- Email: [email protected]
Water dew points of binary nitrogen+water and propane+water mixtures. Measurement and correlation
Fluid Phase Equilibria 161 Ž1999. 107–117
Water dew points of binary nitrogenq water and propaneq water mixtures. Measurement and correlation Sofıa ´ T. Blanco a , Inmaculada Velasco a , Evelyne Rauzy b , Santos Otın ´ a
a, )
Departamento de Quımica Organica y Quımica Fısica, Facultad de Ciencias, UniÕersidad de Zaragoza, 50.009, Zaragoza, ´ ´ ´ ´ Spain b Laboratoire de Chimie-Physique de Marseille, Faculte´ des Sciences de Luminy, UniÕersite´ de la Mediterranee, ´ 13.288, Marseille Cedex 9, France Received 30 September 1998; accepted 3 March 1999
Abstract A water dew point generation bench has been built and tested. Experimental measurements of dew point for binary nitrogenq water and propaneq water were carried out between 1.01 = 10 5 Pa and 109.61 = 10 5 Pa and temperatures from 249.80 to 283.93 K. An excess function–equation of state method reproduces quite accurately the experimental curves independently of the pressure range. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Dew point; Experimental method; Equation of state; Excess function
1. Introduction The exact knowledge of the experimental water dew point in natural gases is important in the design of dehydration units to prevent the undesired formation of ice or hydrates and the corrosion of the pipes or blockages during transport. On the other hand, the demand for reliable calculation procedures for the estimation of these dew points in natural gases becomes more and more important. We present here experimental dew points of the binary nitrogenq water and propaneq water mixtures between 1.01 = 10 5 Pa and 109.61 = 10 5 Pa from 249.80 to 283.93 K. The experimental results were analysed in terms of an excess-equation of state method developed by Peneloux et al. w1x. ´
)
Corresponding author. Tel.: q34-976-761199; fax: q34-976-761202; e-mail: [email protected]
0378-3812r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 Ž 9 9 . 0 0 1 6 4 - 8
S.T. Blanco et al.r Fluid Phase Equilibria 161 (1999) 107–117
108
2. Experimental 2.1. Apparatus and operating procedure The experimental method used for 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 water concentration of the gas is measured at the outlet of the moisture generation bench, using a Karl Fischer titration, according to the standard method ISO 10101r3 w2x. Doing so, a water content reference value of the gaseous phase is obtained. In the titration cell, the Karl Fischer reagent w3x is the electrolyte in the anodic cell, composed of methanol, dioxide of sulphur associated to pyridine and iodine associated to pyridine. Methanol and pyridine are contained in the cathodic cell. When the sample is introduced by bubbling into the solution of the anodic cell, the molecules of water react according to Ž1. with the iodine generated in Ž2., I 2 q SO 2 q 3 Py q CH 3 OH q H 2 O ™ 2 Py HI q Py HSO4CH 3
Ž1.
2 Iyy 2 ey™ I 2
Ž2.
Whereas the reaction Ž3. is produced in the cathode, CH 3 OH q ey™ CH 3 Oyq
1 2
H2.
Ž3.
According to the Faraday’s law, the quantity of iodine generated in Ž 2. is directly proportional to the quantity of electricity. Based on this principle, the quantity of water in the gas can be calculated from the quantity of electricity required to the electrolysis. The volume of the gas that passes through the titration cell is measured by means of a gas meter, which it is equipped with systems to measure the pressure and the temperature, in order to calculate the volume of gas in normal conditions Ž 273.15 K and 1.01325 = 10 5 Pa. . The dew point values are measured by a chilled mirror instrument achieved at line pressure, in parallel with the Karl Fischer titration at atmospheric pressure. By means of a control valve, the pressure inlet to the chilled mirror instrument is engaged. After that, the dew point temperature is measured. Doing so, we obtain the values of the dew point temperature and pressure of the wet gas generated dew point curve. The water dew point generation bench used for our experimental data collection is presented in Fig. 1. After controlled expansion ŽPI1. , the gas is saturated with water vapour by flowing through liquid water in a thermally insulated saturator held at laboratory temperature. The temperature-controlled water condensation is then achieved in two successive stainless steel condensers. The first condenser temperature ŽTI2. is set to a value lying between ambient and the temperature of the second condenser ŽTI3. . Doing so, the quantity of liquid collected into the second condenser is minimised. In order to avoid any recondensation, the expansion at the Karl Fischer Titrator inlet is made using a heated valve ŽRV3. . The instrumentation used for water content and dew point measurements are the following: –Mitsubishi CA 06 Karl Fischer Titrator, coupled with an Elster wet gas meter Type Gr. 00, E51, 0.2% uncertainty.
S.T. Blanco et al.r Fluid Phase Equilibria 161 (1999) 107–117
109
Fig. 1. Moisture generation bench. RV: Control valve, V: Ball valve, TI: Temperature measurement, PI: Pressure measurement, QI: Coulometric measurement, XI: Volume measurement.
–MBW dew point instrument Mod. DP3-D. The cooling of the mirror is achieved by a Peltier cooling with automatic mirror check device. The uncertainty on the dew temperature is better than "0.4 K. –Pressure transmitter with a maximum error of 0.2% in the calibrated range. 2.2. Results and comparison with literature data The dew point pressure values range from 4.21 = 10 5 Pa to 109.61 = 10 5 Pa and the temperature values range from 249.80 to 283.93 K for nitrogenq water mixtures. The dew point pressure values range from 1.01 = 10 5 Pa to 4.99 = 10 5 Pa and the temperature values range from 256.21 to 283.84 K for propaneq water mixtures. The propaneq water system is studied in the low-pressure range because of the vapour pressure values of propane in the temperature values range where the generation of the mixtures propaneq water is carried out. Nitrogen and propane gases were supplied by Air Liquide with the specified purity of 99.999 vol.% and 99.95 vol.%, respectively, and were used without further treatment. Previous to the study of nitrogenq water and propaneq water, we determined the performance of the methods used for the present work. Repeatability and reproducibility of the Karl Fischer titration and the dewpoint generation were calculated according to ISO 5725 w4x after repetitive measurements. The results are presented in Table 1. Reference conditions for volume are 273.15 K and 1.01325 = 10 5 Pa. Test A was achieved on one standard gas prepared by Air Liquide. Test B was achieved on a
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S.T. Blanco et al.r Fluid Phase Equilibria 161 (1999) 107–117
Table 1 Performance evaluation of water content measurements
Mean valuer10y6 kg my3 Ž n. Repeatabilityr10y6 kg my3 Ž n. Reproducibilityr10y6 kg my3 Ž n.
Test A Karl Fischer
Test B Dew point generation 263.15 K and 60=10 5 Pa
59.26 0.73 1.68
43.08 3.64 8.90
water dewpoint of 263.15 K and 60 = 10 5 Pa in pure nitrogen. The reliability tests result is taken as consistency criteria: the maximum acceptable standard deviation of measurements is derived from the repeatability value, and the maximum acceptable discrepancy with the literature measurements is derived from the reproducibility value. The water concentration in the vapour phase and the dew point curve of the mixtures generated at the generation bench are determined. The results of the experiments are recorded in Tables 2 and 3. The literature data w5,6x agree quite well with our results obtained for the nitrogenq water system. There are differences in the dew point temperature, which fluctuate between 0.15 to 28 with data from Bogoya et al. w5x and up to 58 with data from Kosyakov et al. w6x. For the propaneq water system we could not compare the results obtained.
3. Theory 3.1. Introduction Classical models such as UNIQUAC or NRTL yield good results for vapour–liquid equilibrium under low pressure for binary systems but are not applicable for high-pressure phase equilibrium calculations. In this work, we use an excess function–equation of state method developed by Peneloux et al. w1x ´ founded on the zeroth order approximation of Guggenheim’s reticular model. Other simpler correlation as Dalton’s law calculates properly the dew point curves of the systems studied below 80 = 10 5 Pa. This work is the first part of a research that aims to study the influence of the presence of methanol, as an additive of natural gas, in the water dew point. The excess function–equation of state method used in this work allows to be modified to have into account the self-association of methanol in the mixtures. 3.2. Description of the model This model is characterised as follows: Ž1. The pure component Helmholtz energies are calculated from equations of state. Ž2. The excess functions are defined at constant packing fraction, the latter described by Õ 0rÕ, Õ 0 being the molar close-packed volume. It is assumed that it is possible to define a ‘covolume’ bi
S.T. Blanco et al.r Fluid Phase Equilibria 161 (1999) 107–117
111
Table 2 Experimental dew points temperatures and pressures for binary mixtures Ž1y y . nitrogenq y water4 T ŽK.
P Ž10 5 Pa.
T ŽK.
P Ž10 5 Pa.
y s 0.00008 253.17 259.64 263.39 266.30 268.34 270.23
9.81 19.74 29.49 39.63 49.15 59.94
271.71 273.04 274.10 275.20 276.13
69.80 80.04 89.11 99.71 109.61
y s 0.00010 249.80 255.63 259.77 262.52 264.67 266.64 268.20
4.72 9.94 14.93 19.72 24.80 30.07 34.89
269.81 272.08 274.32 275.78 277.09 278.43 279.55
39.75 49.52 59.75 69.61 79.65 89.77 100.57
y s 0.00014 252.61 260.02 264.25 267.26 269.50 271.48 272.85 274.06 275.47
4.21 9.39 15.05 20.19 25.31 30.06 35.09 39.89 45.56
276.72 277.90 278.70 279.74 280.63 281.50 282.53 283.93
49.99 54.47 60.00 64.46 69.76 74.86 84.91 99.22
y s 0.00026 257.44 265.12 269.29 272.39 275.07
4.37 9.88 14.91 19.59 24.71
277.40 279.27 280.92 282.34 283.24
29.53 34.55 39.44 44.44 49.21
proportional to Õ 0 , which enables measuring the packing fraction by the ratio h s brÕ. The packing fraction for pure components as for the mixture are the same. Those assumptions lead to:
hs
b s Õ
bi Õi
Ž i s 1, . . . , p .
Ž1.
The molar Helmholtz energy of a mixture may be written as follows: p id
A s A y RT ln Ž 1 y h . y
Ý is1
x i ai bi
Q Ž h . q AEres
Ž2.
S.T. Blanco et al.r Fluid Phase Equilibria 161 (1999) 107–117
112
Table 3 Experimental dew points temperatures and pressures for binary mixtures Ž1y y . propaneq y water4 T ŽK.
P Ž10 5 Pa.
T ŽK.
P Ž10 5 Pa.
y s 0.00127 256.21 258.05 259.66 261.10 262.40 263.50 265.61 266.52 267.33 268.12
1.01 1.21 1.41 1.61 1.81 2.01 2.41 2.61 2.80 3.00
268.89 269.57 270.26 270.88 271.31 272.07 272.70 273.33 273.63
3.21 3.40 3.61 3.80 4.00 4.20 4.40 4.60 4.66
y s 0.00147 257.45 259.22 260.90 262.46 263.78 264.99 265.99 266.99 267.95 268.82
1.01 1.19 1.41 1.61 1.80 2.01 2.21 2.41 2.60 2.81
269.62 270.53 271.74 272.44 273.22 273.94 274.61 275.22 275.45
3.01 3.21 3.61 3.80 4.01 4.21 4.41 4.60 4.68
y s 0.00178 257.54 258.63 260.71 262.43 263.96 265.43 266.45 268.65 269.62 270.57
1.04 1.15 1.36 1.57 1.78 2.01 2.16 2.56 2.77 2.96
271.49 272.43 273.35 274.14 274.91 275.52 276.26 276.90 277.53 278.12
3.16 3.39 3.58 3.80 4.00 4.20 4.40 4.60 4.80 4.99
y s 0.00215 259.91 261.91 263.72 265.34 266.82 268.16 269.44 270.60 271.72 272.72 273.67
1.02 1.21 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00
274.59 275.38 276.23 277.02 277.69 278.49 279.06 279.71 280.46 280.87
3.20 3.40 3.60 3.81 4.00 4.21 4.40 4.60 4.80 4.99
S.T. Blanco et al.r Fluid Phase Equilibria 161 (1999) 107–117
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Table 3 Žcontinued. T ŽK.
P Ž10 5 Pa.
T ŽK.
P Ž10 5 Pa.
y s 0.00278 262.29 264.44 266.30 268.07 269.61 271.05 272.29 273.40 274.68 275.65 276.65
1.01 1.21 1.40 1.60 1.81 2.00 2.21 2.40 2.61 2.80 3.00
277.48 278.43 279.19 280.06 280.84 281.47 282.16 282.83 283.55 283.84
3.20 3.40 3.61 3.81 4.01 4.20 4.41 4.61 4.81 4.93
where Aid is the ideal mixture molar Helmholtz energy, a i is the component i attractive parameter of a translated Peng–Robinson cubic equation of state w7,8x, bi is the component i covolume, QŽh . is a function of the packing fraction h , and AEres is the residual excess Helmholtz energy which we shall explain later. The properties of pure components have been represented by a translated Peng–Robinson cubic equation of state w7,8x of the form: Ps
RT
aŽ T .
y
ÕŽ Õqg b.
Õyb
Ž3.
where Õ is a translated volume called the pseudo-volume and b is the pseudo-covolume, calculated as follows: b s 0.045572
RTc
Ž4.
Pc
The parameter a is a function of the temperature; the equations used for its calculation are proposed by Carrier w9x and Carrier et al. w10x. The compressibility factor is expressed as follows: zs
1 1yh
y a QX Ž h .
Ž5.
where P
as
Ý is1
x i ai
y
bi RT
EŽT , x . RT
Ž6.
with QX Ž h . s
h 1 q gh
and g s 2 Ž '2 q 1 .
Ž7.
S.T. Blanco et al.r Fluid Phase Equilibria 161 (1999) 107–117
114
Table 4 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
0 1 Bk l
2
Nitrogenqwater Propaneqwater
2274.281 w11x 3121.348 a
y1.1148 w11x y1.7930 a
8712.375a 5553.582 a
a
A0k l
2
Bk0l
7.140 a 1.283 a
This work.
The parameter g value used is characteristic of the equation of state under consideration, namely the translated Peng–Robinson cubic equation of state w7,8x. The residual excess Helmholtz energy, AEres depends on the temperature, the composition and the packing fraction, and is written by means of a formalism which enables separating the composition and packing fraction variables: AEres s E Ž T , x . Q Ž h . where QŽh . is the integral of QX Žh .rh ŽEq. Ž7.. whose lower limit is zero if h ™ 0. For the first term on the right hand side of Eq. Ž8., the following equations are used w11x: p p p p 1 EŽT , x . s q x q x K q q x x j L1r3 Ý Ý Ý i i Ý q 1r3 j ji 2 qm is1 i i jsi j j i j is1 js1
Ž8.
Ž9.
with Kijs
Ei1j q Ei2j
and
2
L i j s Ei2j y Ei1j L i j s yL ji
Ž 10.
p
qm s
Ý qk x k
and
qk s d k b k
Ž 11.
ks1
where qirq j s Ž birbj . d , d being an adjustable parameter. K i j and L i j are two binary interaction parameters, which depend on the terms of the interchange energy, Ei1j and Ei2j , are calculated using a group contribution method as follows w11x: 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
N
Ý Ý Ž a i k y a jk .Ž a il y a jl . A2k l Ž T . ks1 ls1
with
A2k l s2 A0k l
T0
ž / ž /
0 1 Bk l
Ž 12.
T
T0 T
0 2 Bk l
Ž 13.
where 1 A0k l , 1 Bk0l , 2 A0k l and 2 Bk0l are four group interaction parameters. In this work, we obtain some of these parameters using the experimental results presented in this paper and others from the literature w12x. The values of these parameters used in this work are presented in Table 4. 4. Comparison with experiment and discussion As can be seen in Figs. 2 and 3, an increase of the water content in the mixtures of each system studied leads to higher values of temperature at constant pressure or lower values of pressure at constant temperature.
S.T. Blanco et al.r Fluid Phase Equilibria 161 (1999) 107–117
115
Fig. 2. Comparison between experimental dew point curves Žsymbol. and calculated with the excess function–equation of state method Žline. for the system Ž1y y . nitrogenq y water4: B, y s 0.00008; I, y s 0.00010; v, y s 0.00014; ` y s 0.00026.
The excess function–equation of state method used in this work reproduces quite accurately the dew point curves independently of the pressure range. We obtain mean deviations between 1.03 and 1.96 K on the nitrogenq water system ŽFig. 2. and between 0.19 and 1.94 K on the propaneq water ŽFig. 3.. For each one of nine binary mixtures studied, the calculated values for dew points temperatures are those for which the experimental and calculated values for molar fraction of water vapour are exactly the same.
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 . propaneq y water4: B, y s 0.00127; I, y s 0.00147; v, y s 0.00178; ` y s 0.00215; ', y s 0.00278.
S.T. Blanco et al.r Fluid Phase Equilibria 161 (1999) 107–117
116
To apply correctly the thermodynamic method, it was necessary to calculate new values only for the group interaction parameters concerning the terms for the interchange energy Ei2j between water and nitrogen or propane molecules in the vapour phase. This term represents the molecular interactions between the components of the mixture in the phase of the liquid–vapour equilibrium where the non polar component is the majority; in the systems studied in this paper this phase is the vapour one. On the dew point curve, the mixture is totally a vapour phase w13x, so this fact can explain the results obtained. For the dew temperature calculations, the greatest deviations of the two binary systems occur for the mixtures with lowest water contents. It can be due, on the one hand, to the experimental error for the very low water content analysis and on the other, to the greater difficulty calculations with the theoretical method the dew temperature for these kind of mixtures.
5. List of symbols a A A k l , Bk l b b Ei1j , Ei2j K i j, Li j N p P q Q QX R T T0 Õ Õ Õ0 y
Equation of state energy parameter Ž Pa m6 moly2 . Molar Helmholtz energy Ž J moly1 . Group interaction parameters between groups k and l ŽJ my3 . Covolume; equation of state size parameter Ž m3 moly1 . Pseudo covolume Žm3 moly1 . Terms of the interchange energy Ž J my3 . Binary interaction parameters Ž J my3 . Number of groups in a solution Number of components in the mixture Pressure Ž Pa. Molecular surface Žm2 . QXrh integral between 0 and h A packing fraction function Gas constant Ž8.314 J moly1 Ky1 . Temperature ŽK. Reference temperature Ž298.15 K. Molar volume Žm3 moly1 . Pseudo molar volume Ž m3 moly1 . Molar close packed fraction Žm3 moly1 . Molar fraction of water in the vapour phase, its value is calculated multiplying the water content value in Ž10y6 kg my3 Žn.. by Ž10y6 22.4r18.01.
Greek letters aik 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
S.T. Blanco et al.r Fluid Phase Equilibria 161 (1999) 107–117
Subscripts c i, j k, l res
117
Critical property Referring to components i, j Referring to groups k, l Residual
Superscripts E Excess property id Ideal solution property
Acknowledgements The authors acknowledge the financial and technical support of ENAGAS, during the experimental part of this work.
References w1x A. Peneloux, W. Abdoul, E. Rauzy, Fluid Phase Equilibria 47 Ž1989. 115–132. ´ w2x International Standard ISO 10101, 1993. w3x K. Fischer, Neues vertahren zur wass-analytischen bestimmung des wassergehaltes von flussigkeiten und festen ¨ koorpen, Angewandte Chemie 26 Ž1935. 394. ¨ w4x International Standard ISO 5725, 1986. w5x D. Bogoya, C. Muller, L.R. Oellrich, Wiss. Abschlubber 28 Ž1993. 54–63. ¨ w6x N.E. Kosyakov, B.Y. Ivchenko, P.P. Krishtopa, Vopr. Khim. Tekhnol. 11 Ž1977. 2568–2570. w7x A. Peneloux, E. Rauzy, R. Freze, ´ ´ Fluid Phase Equilibria 8 Ž1982. 7–23. w8x E. Rauzy. These ` d’Etat-Sciences, Universite´ Aix-Marseille II, 1982. w9x B. Carrier. These ` de Docteur en Sciences, Universite´ Aix-Marseille III, 1989. w10x B. Carrier, M. Rogalski, A. Peneloux, Ind. Eng. Chem. Res. 27 Ž1988. 1714–1721. ´ w11x H. Hocq. These ` en Sciences, Universite´ de Droit, d’Economie et des Sciences d’Aix-Marseille III, 1994. w12x R. Kobayashi, D.L. Katz, Industrial and engineering chemistry 45 Ž1953. 440–446. w13x J.M. Prausnitz, R.N. Lichtenthaler, E. Gomes de Azevedo, Molecular Thermodynamics of Fluid Phase Equilibria, PTR Prentice-Hall, Englewood Cliffs, NJ 07632, 1986, p. 449.
Water dew points of binary nitrogenq water and propaneq water mixtures. Measurement and correlation Sofıa ´ T. Blanco a , Inmaculada Velasco a , Evelyne Rauzy b , Santos Otın ´ a
a, )
Departamento de Quımica Organica y Quımica Fısica, Facultad de Ciencias, UniÕersidad de Zaragoza, 50.009, Zaragoza, ´ ´ ´ ´ Spain b Laboratoire de Chimie-Physique de Marseille, Faculte´ des Sciences de Luminy, UniÕersite´ de la Mediterranee, ´ 13.288, Marseille Cedex 9, France Received 30 September 1998; accepted 3 March 1999
Abstract A water dew point generation bench has been built and tested. Experimental measurements of dew point for binary nitrogenq water and propaneq water were carried out between 1.01 = 10 5 Pa and 109.61 = 10 5 Pa and temperatures from 249.80 to 283.93 K. An excess function–equation of state method reproduces quite accurately the experimental curves independently of the pressure range. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Dew point; Experimental method; Equation of state; Excess function
1. Introduction The exact knowledge of the experimental water dew point in natural gases is important in the design of dehydration units to prevent the undesired formation of ice or hydrates and the corrosion of the pipes or blockages during transport. On the other hand, the demand for reliable calculation procedures for the estimation of these dew points in natural gases becomes more and more important. We present here experimental dew points of the binary nitrogenq water and propaneq water mixtures between 1.01 = 10 5 Pa and 109.61 = 10 5 Pa from 249.80 to 283.93 K. The experimental results were analysed in terms of an excess-equation of state method developed by Peneloux et al. w1x. ´
)
Corresponding author. Tel.: q34-976-761199; fax: q34-976-761202; e-mail: [email protected]
0378-3812r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 Ž 9 9 . 0 0 1 6 4 - 8
S.T. Blanco et al.r Fluid Phase Equilibria 161 (1999) 107–117
108
2. Experimental 2.1. Apparatus and operating procedure The experimental method used for 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 water concentration of the gas is measured at the outlet of the moisture generation bench, using a Karl Fischer titration, according to the standard method ISO 10101r3 w2x. Doing so, a water content reference value of the gaseous phase is obtained. In the titration cell, the Karl Fischer reagent w3x is the electrolyte in the anodic cell, composed of methanol, dioxide of sulphur associated to pyridine and iodine associated to pyridine. Methanol and pyridine are contained in the cathodic cell. When the sample is introduced by bubbling into the solution of the anodic cell, the molecules of water react according to Ž1. with the iodine generated in Ž2., I 2 q SO 2 q 3 Py q CH 3 OH q H 2 O ™ 2 Py HI q Py HSO4CH 3
Ž1.
2 Iyy 2 ey™ I 2
Ž2.
Whereas the reaction Ž3. is produced in the cathode, CH 3 OH q ey™ CH 3 Oyq
1 2
H2.
Ž3.
According to the Faraday’s law, the quantity of iodine generated in Ž 2. is directly proportional to the quantity of electricity. Based on this principle, the quantity of water in the gas can be calculated from the quantity of electricity required to the electrolysis. The volume of the gas that passes through the titration cell is measured by means of a gas meter, which it is equipped with systems to measure the pressure and the temperature, in order to calculate the volume of gas in normal conditions Ž 273.15 K and 1.01325 = 10 5 Pa. . The dew point values are measured by a chilled mirror instrument achieved at line pressure, in parallel with the Karl Fischer titration at atmospheric pressure. By means of a control valve, the pressure inlet to the chilled mirror instrument is engaged. After that, the dew point temperature is measured. Doing so, we obtain the values of the dew point temperature and pressure of the wet gas generated dew point curve. The water dew point generation bench used for our experimental data collection is presented in Fig. 1. After controlled expansion ŽPI1. , the gas is saturated with water vapour by flowing through liquid water in a thermally insulated saturator held at laboratory temperature. The temperature-controlled water condensation is then achieved in two successive stainless steel condensers. The first condenser temperature ŽTI2. is set to a value lying between ambient and the temperature of the second condenser ŽTI3. . Doing so, the quantity of liquid collected into the second condenser is minimised. In order to avoid any recondensation, the expansion at the Karl Fischer Titrator inlet is made using a heated valve ŽRV3. . The instrumentation used for water content and dew point measurements are the following: –Mitsubishi CA 06 Karl Fischer Titrator, coupled with an Elster wet gas meter Type Gr. 00, E51, 0.2% uncertainty.
S.T. Blanco et al.r Fluid Phase Equilibria 161 (1999) 107–117
109
Fig. 1. Moisture generation bench. RV: Control valve, V: Ball valve, TI: Temperature measurement, PI: Pressure measurement, QI: Coulometric measurement, XI: Volume measurement.
–MBW dew point instrument Mod. DP3-D. The cooling of the mirror is achieved by a Peltier cooling with automatic mirror check device. The uncertainty on the dew temperature is better than "0.4 K. –Pressure transmitter with a maximum error of 0.2% in the calibrated range. 2.2. Results and comparison with literature data The dew point pressure values range from 4.21 = 10 5 Pa to 109.61 = 10 5 Pa and the temperature values range from 249.80 to 283.93 K for nitrogenq water mixtures. The dew point pressure values range from 1.01 = 10 5 Pa to 4.99 = 10 5 Pa and the temperature values range from 256.21 to 283.84 K for propaneq water mixtures. The propaneq water system is studied in the low-pressure range because of the vapour pressure values of propane in the temperature values range where the generation of the mixtures propaneq water is carried out. Nitrogen and propane gases were supplied by Air Liquide with the specified purity of 99.999 vol.% and 99.95 vol.%, respectively, and were used without further treatment. Previous to the study of nitrogenq water and propaneq water, we determined the performance of the methods used for the present work. Repeatability and reproducibility of the Karl Fischer titration and the dewpoint generation were calculated according to ISO 5725 w4x after repetitive measurements. The results are presented in Table 1. Reference conditions for volume are 273.15 K and 1.01325 = 10 5 Pa. Test A was achieved on one standard gas prepared by Air Liquide. Test B was achieved on a
110
S.T. Blanco et al.r Fluid Phase Equilibria 161 (1999) 107–117
Table 1 Performance evaluation of water content measurements
Mean valuer10y6 kg my3 Ž n. Repeatabilityr10y6 kg my3 Ž n. Reproducibilityr10y6 kg my3 Ž n.
Test A Karl Fischer
Test B Dew point generation 263.15 K and 60=10 5 Pa
59.26 0.73 1.68
43.08 3.64 8.90
water dewpoint of 263.15 K and 60 = 10 5 Pa in pure nitrogen. The reliability tests result is taken as consistency criteria: the maximum acceptable standard deviation of measurements is derived from the repeatability value, and the maximum acceptable discrepancy with the literature measurements is derived from the reproducibility value. The water concentration in the vapour phase and the dew point curve of the mixtures generated at the generation bench are determined. The results of the experiments are recorded in Tables 2 and 3. The literature data w5,6x agree quite well with our results obtained for the nitrogenq water system. There are differences in the dew point temperature, which fluctuate between 0.15 to 28 with data from Bogoya et al. w5x and up to 58 with data from Kosyakov et al. w6x. For the propaneq water system we could not compare the results obtained.
3. Theory 3.1. Introduction Classical models such as UNIQUAC or NRTL yield good results for vapour–liquid equilibrium under low pressure for binary systems but are not applicable for high-pressure phase equilibrium calculations. In this work, we use an excess function–equation of state method developed by Peneloux et al. w1x ´ founded on the zeroth order approximation of Guggenheim’s reticular model. Other simpler correlation as Dalton’s law calculates properly the dew point curves of the systems studied below 80 = 10 5 Pa. This work is the first part of a research that aims to study the influence of the presence of methanol, as an additive of natural gas, in the water dew point. The excess function–equation of state method used in this work allows to be modified to have into account the self-association of methanol in the mixtures. 3.2. Description of the model This model is characterised as follows: Ž1. The pure component Helmholtz energies are calculated from equations of state. Ž2. The excess functions are defined at constant packing fraction, the latter described by Õ 0rÕ, Õ 0 being the molar close-packed volume. It is assumed that it is possible to define a ‘covolume’ bi
S.T. Blanco et al.r Fluid Phase Equilibria 161 (1999) 107–117
111
Table 2 Experimental dew points temperatures and pressures for binary mixtures Ž1y y . nitrogenq y water4 T ŽK.
P Ž10 5 Pa.
T ŽK.
P Ž10 5 Pa.
y s 0.00008 253.17 259.64 263.39 266.30 268.34 270.23
9.81 19.74 29.49 39.63 49.15 59.94
271.71 273.04 274.10 275.20 276.13
69.80 80.04 89.11 99.71 109.61
y s 0.00010 249.80 255.63 259.77 262.52 264.67 266.64 268.20
4.72 9.94 14.93 19.72 24.80 30.07 34.89
269.81 272.08 274.32 275.78 277.09 278.43 279.55
39.75 49.52 59.75 69.61 79.65 89.77 100.57
y s 0.00014 252.61 260.02 264.25 267.26 269.50 271.48 272.85 274.06 275.47
4.21 9.39 15.05 20.19 25.31 30.06 35.09 39.89 45.56
276.72 277.90 278.70 279.74 280.63 281.50 282.53 283.93
49.99 54.47 60.00 64.46 69.76 74.86 84.91 99.22
y s 0.00026 257.44 265.12 269.29 272.39 275.07
4.37 9.88 14.91 19.59 24.71
277.40 279.27 280.92 282.34 283.24
29.53 34.55 39.44 44.44 49.21
proportional to Õ 0 , which enables measuring the packing fraction by the ratio h s brÕ. The packing fraction for pure components as for the mixture are the same. Those assumptions lead to:
hs
b s Õ
bi Õi
Ž i s 1, . . . , p .
Ž1.
The molar Helmholtz energy of a mixture may be written as follows: p id
A s A y RT ln Ž 1 y h . y
Ý is1
x i ai bi
Q Ž h . q AEres
Ž2.
S.T. Blanco et al.r Fluid Phase Equilibria 161 (1999) 107–117
112
Table 3 Experimental dew points temperatures and pressures for binary mixtures Ž1y y . propaneq y water4 T ŽK.
P Ž10 5 Pa.
T ŽK.
P Ž10 5 Pa.
y s 0.00127 256.21 258.05 259.66 261.10 262.40 263.50 265.61 266.52 267.33 268.12
1.01 1.21 1.41 1.61 1.81 2.01 2.41 2.61 2.80 3.00
268.89 269.57 270.26 270.88 271.31 272.07 272.70 273.33 273.63
3.21 3.40 3.61 3.80 4.00 4.20 4.40 4.60 4.66
y s 0.00147 257.45 259.22 260.90 262.46 263.78 264.99 265.99 266.99 267.95 268.82
1.01 1.19 1.41 1.61 1.80 2.01 2.21 2.41 2.60 2.81
269.62 270.53 271.74 272.44 273.22 273.94 274.61 275.22 275.45
3.01 3.21 3.61 3.80 4.01 4.21 4.41 4.60 4.68
y s 0.00178 257.54 258.63 260.71 262.43 263.96 265.43 266.45 268.65 269.62 270.57
1.04 1.15 1.36 1.57 1.78 2.01 2.16 2.56 2.77 2.96
271.49 272.43 273.35 274.14 274.91 275.52 276.26 276.90 277.53 278.12
3.16 3.39 3.58 3.80 4.00 4.20 4.40 4.60 4.80 4.99
y s 0.00215 259.91 261.91 263.72 265.34 266.82 268.16 269.44 270.60 271.72 272.72 273.67
1.02 1.21 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00
274.59 275.38 276.23 277.02 277.69 278.49 279.06 279.71 280.46 280.87
3.20 3.40 3.60 3.81 4.00 4.21 4.40 4.60 4.80 4.99
S.T. Blanco et al.r Fluid Phase Equilibria 161 (1999) 107–117
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Table 3 Žcontinued. T ŽK.
P Ž10 5 Pa.
T ŽK.
P Ž10 5 Pa.
y s 0.00278 262.29 264.44 266.30 268.07 269.61 271.05 272.29 273.40 274.68 275.65 276.65
1.01 1.21 1.40 1.60 1.81 2.00 2.21 2.40 2.61 2.80 3.00
277.48 278.43 279.19 280.06 280.84 281.47 282.16 282.83 283.55 283.84
3.20 3.40 3.61 3.81 4.01 4.20 4.41 4.61 4.81 4.93
where Aid is the ideal mixture molar Helmholtz energy, a i is the component i attractive parameter of a translated Peng–Robinson cubic equation of state w7,8x, bi is the component i covolume, QŽh . is a function of the packing fraction h , and AEres is the residual excess Helmholtz energy which we shall explain later. The properties of pure components have been represented by a translated Peng–Robinson cubic equation of state w7,8x of the form: Ps
RT
aŽ T .
y
ÕŽ Õqg b.
Õyb
Ž3.
where Õ is a translated volume called the pseudo-volume and b is the pseudo-covolume, calculated as follows: b s 0.045572
RTc
Ž4.
Pc
The parameter a is a function of the temperature; the equations used for its calculation are proposed by Carrier w9x and Carrier et al. w10x. The compressibility factor is expressed as follows: zs
1 1yh
y a QX Ž h .
Ž5.
where P
as
Ý is1
x i ai
y
bi RT
EŽT , x . RT
Ž6.
with QX Ž h . s
h 1 q gh
and g s 2 Ž '2 q 1 .
Ž7.
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114
Table 4 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
0 1 Bk l
2
Nitrogenqwater Propaneqwater
2274.281 w11x 3121.348 a
y1.1148 w11x y1.7930 a
8712.375a 5553.582 a
a
A0k l
2
Bk0l
7.140 a 1.283 a
This work.
The parameter g value used is characteristic of the equation of state under consideration, namely the translated Peng–Robinson cubic equation of state w7,8x. The residual excess Helmholtz energy, AEres depends on the temperature, the composition and the packing fraction, and is written by means of a formalism which enables separating the composition and packing fraction variables: AEres s E Ž T , x . Q Ž h . where QŽh . is the integral of QX Žh .rh ŽEq. Ž7.. whose lower limit is zero if h ™ 0. For the first term on the right hand side of Eq. Ž8., the following equations are used w11x: p p p p 1 EŽT , x . s q x q x K q q x x j L1r3 Ý Ý Ý i i Ý q 1r3 j ji 2 qm is1 i i jsi j j i j is1 js1
Ž8.
Ž9.
with Kijs
Ei1j q Ei2j
and
2
L i j s Ei2j y Ei1j L i j s yL ji
Ž 10.
p
qm s
Ý qk x k
and
qk s d k b k
Ž 11.
ks1
where qirq j s Ž birbj . d , d being an adjustable parameter. K i j and L i j are two binary interaction parameters, which depend on the terms of the interchange energy, Ei1j and Ei2j , are calculated using a group contribution method as follows w11x: 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
N
Ý Ý Ž a i k y a jk .Ž a il y a jl . A2k l Ž T . ks1 ls1
with
A2k l s2 A0k l
T0
ž / ž /
0 1 Bk l
Ž 12.
T
T0 T
0 2 Bk l
Ž 13.
where 1 A0k l , 1 Bk0l , 2 A0k l and 2 Bk0l are four group interaction parameters. In this work, we obtain some of these parameters using the experimental results presented in this paper and others from the literature w12x. The values of these parameters used in this work are presented in Table 4. 4. Comparison with experiment and discussion As can be seen in Figs. 2 and 3, an increase of the water content in the mixtures of each system studied leads to higher values of temperature at constant pressure or lower values of pressure at constant temperature.
S.T. Blanco et al.r Fluid Phase Equilibria 161 (1999) 107–117
115
Fig. 2. Comparison between experimental dew point curves Žsymbol. and calculated with the excess function–equation of state method Žline. for the system Ž1y y . nitrogenq y water4: B, y s 0.00008; I, y s 0.00010; v, y s 0.00014; ` y s 0.00026.
The excess function–equation of state method used in this work reproduces quite accurately the dew point curves independently of the pressure range. We obtain mean deviations between 1.03 and 1.96 K on the nitrogenq water system ŽFig. 2. and between 0.19 and 1.94 K on the propaneq water ŽFig. 3.. For each one of nine binary mixtures studied, the calculated values for dew points temperatures are those for which the experimental and calculated values for molar fraction of water vapour are exactly the same.
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 . propaneq y water4: B, y s 0.00127; I, y s 0.00147; v, y s 0.00178; ` y s 0.00215; ', y s 0.00278.
S.T. Blanco et al.r Fluid Phase Equilibria 161 (1999) 107–117
116
To apply correctly the thermodynamic method, it was necessary to calculate new values only for the group interaction parameters concerning the terms for the interchange energy Ei2j between water and nitrogen or propane molecules in the vapour phase. This term represents the molecular interactions between the components of the mixture in the phase of the liquid–vapour equilibrium where the non polar component is the majority; in the systems studied in this paper this phase is the vapour one. On the dew point curve, the mixture is totally a vapour phase w13x, so this fact can explain the results obtained. For the dew temperature calculations, the greatest deviations of the two binary systems occur for the mixtures with lowest water contents. It can be due, on the one hand, to the experimental error for the very low water content analysis and on the other, to the greater difficulty calculations with the theoretical method the dew temperature for these kind of mixtures.
5. List of symbols a A A k l , Bk l b b Ei1j , Ei2j K i j, Li j N p P q Q QX R T T0 Õ Õ Õ0 y
Equation of state energy parameter Ž Pa m6 moly2 . Molar Helmholtz energy Ž J moly1 . Group interaction parameters between groups k and l ŽJ my3 . Covolume; equation of state size parameter Ž m3 moly1 . Pseudo covolume Žm3 moly1 . Terms of the interchange energy Ž J my3 . Binary interaction parameters Ž J my3 . Number of groups in a solution Number of components in the mixture Pressure Ž Pa. Molecular surface Žm2 . QXrh integral between 0 and h A packing fraction function Gas constant Ž8.314 J moly1 Ky1 . Temperature ŽK. Reference temperature Ž298.15 K. Molar volume Žm3 moly1 . Pseudo molar volume Ž m3 moly1 . Molar close packed fraction Žm3 moly1 . Molar fraction of water in the vapour phase, its value is calculated multiplying the water content value in Ž10y6 kg my3 Žn.. by Ž10y6 22.4r18.01.
Greek letters aik 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
S.T. Blanco et al.r Fluid Phase Equilibria 161 (1999) 107–117
Subscripts c i, j k, l res
117
Critical property Referring to components i, j Referring to groups k, l Residual
Superscripts E Excess property id Ideal solution property
Acknowledgements The authors acknowledge the financial and technical support of ENAGAS, during the experimental part of this work.
References w1x A. Peneloux, W. Abdoul, E. Rauzy, Fluid Phase Equilibria 47 Ž1989. 115–132. ´ w2x International Standard ISO 10101, 1993. w3x K. Fischer, Neues vertahren zur wass-analytischen bestimmung des wassergehaltes von flussigkeiten und festen ¨ koorpen, Angewandte Chemie 26 Ž1935. 394. ¨ w4x International Standard ISO 5725, 1986. w5x D. Bogoya, C. Muller, L.R. Oellrich, Wiss. Abschlubber 28 Ž1993. 54–63. ¨ w6x N.E. Kosyakov, B.Y. Ivchenko, P.P. Krishtopa, Vopr. Khim. Tekhnol. 11 Ž1977. 2568–2570. w7x A. Peneloux, E. Rauzy, R. Freze, ´ ´ Fluid Phase Equilibria 8 Ž1982. 7–23. w8x E. Rauzy. These ` d’Etat-Sciences, Universite´ Aix-Marseille II, 1982. w9x B. Carrier. These ` de Docteur en Sciences, Universite´ Aix-Marseille III, 1989. w10x B. Carrier, M. Rogalski, A. Peneloux, Ind. Eng. Chem. Res. 27 Ž1988. 1714–1721. ´ w11x H. Hocq. These ` en Sciences, Universite´ de Droit, d’Economie et des Sciences d’Aix-Marseille III, 1994. w12x R. Kobayashi, D.L. Katz, Industrial and engineering chemistry 45 Ž1953. 440–446. w13x J.M. Prausnitz, R.N. Lichtenthaler, E. Gomes de Azevedo, Molecular Thermodynamics of Fluid Phase Equilibria, PTR Prentice-Hall, Englewood Cliffs, NJ 07632, 1986, p. 449.