . A molar Helmholtz energy Ž J moly1 . Akl group interaction parameter between groups k and l ŽJ my3 . b covolume; equation of state size parameter Ž m3 moly1 . b pseudo covolume Žm3 moly1 . 1 2 Ei j , Ei j terms of the interchange energy Ž J my3 . K i j , L i j binary interaction parameters ŽJ my3 . N number of groups in a solution p number of components in the mixture P pressure Ž Pa. q molecular surface Žm2 . Q QXrh integral between 0 and h QX a packing fraction function R gas constant Ž8.314 J moly1 Ky1 . T temperature Ž K. 0 T reference temperature Ž 298.15 K. Õ molar volume Žm3 moly1 . Õ pseudo molar volume Žm3 moly1 . 0 Õ molar close-packed fraction Žm3 moly1 . Greek letters a ik surface area fraction of group k in molecule i g constant of the translated Peng–Robinson cubic equation of state d adjustable parameter, proportionality coefficient between the surface measure, q, and the covolume, Õ h packing fraction Subscripts i,j referring to components i,j k, l referring to groups k, l res residual Superscripts E excess property id ideal solution property
Acknowledgements The authors acknowledge financial and technical support from Enagas ´ during the experimental part of this work.
S.T. Blanco et al.r Fluid Phase Equilibria 171 (2000) 233–242
242
References w1x w2x w3x w4x w5x w6x w7x w8x w9x
A. Peneloux, W. Abdoul, E. Rauzy, Fluid Phase Equilibria 47 Ž1989. 115–132. ´ S.T. Blanco, I. Velasco, E. Rauzy, S. Otın, ´ Fluid Phase Equilibria 161 Ž1999. 107–111. International Standard ISO 10101, 1993. D.Y. Peng, D.B. Robinson, Industrial & Engineering Chemistry Fundamentals 15 Ž1976. 59–64. A. Peneloux, E. Rauzy, R. Freze, ´ ´ Fluid Phase Equilibria 8 Ž1982. 7–23. E. Rauzy. These ` d’Etat–Sciences, Universite´ Aix–Marseille II, 1982. H. Hocq. These ` en Sciences, Universite´ de Droit, d’Economie et des Sciences d’Aix–Marseille III, 1994. H.H. Reamer, R.H. Olds, B.H. Sage, W.N. Lacey, Industrial and Engineering Chemistry 35 Ž1943. 790–793. H.H. Reamer, B.H. Sage, W.N. Lacey, Industrial and Engineering Chemistry 44 Ž1952. 609–615.
Dew points of ternary methaneq ethane q butane and quaternary methaneq ethane q butaneq water mixtures: measurement and correlation Sofıa ´ T. Blanco a , Susana Avila a , Inmaculada Velasco a , Evelyne Rauzy b , Santos Otın ´ a, ) a
Departamento de Quımica Organica y Quımica Fısica, Facultad de Cienciasr Ciudad UniÕersitaria, ´ ´ ´ ´ UniÕersidad de Zaragoza, 50009 Zaragoza, Spain b Laboratoire de Chimie – Physique de Marseille, Faculte´ des Sciences de Luminy, UniÕersite´ de la Mediterranee, ´ 13288 Marseille Cedex 9, France Received 2 February 2000; accepted 2 May 2000
Abstract Dew points for ternary methaneq ethaneq butane and quaternary methaneq ethane q butaneq water mixtures were determined experimentally between 4.77 = 10 5 and 99.45 = 10 5 Pa and at temperatures from 250.92 to 288.54 K. The experimental dew point curves of the mixtures with water were reproduced quite accurately with an excess function–equation of state method, independent of the temperature and pressure ranges. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Dew point; Experimental method; Equation of state; Excess function
1. Introduction Nowadays, there are several suppliers of natural gas in Europe. One of them directly imports natural gas from Algeria through the Magreb–Europe gas pipeline. Previously, most imports were carried out as liquefied natural gas ŽLNG.. LNG contains nitrogen, methane and other light hydrocarbons, which rarely have more than six carbon atoms. The natural gas imported through the gas pipeline, however, can reach a content of heavier hydrocarbons of 0.3% and water content of 65 = 10y6 kg my3 ŽSTP 1 .. Because of this, there is a risk of condensation in pipes, undesired formation of ice or hydrates and the corrosion of the pipes or blockages during transport of LNG. )
Corresponding author. Tel.: q34-976-761199; fax: q34-976-761202. E-mail address: [email protected] ŽS. Otın ´ .. 1 STP: standard temperature and pressure Ž273.15 K, 1.01325=10 5 Pa..
0378-3812r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 Ž 0 0 . 0 0 3 6 8 - X
234
S.T. Blanco et al.r Fluid Phase Equilibria 171 (2000) 233–242
In order to know the vapour–liquid equilibrium behaviour of the Algerian natural gas, in the present work, a synthetic dry mixture of methaneq ethaneq butane is studied, whose composition is defined so that it has the same values of density, high-caloric value and higher dew temperature as the Algerian natural gas transported by the Magreb–Europe gas pipeline. Experimental dew points of one ternary methaneq ethane q butane mixture, and of various methaneq ethane q butane q water mixtures between 4.77 = 10 5 and 99.45 = 10 5 Pa and temperatures from 250.92 to 288.54 K have been measured in order to get an approximate knowledge of the experimental water dew point in Algerian natural gas, which is important for the design of dehydration units. The demand for reliable calculation procedures to estimate these dew points in natural gases is becoming more and more important. Therefore, the experimental results obtained on the quaternary system were analysed in terms of an excess function–equation of state method developed by Peneloux ´ et al. w1x, which reproduces quite well the experimental dew point curves.
2. Experimental 2.1. Gases The gas, a synthetic methaneq ethaneq butane mixture, was supplied by Air Liquide with the specified composition of Ž7 " 0.14. vol.% of ethane and Ž 3.99 " 0.08. vol.% of butane which was verified by chromatographic analysis. 2.2. Apparatus The experimental method used in this work is based on the generation of wet gases by water condensation in two temperature-controlled condensers with continuous gas flow at specified pressures. The experimental device used Žsee Fig. 1. was tested in a previous work w2x. The water concentration in the gas is measured at the outlet of the moisture-generation system using Karl Fischer
Fig. 1. Schematic representation of the experimental device for the generation of wet gases and measurement of dew point curves and water content at saturation.
S.T. Blanco et al.r Fluid Phase Equilibria 171 (2000) 233–242
235
titration, which is carried out at atmospheric pressure, according to the standard method ISO 10101r3 w3x. By doing so, a water content reference value of the gaseous phase is obtained. The dew point values are measured by means of a chilled mirror instrument. The chilled mirror-instrument input pressure is set using a regulator valve. When the apparatus reaches a stable value of dew temperature, both pressure and temperature are recorded. In this way, the value of the dew point pressure as function of temperature of the wet gas is obtained. The dew point curve of the dry mixture is obtained directly, without passing the gas through the moisture-generation system. The instrumentations used for water content and dew point measurements are the following. Ø Mitsubishi CA 06 Karl Fischer Titrator, coupled with an Elster wet gas meter Type Gr. 00, E51, 0.2% accuracy. Ø MBW dew point instrument mod. DP3-D. The cooling of the mirror is achieved by a Peltier cooling unit with automatic mirror check device. The uncertainty in the dew temperature is better than "0.4 K. Ø Pressure transmitter with a maximum error of 0.2% in the calibrated range.
Table 1 Experimental dew point temperatures and pressures for a ternary mixture methaneqethaneqbutane with 7 vol.% ethane and 4 vol.% butane T ŽK.
P Ž10 5 Pa.
T ŽK.
P Ž10 5 Pa.
T ŽK.
P Ž10 5 Pa.
T ŽK.
P Ž10 5 Pa.
253.7 254.0 254.3 254.5 254.7 255.0 255.2 255.4 255.6 255.9 256.1 256.3 256.5 256.7 256.9 257.1 257.3 257.6 257.8 258.6 259.0 259.8 260.7 261.5 262.3
12.7 12.9 13.1 13.3 13.5 13.7 13.8 14.0 14.2 14.4 14.6 14.8 15.0 15.2 15.3 15.5 15.7 15.9 16.1 17.0 17.4 18.2 19.3 20.3 21.3
263.1 263.8 264.5 265.2 265.8 266.4 266.9 267.4 268.0 268.4 268.8 269.2 269.6 270.0 270.3 270.7 270.9 271.1 271.3 271.5 271.8 271.9 272.1 272.3 272.5
22.3 23.4 24.5 25.5 26.6 27.6 28.7 29.8 30.9 31.9 33.0 34.0 35.1 36.1 37.1 38.2 39.3 40.1 41.0 41.9 42.8 43.7 44.7 45.7 46.7
272.6 272.7 272.8 272.9 273.0 273.1 273.1 273.2 273.2 273.3 273.3 273.3 273.3 273.3 273.3 273.3 273.3 273.2 273.2 273.1 273.0 272.9 272.9 272.7 272.7
47.7 48.7 49.7 50.5 51.4 52.2 53.1 54.0 55.0 55.9 56.9 57.8 58.7 59.6 60.6 61.5 62.4 63.4 64.4 65.3 66.2 67.1 68.0 69.0 69.9
272.6 272.4 272.2 272.1 271.9 271.8 271.6 271.4 271.2 270.9 270.7 270.5 270.2 269.9 269.6 269.3 268.9 268.5 268.1 267.7 267.3 266.9 266.6 266.1 265.8
70.8 71.7 72.7 73.6 74.6 75.5 76.4 77.3 78.2 79.2 80.1 80.9 81.9 82.8 83.7 84.6 85.5 86.4 87.3 88.2 89.1 90.0 90.8 91.7 92.5
236
S.T. Blanco et al.r Fluid Phase Equilibria 171 (2000) 233–242
Prior to the study of methaneq ethane q butane and methaneq ethane q butaneq water mixtures, the performance of both the analytical method and the experimental procedures used for the present work was determined w2x. Repeatability and reproducibility of the Karl Fischer titration were Table 2 Experimental dew point temperatures and pressures for quaternary mixtures Ž1y y .Žmethaneqethaneqbutane.q y water4 T ŽK.
P Ž10 5 Pa.
T ŽK.
P Ž10 5 Pa.
y s 0.00012 250.92 256.64 260.07 264.15 266.87 269.04
4.91 10.00 14.90 20.11 25.09 29.94
270.91 272.41 273.15 273.71 274.64 275.47
34.92 39.89 44.96 49.88 54.99 59.84
y s 0.00014 254.77 261.25 266.81 270.78
7.69 15.10 24.96 34.96
273.91 276.55 278.20 279.07
44.90 54.92 64.95 72.95
y s 0.00018 253.65 259.18 264.60 267.90
4.93 9.99 15.15 19.98
270.15 272.56 274.26 275.65
24.90 29.92 35.04 39.88
y s 0.00021 255.37 261.80 266.92 269.42 272.17 273.50 274.91 276.53 278.08 280.02
4.77 9.98 15.57 20.25 25.21 30.32 35.20 40.04 46.59 54.89
281.06 281.85 282.56 283.30 284.13 284.78 285.40 285.84 286.16
60.35 65.16 70.02 74.87 79.96 85.12 89.92 94.69 99.45
y s 0.00031 256.53 263.15 268.11 270.54 272.62 274.72 276.97 278.47 280.22 281.72
4.98 9.68 15.36 19.91 24.98 29.67 34.86 39.43 44.90 49.75
282.74 283.95 284.44 284.99 285.35 286.11 286.81 287.38 288.35 288.54
51.26 60.09 64.93 69.65 74.95 79.21 84.84 88.75 95.30 97.05
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0.73 = 10y6 and 1.68 = 10y6 kg my3 ŽSTP., respectively, and of the water dew point generation in pure nitrogen, were 3.64 = 10y6 and 8.90 = 10y6 kg my3 ŽSTP., respectively. 2.3. Results The experimental dew points obtained for the methaneq ethaneq butane system are presented in Table 1. The water content in the vapour phase and the dew point curves of the mixtures generated with the moisture-generation system were also determined, and the results of the experiments are collected in Table 2.
3. Theory 3.1. Introduction Classical models as UNIQUAC or NRTL yield good results for vapour–liquid equilibrium of binary systems at low pressures, but are not suitable for high-pressure phase equilibrium calculations. In this work, an excess function–equation of state method developed by Peneloux et al. w1x is used, ´ which allows to describe high-pressure phase equilibria. This approach is found on the zeroth order approximation of Guggenheim’s regular solution model. Other simpler models, like the Peng–Robinson EOS w4x, describes properly the dew point curves of the mixtures with the lowest content of water studied. This work is part of a research that aims to study the influence of the presence of methanol, as an additive of natural gas, on the water dew point. The excess function–equation of state method used in this work includes components with self-association, like methanol. The values of dew temperature and composition of the vapour phase for the quaternary system are calculated by means of the excess function–equation of state method, using the experimental values of pressure obtained in the present work. In order to stand the ability of this method to predict the dew point curves of the quaternary system in the temperature and pressure range studied, a comparison between experimental and calculated values is made. 3.2. Description of the model The model used in the present work is characterised by the following conditions. Ž1. The pure component Helmholtz energies are calculated using equations of state. Ž2. The excess functions are defined at constant packing fraction, given by Õ 0rÕ, where Õ 0 is the molar close-packed volume and Õ the molar volume. It is assumed that it is possible to define a ‘‘covolume’’ b which is proportional to Õ 0 , which enables to evaluate the packing fraction by the ratio h s brÕ. If the packing fraction for the pure components and for the mixture is assumed to be the same, then
hs
b s Õ
bi Õi
Ž i s 1, . . . , p . .
Ž1.
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The equation of state used in this model is the translated Peng–Robinson cubic equation of state w5,6x of the form Ps
RT
aŽ T .
y
Ž2.
ÕŽ Õqg b.
Õyb
where P and T are the system pressure and temperature, R is the gas constant, Õ is a translated molar volume, also called the pseudo molar volume, and b is the pseudo covolume. The molar Helmholtz energy of a mixture, A, may be written as follows p
A s Aid y RT ln Ž 1 y h . y
Ý is1
x i ai bi
Q Ž h . q AEres
Ž3.
where Aid is the ideal mixture molar Helmholtz energy, a i is the attractive parameter of the translated Peng–Robinson cubic equation of state for the component i w5,6x, bi is the molar covolume for the component i. AEres is the residual excess Helmholtz energy, which depends on the temperature, composition and packing fraction, and which can be written by means of a formalism which enables a separation of composition and packing fraction variables AEres s E Ž T , x . Q Ž h . .
Ž4.
For the first factor on the right hand side of Eq. Ž4., the following equations are used w7x EŽT , x . s
p
1 2 qm
p
Ý qi x i Ý q j x j K i j is1
p
q
js1
p
x j L1r3 Ý qi x i Ý q 1r3 j ji is1
Ž5.
js1
with Kijs
Ei1j q Ei2j
L i j s Ei2j y Ei1j
2
L i j s yL ji
Ž6.
p
qm s
Ý qi x i
and
q i s d i bi
Ž7.
is1
where the subscripts i and j refer to the components i and j of the mixture with p components, and qi is the molecular surface of the component i. It is supposed that Ž qi . rŽ q j . s ŽŽ bi .rŽ bj .. d , where d is an adjustable parameter. K i j and L i j are two binary interaction parameters between components i and j, which depend on the terms of the binary interchange energy, Ei1j and Ei2j , calculated using a group contribution method as follows w7x Ei1j s y Ei2j s y
1 2 1 2
N
N
Ý Ý Ž a i k y a jk .Ž a il y a jl .
A1k l
Ž T . with
A1k l s1
A0k l
ks1 ls1 N
Ý
N
Ý Ž a i k y a jk .Ž a il y a jl . A2k l Ž T . with
ks1 ls1
A2k l s2 A0k l
T0
ž / ž / T
Bk0l 1
T0 T
Bk0l 2
Ž8. Ž9.
where the subscripts k and l refer to groups k and l of the mixture with N different groups, a i k is the surface area fraction of group k in molecule i, T 0 is the reference temperature and 1 A0k l , 1 Bk0l ,
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Table 3 Values of the group interaction parameters, 1 A0k l , 1 Bk0l , 2 A0k l and 2 Bk0l , used in this work Binary
0 1 Ak l
methaneqwater ethaneqwater butaneqwater
1279.540 w7x 1288.287 w7x 3821.641a
a
Ž10 6 J my3 .
0 1 Bk l
Ž10 6 J my3 .
y0.7259 w7x y1.5595 w7x y0.2890 a
2
A0k l Ž10 6 J my3 .
6234.785a 5946.637 a 6697.505a
2
Bk0l Ž10 6 J my3 .
1.476 a 0.390 a 0.683 a
This work.
A0k l and 2 Bk0l are group interaction parameters. In this work, new values for group interaction parameters 2 A0k l and 2 Bk0l for the binary interchange energy Ei2j between methane and water, and ethane and water are obtained using experimental dew point results available in Enagas, ´ and data from the literature w8x. New values for 1 A0k l , 1 Bk0l , 2 A0k l and 2 Bk0l necessary to calculate the terms of binary interchange energy, Ei1j and Ei2j , between butane and water, have been determined in the present work making use of vapour–liquid equilibrium data from literature w9x. The values obtained for these parameters used in later calculations of the present work are presented in Table 3. 2
4. Discussion As can be seen in Fig. 3, where the experimental and calculated dew point curves obtained for the quaternary system are represented, an increase of water content in the mixtures leads to a shift to
Fig. 2. Experimental dew point curve for the synthetic methaneqethaneqbutane mixture.
240
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higher values of the water dew temperature for any value of the pressure. For instance, if the experimental curves in Figs. 2 and 3 are compared, the dew temperature of methaneq ethane q butane mixture is 273.15 K at 60 = 10 5 Pa ŽFig. 2. . If 100.79 = 10y6 kg my3 ŽSTP. Ž y s 0.00012. of water is added, the dew temperature of the mixture is displaced by approximately 2 K Ž Fig. 3. . For the same value of the pressure, the dew temperature of the mixture is 283.95 K when the water content is 248.00 = 10y6 kg my3 ŽSTP. Ž y s 0.00031. ŽFig. 3.. It was also observed that the difference in the dew temperature of the quaternary system and of the ternary system ŽFig. 3. increases as the pressure increases. Thus, the presence of water in the mixture of hydrocarbons leads to an augmentation of the risk of condensation, which is greater as the pressure increases. After comparing the experimental and calculated dew point curves in Fig. 3, it can be concluded that the excess function–equation of state method used in this work for quaternary mixtures reproduces quite accurately the dew point curves in the pressure and temperature range studied. The mean dew point temperature deviations obtained are between 0.78 and 4.08 K, and decrease when the water content increases. The greatest deviations between calculated and experimental dew point temperature are found for the mixtures with the lowest water content. This can be due to the difficulty of measuring dew point curves of these kind of mixtures or to the use of values for the interchange energy Ei1j and Ei2j between butane and water, which were calculated without using experimental dew point results. These data are not available in literature and cannot be obtained using our experimental device.
Fig. 3. Comparison between experimental dew point curves Žsymbol. and calculated with the excess function–equation of state method Žline. for the system Ž1y y .methaneqethaneqbutaneq y water4: B, y s 0.00012; I, y s 0.00014; ', y s 0.00018; D, y s 0.00021; l, y s 0.00031.
S.T. Blanco et al.r Fluid Phase Equilibria 171 (2000) 233–242
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5. Nomenclature List of symbols a equation of state energy parameter Ž Pa m6 moly2 . A molar Helmholtz energy Ž J moly1 . Akl group interaction parameter between groups k and l ŽJ my3 . b covolume; equation of state size parameter Ž m3 moly1 . b pseudo covolume Žm3 moly1 . 1 2 Ei j , Ei j terms of the interchange energy Ž J my3 . K i j , L i j binary interaction parameters ŽJ my3 . N number of groups in a solution p number of components in the mixture P pressure Ž Pa. q molecular surface Žm2 . Q QXrh integral between 0 and h QX a packing fraction function R gas constant Ž8.314 J moly1 Ky1 . T temperature Ž K. 0 T reference temperature Ž 298.15 K. Õ molar volume Žm3 moly1 . Õ pseudo molar volume Žm3 moly1 . 0 Õ molar close-packed fraction Žm3 moly1 . Greek letters a ik surface area fraction of group k in molecule i g constant of the translated Peng–Robinson cubic equation of state d adjustable parameter, proportionality coefficient between the surface measure, q, and the covolume, Õ h packing fraction Subscripts i,j referring to components i,j k, l referring to groups k, l res residual Superscripts E excess property id ideal solution property
Acknowledgements The authors acknowledge financial and technical support from Enagas ´ during the experimental part of this work.
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References w1x w2x w3x w4x w5x w6x w7x w8x w9x
A. Peneloux, W. Abdoul, E. Rauzy, Fluid Phase Equilibria 47 Ž1989. 115–132. ´ S.T. Blanco, I. Velasco, E. Rauzy, S. Otın, ´ Fluid Phase Equilibria 161 Ž1999. 107–111. International Standard ISO 10101, 1993. D.Y. Peng, D.B. Robinson, Industrial & Engineering Chemistry Fundamentals 15 Ž1976. 59–64. A. Peneloux, E. Rauzy, R. Freze, ´ ´ Fluid Phase Equilibria 8 Ž1982. 7–23. E. Rauzy. These ` d’Etat–Sciences, Universite´ Aix–Marseille II, 1982. H. Hocq. These ` en Sciences, Universite´ de Droit, d’Economie et des Sciences d’Aix–Marseille III, 1994. H.H. Reamer, R.H. Olds, B.H. Sage, W.N. Lacey, Industrial and Engineering Chemistry 35 Ž1943. 790–793. H.H. Reamer, B.H. Sage, W.N. Lacey, Industrial and Engineering Chemistry 44 Ž1952. 609–615.