Experimental determination of carbon dioxide and nitrous oxide co-solubility in liquid oxygen

Fluid Phase Equilibria 207 (2003) 131–142

Experimental determination of carbon dioxide and nitrous oxide co-solubility in liquid oxygen V. De Stefani, A. Baba-Ahmed, D. Richon∗ Laboratoire de Thermodynamique, Ecole Nationale Supérieure des Mines de Paris, CENERG/TEP, 35, rue Saint Honoré, 77305 Fontainebleau, France Received 20 September 2002; accepted 2 January 2003

Abstract Knowledge of solid solubility in condensed gases is of great practical interest, e.g. in designing the cryogenic processes involving separation of gas mixtures into their components. Great attention has been paid to developing and implementing an operational procedure in order to reduce the probability of accidents in low temperature industry. The interest in the solubility data is closely connected to the problem of accumulation of impurities in process plant and storage tanks. Such accumulations in liquid oxygen may cause fouling and blockage in heat exchangers and pipelines and it may eventually cause serious explosions, for instance that occurred in Bintulu, Malaysia, in 1997 [J. Loss Prevent. Process Ind. 14 (2001) 167]. Solubility data for pure compounds in liquid solvents are available for various systems, but co-solubility data are drastically lacking. As an attempt to begin filling this gap, the CO2 –N2 O co-solubility has been measured in liquid oxygen at 90.44 K. For this purpose a new device named “atomiser–injector”, was designed, constructed and tested in our laboratory. © 2003 Elsevier Science B.V. All rights reserved. Keywords: Solid–liquid equilibrium; Co-solubility; Cryogenics; Carbon dioxide; Nitrous oxide; Liquid oxygen

1. Introduction Flammability, high-pressure gas and materials of construction are the principal areas of hazard, related to processing cryogenic liquids. These categories of hazards are usually present and must be carefully considered in air separation plants or processes, in order to reduce the probability of incidents to acceptable values. Equipment and systems should be kept scrupulously clean and contaminating materials avoided, since they may lead to hazardous conditions if in contact with the liquefied gases in the apparatuses. This is ∗

Corresponding author. Tel.: +33-164694965; fax: +33-164694968. E-mail address: [email protected] (D. Richon). 0378-3812/03/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0378-3812(03)00007-4

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particularly important when working with liquid or gaseous oxygen: the air impurities should be strictly controlled to prevent the formation of flammable or explosive mixtures. The flammability hazard occurs obviously when gases such as hydrogen, methane, and acetylene are involved in the process. Moreover the presence of highly-concentrated oxygen mixtures leads to very high reactivity of ordinary combustibles, and may even cause some non-combustible materials like carbon steel to burn readily under the appropriate conditions. At the state of the art one of the main unsolved problems in air separation industries is the accurate knowledge of the solid deposition rate of air contaminants in the cryogenics unit. If air contaminants, i.e. hydrocarbons and carbon dioxide, have a high melting point with respect to the liquid oxygen (LOX) temperature, then they can solidify and cause plugs during the air separation process. This has been the main reason of serious safety problems in many plants throughout the world [1], especially when the solid deposits are flammable. Consequently, it is very important to know the solubility of the flammable hydrocarbon mixtures deposits in LOX, in order to reach a safe working condition, for example in the reboiler—condenser of an air distillation tower, where LOX evaporates. The knowledge of the thermodynamic behaviour of the solid deposits in cryogenic liquids is very limited and experimental data are lacking not only for hydrocarbons but also for most of the other contaminants. Among them, there are two components that can be typically present in LOX in non-negligible concentrations and that can consequently precipitate: CO2 and N2 O. Only two authors [2,3] have measured the co-solubility of CO2 and N2 O in liquid oxygen. Their data show both positive and negative deviations from ideality. They explained this behaviour by the formation of a complex between CO2 and N2 O. In the present work, a new apparatus is presented for measuring the co-solubility of solid solutions in cryogenic systems: it has been developed to overcome the uncertainties related to the techniques used by the others authors. For instance, to determine the solubility of CO2 –N2 O solid mixtures in liquid oxygen, Miller et al. [2] have used the following experimental procedure. At room temperature, a known quantity of gaseous components of the mixture to be studied is first introduced into the evacuated cell. Then the solvent, i.e. oxygen, is loaded and the temperature is reduced. When the target temperature is reached (T = 90.2 K), the equipment is ready for sampling and measurements. This loading procedure can lead to a non-homogeneous solid system, altering the measured solubility data. Because of their different melting points, the two mixture components could freeze and deposit in the equilibrium cell independently, forming two quite independent solid layers. Then the liquid phase would be in equilibrium mostly with the solid phase of the component having the lowest melting point, i.e. the component of the last layer. This assumption is valid only if the solids formed have a density higher than the density of the solvent liquid. In this hypothesis, the experiment would not describe the mixture solubility with respect to the composition of the loading mixture, but only with respect to the composition of the surface of the solid formed in the equilibrium cell. This surface composition results from several parameters depending on loading composition, kinetics and hydrodynamics, etc. The mechanism of solidification of a liquid solution, in fact, is not well known yet. What we know is that solidification is driven by forces that depend on physical and molecular nature of components. Furthermore, a previous study [4] on the CO2 –N2 O solid system, based on spectroscopic technique, suggests the formation of co-crystals. Therefore, it is quite impossible to reproduce the loadings in exactly the same conditions and we can expect very large deviations in the co-solubility measurements with the loading procedures of Miller

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et al. [2]. In order to overcome this problem, our apparatus used to measure the solubility of pure N2 O and CO2 in liquid oxygen [5] has been adapted to measure their co-solubility in liquid oxygen. A new device, named “atomiser–injector”, has been developed. This new equipment represents a significant improvement over the previous traditional apparatuses.

2. Experimental method and apparatus 2.1. The “atomiser–injector”: principle and set-up In order to introduce into the equilibrium cell a fine powder of an homogeneously dispersed solid mixture, a new device, the “atomiser–injector” system (Fig. 1) was designed and set-up. This device is fitted to the apparatus based on a static–analytic method [5,6] using an on-line pneumatic micro-sampler for gas-chromatographic analyses of liquid samples. The “atomiser–injector” system is composed as follows. A thin tube with an internal diameter of 0.5 mm connects the injector (I) to the equilibrium cell (EC). The solute mixture is loaded from the feeding cell solvent reservior (SR) to the injector via the loading circuit, solute loading circuit (SLC), opening V1. The control of solute mixture injection is allowed by a manual differential screw fitted in the injector. To improve the atomisation, the end of the tube connected to the equilibrium cell, i.e. the atomiser, is a spray tip (ST) (internal diameter = 0.1 mm by 5 mm length). In this way, through the reduction from 0.1 to 0.1 mm, the pressure drop is achieved just in this location, enhancing the dispersion of solute as a fog into the cell. The tube that connects the equilibrium cell to the injector is heated (HC) in order to avoid formation of CO2 or N2 O solid plugs during injection. Moreover

Fig. 1. Overview of the atomiser–injector system. EC: equilibrium cell; HC: heating cartridge; He: helium; HE: heat exchanger; I: injector; PT: pressure transducer; SP: screw plug; SLC: solute loading circuit; SR: solvent reservoir; ST: spray tip; TI: thermal insulator; TR: PID temperature regulator; Vi : valve i; VP: vacuum pump.

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the end of the tube is thermally isolated by a TeflonTM heat shield (TI) for isolating the cell from heat produced by the heating cartridges, HC. 2.2. Experimental method and procedure The experimental method used in this work to measure the SLE data is the static analytic method with liquid phase sampling and on-line analysis [5,6]. Since the corresponding apparatus has been described in detail elsewhere, [5] only the pertinent aspects are given herein for convenience. Special attention is paid to the way of feeding the solute mixture, since this is the main difference, in the present work. The experimental procedure consists of three steps: filling the equilibrium cell, setting up experimental conditions, and taking the measurements at the equilibrium. In the following, more details are provided, referring to Figs. 1 and 2. At room temperature the solvent S2 (oxygen) is first introduced into the evacuated equilibrium cell (EC) by opening the valves V4 and V5, to reach a pressure of 10 MPa. Then the cryostat (C) is partially filled with liquid nitrogen and the temperature is set at 87 K. As the temperature and consequently the pressure in the equilibrium cell decrease, more oxygen is loaded to ensure that the quantity introduced is enough to fill half the cell with the liquid phase. At 87 K the equipment is then ready for introducing the solute.

Fig. 2. Static–analytic apparatus for SLE measurements. AIS: atomiser–injector system (see Fig. 1); BHE: brass heating envelope; C: cryostat; DA: data acquisition; EC: equilibrium cell; F: fan; GC: gas chromatograph; SM: sample; He: helium; LS: liquid sampler; M: variable speed motor; MR: magnetic rod; PP: platinum probe; PT: pressure transducer; SR: solvent reservoir; S1: solvent 1 reserve, S2: solvent 2 reserve; SA: stirring assembly; TR: PID temperature regulator; Vi : Valve i; VP: vacuum pump.

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The solute mixture (N2 O–CO2 ), is introduced inside an evacuated reservoir (SR): the number of moles of each component is found by accurate weightings, using a Sartorius CC1200 balance with a sensitivity of 10−4 g. The relative uncertainty of the solute mole composition is estimated to be lower than 0.2%. Helium at 15 MPa is added and its dissolution into the solute mixture is improved by stirring. Then the solute reservoir is connected at the injector via V1. The presence of dissolved helium (which also plays the role of the carrier gas for chromatographic analyses) into the solute mixture, improves the effect of atomisation, increasing the segregation of particles. The temperatures of the heating cartridges (HC, in Fig. 1) of the “atomiser–injector” system are set to be slightly higher than the melting point of the solute. The mixture (CO2 –N2 O–He) contained in SR, is rapidly introduced into the solute loading circuit (in Fig. 2) (which has previously been thoroughly evacuated) by opening valve V1. Then valve V1 is closed and valve V2 is opened to introduce helium at a pressure of about 18 MPa. Soon after, valve V2 is closed and the ternary mixture (CO2 , N2 O and He) is injected into the cell by activating the differential screw of the injector (I). Then valve V2 is opened to introduce more helium into the cell to reach the pressure required for the sampling operation (0.4 MPa) and injector I is closed. In this step the loading circuit between injector I and the equilibrium cell is cleaned. The temperature is set to the chosen value. A brass jacket (brass heating envelope, BHE) maintains a fine local temperature regulation in the equilibrium cell by means of an electrical resistance powered using a proportional-integral-differential regulator, thermal regulator (TR) (West mini 6100). Temperatures at the top and at the bottom of the equilibrium cell are measured by two 100  platinum probes (PP), and thermal equilibrium is reached when temperature inside the cell is constant at 90.44 K within 0.05 K. In order to rapidly reach the equilibrium in the cell, efficient stirring is provided through a magnetic stirrer (MR). When the equilibrium is reached (after approximately 15 h) the stirring assembly is stopped and the equipment is ready for sampling. Samples of liquid phase are withdrawn by means of a pneumatic sampler ROLSITM [7] and analysed. It is essential that a representative liquid sample is withdrawn through the sampler capillary: the temperature of the capillary is maintained at temperature identical to that of the cell through a thermal regulator (TR) connected to a heating cartridge. For a given temperature at least 20 samples are withdrawn and analysed in order to check for repeatability: the mean relative deviation 1 on solubility due to the analysis dispersion is estimated to be within 3.1% for xN1 2 O and 1.9% for xCO . 2 More solute through the solute loading circuit (SLC) or more solvent by opening valves V4 and V5 is introduced in order to check for the reproducibility. The liquid samples are analysed by means of a gas chromatograph (Varian model 3800) equipped with a 4 m column of 100–120 mesh Hayesep DB and with a thermal conductivity detector and a flame ionisation detector. In order to measure small quantities of CO2 , an on-line catalytic reduction is performed in a methaniser (Varian model 3700), where carbon dioxide reacts with hydrogen on a nickel oxide catalyst bed producing methane. Methane is detected by the flame ionisation detector giving indirect measurement of CO2 quantity. Details of the analysis equipment are given in De Stefani et al. [5]. 2.3. Chemicals Carbon dioxide, nitrous oxide and oxygen used in these measurements are provided by Air Liquide (France) with the following certified purities, which were checked by gas chromatography: • carbon dioxide: 99.998 mol%,

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• nitrous oxide: 99.998 mol%, • oxygen: 99.9995 mol%. 3. Results and discussion The experimental solid–liquid equilibrium data for the CO2 –N2 O–O2 system, at 90.44 K, are presented in Table 1 and Figs. 3 and 4. For each solid phase composition, the results of reproducibility tests are also reported, in order to underline the accuracy of the experimental technique. The solid phase composition is assumed to be that gravimetrically determined when preparing the CO2 –N2 O mixture. The mean relative deviation on solubility, due to the combined analysis dispersion and the calibration 1 uncertainties, is estimated to be <6.5% for xN1 2 O and 4.5% for the xCO . 2 The straight dotted line between the pure solute solubility limits is the behavior expected for an ideal mixture. Surprisingly the data trend shows both positive and negative deviations with respect to this line. This occurs because the excess Gibbs energy for this system ranges from positive values to negative ones with increasing concentration of nitrous oxide in the solid phase (see Fig. 5). The following assumptions have been made to correlate our data: 1. The solubility of liquid oxygen in solid phase is neglected; 2. As the solute components are close to an infinite dilution, the activity coefficient in liquid phase is calculated using the solubility data of CO2 in O2 and N2 O in O2 [5]. A relation for the calculation of solid–liquid equilibrium can be derived starting from the iso-fugacity criterion: xil γil = xis γis ψi

(1)

Table 1 Co-solubility for CO2 and N2 O in LOX xNs 2 O

xNl 2 O,exp (×10−6 )

xNl 2 O,cal (×10−6 )

∆(xN2 O ) (%)a

l xCO (×10−6 ) 2 ,exp

l xCO (×10−6 ) 2 ,cal

∆(xCO2 ) (%)a

0.069 0.270 0.448 0.510 0.510b 0.510b 0.510b 0.647 0.647b 0.647b 0.778 0.778b

27 40 61 76 76 76 80 107 107 102 134 134

32 43 62 72 72 72 72 102 102 102 136 136

18.5 7.5 1.6 −5.3 −5.3 −5.3 −10.0 −4.7 −4.7 0.0 1.5 1.5

4.0 3.6 2.8 2.5 2.5 2.5 2.5 1.6 1.6 1.6 0.8 0.8

3.9 3.7 3.0 2.6 2.6 2.6 2.6 1.6 1.6 1.6 0.8 0.8

−2.5 2.8 7.1 4.0 4.0 4.0 4.0 0.0 0.0 0.0 0.0 0.0

MRDc

5.5

T = 90.44 ± 0.05 K. a Uexp = experimental, Ucal = calculated, ∆(U) = 100 × (Ucal − Uexp )/Uexp . b Reproducibility test.
c MRDU = (100/N) × |(Ucal − Uexp )/Uexp |.

2.6

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Fig. 3. Co-solubility of N2 O and CO2 in liquid oxygen at T = 90.44 + 0.05 K (this work). (䊉): experimental data; (—): represented by the Redlich–Kister model; (- - -): ideal behaviour.

Fig. 4. Solubility of N2 O and CO2 in LOX vs. the N2 O molar fraction in solid phase (this work). (䊉): N2 O solubility experimental data; (—): N2 O solubility represented by the Redlich–Kister model; (䉱): CO2 solubility experimental data; (- - -): CO2 solubility represented by the Redlich–Kister model.

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Fig. 5. Solid activity coefficients and Gibbs excess energy of N2 O and CO2 in LOX vs. the N2 O molar fraction in solid phase (this work). (䊉): activity coefficient of N2 O in solid phase, experimental data; (—): activity coefficient of N2 O in solid phase, represented by the Redlich–Kister model; (䉱): activity coefficient of CO2 in solid phase, experimental data; (- - -): activity coefficient of CO2 in solid phase, represented by the Redlich–Kister model; ( ): GE,s , experimental data; (– · –): GE,s , represented by the Redlich–Kister model.

where xil is the mole fraction of component i, CO2 or N2 O in liquid oxygen; xis is the mole fraction of component i, CO2 or N2 O in solid phase; γ i is the activity coefficient of component i, CO2 or N2 O in liquid or solid phase; ψ i is the “ideal term” expressed by following relation:    ∆fus Hi Ttr,i 1− (2) ψi = exp RTtr,i T where ∆fus Hi is the enthalpy of fusion of component i; Ttr,i is the triple point temperature of component i; R is the universal gas constant. ∆fus H and Ttr values [9] for N2 O and CO2 are reported in Table 2. Following assumption 2, γil -values are known from the pure component solubility measurements [5]. Then, through Eq. (1) the experimental values of γis can be calculated from co-solubility measurements, xil (see Table 3). In order to correlate our data, the activity coefficients in the solid phase are regressed, using a three-parameter Redlich–Kister model [8]: GE,s s s = A0 + A1 (xNs 2 O − xCO ) + A2 (xNs 2 O − xCO )2 s 2 2 RTxsN2 O xCO 2

(3)

where GE,s is the molar excess Gibbs energy of the solid phase: GE,s s s ln γCO + xNs 2 O ln γNs 2 O = xCO 2 2 RT

(4)

Table 2 Coefficients for the Redlich–Kister model as regressed from our data Component

Ttr (K)

∆fus H (kJ kg−1 )

A0

A1

A2

N2 O CO2

182.34 216.98

148.53 196.52

0.581

−1.075

−0.002

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The optimal values of the parameters of Eq. (3) are calculated by using the least squares method and reported in Table 2. The objective function that has been minimised is defined in Eq. (5): Fobj =

N  E,s 2 (GE,s i,exp − Gi,cal )

(5)

i

E,s where GE,s i,cal is from Eq. (3) and Gi,exp is from Eq. (4) For the calculation of the required activity coefficients in solid phase, derivatives are needed:   ∂(nGE,s /RT) s ln γi = ∂ni T ,P ,nj

(6)

which leads for the CO2 –N2 O binary system to: ln γNs 2 O

=

s (xCO )2 2

m  s s {Aj (xNs 2 O − xCO )j −2 [(2j − 1)xCO − xNs 2 O ]} 2 2

(7)

j =1 s ln γCO 2

=

(xNs 2 O )2

m  s s {Aj (xNs 2 O − xCO )j −2 [xNs 2 O − (2j − 1)xCO ]} 2 2

(8)

j =1

The activity coefficients calculated by the Redlich–Kister model from Eq. (7) and (8) are compared in Table 3 with the experimental ones obtained from Eq. (1). The mean relative deviation in calculated solubility and activity coefficients with respect to experimental ones is around 5.5% for N2 O and 3% for CO2 . Table 3 Activity coefficients in the solid phase for CO2 and N2 O in LOX xNs 2 O

γNs 2 O,exp

γNs 2 O,cal

0.069 0.270 0.448 0.510 0.510b 0.510b 0.510b 0.647 0.647b 0.647b 0.778 0.778b

2.13 0.81 0.74 0.81 0.81 0.81 0.85 0.90 0.90 0.86 0.94 0.94

2.53 0.87 0.75 0.78 0.78 0.78 0.78 0.86 0.86 0.86 0.95 0.95

MRDc

∆(γNs 2 O ) (%)a 18.7 7.4 1.3 −3.7 −3.7 −3.7 −8.2 −4.4 −4.4 0 1 1

s γCO 2 ,exp

s γCO 2 ,cal

s ∆(γCO ) (%)a 2

1.04 1.20 1.23 1.24 1.24 1.24 1.24 1.10 1.10 1.10 0.88 0.88

1.02 1.24 1.33 1.3 1.3 1.3 1.3 1.11 1.11 1.11 0.87 0.87

−2.0 3.3 8.1 4.8 4.8 4.8 4.8 0.9 0.9 0.9 −1.1 −1.1

4.8

T=90.44 ± 0.05 K. a Uexp = experimental, Ucal = calculated, ∆(U) = 100 × (Ucal −Uexp )/Uexp . b Reproducibility test.
c MRDU = (100/N) × |(Ucal − Uexp )/Uexp |.

3.1

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Fig. 6. Solubility of N2 O and CO2 in LOX vs. the N2 O molar fraction in solid phase, at T = 90.2 K. The parameters of model are fitted on data from [3]. (䊉): N2 O solubility experimental data [3]; (—): N2 O solubility represented by the Redlich–Kister model; (䉱): CO2 solubility experimental data [3]; (- - -): CO2 solubility represented by the Redlich–Kister model.

For comparison with the literature, we have calculated SLE data at the published temperatures using the Redlich–Kister Ai parameters adjusted to our data. Regarding the data from Miller et al. [2], they differ widely from the ones calculated from the model. The experimental technique used by these authors is also based on the static–analytic method but it has the drawback already underlined in the introduction of this manuscript. The discontinuity of the N2 O and CO2 data observed for a N2 O mole fraction in the solid at composition around 0.25 (Fig. 6), indicates that the solid phase in equilibrium with the liquid one has not the supposed composition. The experimental data from Meneses et al. [3] present systematic deviation. In this case, the measurements were carried out using an infrared spectroscopy technique. Analyses are performed at a fixed temperature (92.5 K) for several mixtures with a proportion of each component from 0.1 to 99.9%. A gaseous mixture of known composition is injected into a cryostat facing a polished aluminum mirror and then the temperature of the mirror surface is gradually decreased at the target value. For each mixture, the total pressure is decreased up to the appearance of a solid phase. When the system is stabilized, pressure measurements are performed and the composition of the deposited solid phase is quantified by infrared spectroscopy. Meneses et al. have estimated their uncertainties to be within 10% on solid mole fractions and 15% on pressures. Solid–liquid equilibrium is determined from the results obtained for the solid–vapor equilibrium (pressure and composition of solid phase) [3]. The results from all the sources present a strong interaction existing between N2 O and CO2 and the data trend shows both positive and negative deviations with respect to ideal behaviour. The data from literature exhibit significant deviations from our calculations, around 60% for [2] and 300% for [3]. We investigated the reason of this wide divergence and asked ourselves if it was due to our correlation accuracy or to the quality of data from literature. The Redlich–Kister model has been applied to data

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Fig. 7. Solubility of N2 O and CO2 in LOX vs. the N2 O molar fraction in solid phase, at T = 92.5 + 0.05 K. The parameters of model are fitted on data from [4]. (䊉): N2 O solubility experimental data [4]; (—): N2 O solubility represented by the Redlich–Kister model; (䉱): CO2 solubility experimental data [4]; (- - -): CO2 solubility represented by the Redlich–Kister model.

of these authors, using the parameters adjusted on their data (Figs. 6 and 7). The liquid composition deviation is within 50% for [2] and 240% for [3]. This result is particularly significant: since traditional models are not able to fit these data, a question on their quality can be posed.

4. Conclusions A new experimental apparatus has been proposed to measure solubility for solid mixtures in cryogenic solvents. This apparatus is based on the atomisation of the mixture in the liquid solvent. Solid–liquid equilibrium data for the system CO2 –N2 O–O2 have been determined at 90.44 ± 0.05 K. Our experimental data were used to regress the parameters of a three-parameter Redlich–Kister model. The mean relative deviations between the model and the experimental data are within 2.5% for CO2 and 5% for N2 O. The proposed correlation is compared with the data from literature, displaying a great deviation and then the great difficulty of preparing equilibrium systems with a well defined and estimated solid mixture composition. The results underline the performances of our atomisation device to prepare homogeneous and reliable solid mixtures. Compared to other methods [2,3] the present method has the advantage to inject fine and homogeneous highly dispersed solid mixtures into the equilibrium cell. List of symbols A0 , A1 , A2 parameters GE molar excess Gibbs energy (J mol−1 ) H enthalpy (J g−1 ) LOX liquid oxygen m number of parameters MRD mean relative percentage deviation

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n N P R T x

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number of moles number of data pressure (MPa) universal gas constant (kJ kmol−1 K−1 ) temperature (K) mole fraction

Greek letters ∆ relative deviation γ activity coefficient ψ ideal term Subscripts fus fusion i, j component i, j tr triple point Superscripts calc calculated value exp experimental value l liquid s solid Acknowledgements The authors are grateful to Air Liquide for financial support and to D. Marques and H. Legendre for their help developing the apparatus. References [1] F.G. van Dongen, J.D. Graaf, R.M. Groeneveld, R.M. van Hardeveld, in: Proceeding of the 12th Intersociety Cryogenic Symposium, AIChE 2000 Spring National Meeting, Atlanta, GA, 5–9 March 2000, pp. 3–8. [2] E.J. Miller, S.R. Auvil, N.F. Giles, G.M. Wilson, in: Proceeding of the 12th Intersociety Cryogenic Symposium, AIChE 2000 Spring National Meeting, Atlanta, GA, 5–9 March 2000, pp. 18–25. [3] D. Meneses, J.-Y. Thonnelier, C. Szulman, E. Werlen, in: Proceeding of Cryogenics 2000, Praha, Czech Republic, 10–13 October 2000, pp. 109–113 [4] K.R. Witters, J.E. Cahill, J. Chem. Phys. 67 (1977) 2405–2411. [5] V. De Stefani, A. Baba-Ahmed, A. Valtz, D. Meneses, D. Richon, Fluid Phase Equilib. 200 (1) (2002) 19–30. [6] A. Baba-Ahmed, Appareillage pour l’étude des équilibres liquide–vapeur dans le domaine cryogénique, conception et développement. Ph.D. Thesis, ENSMP, EMP 148.984-CCL.TH.988, 1999 [7] Procédé et dispositif pour prélever des micro-échantillons d’un fluide sous pression contenu dans un container. Déposant: Armines. Dˆepot lt 21 August 1998, no. 98 10708. [8] O. Redlich, A.T. Kister, Ind. Eng. Chem. 55 (1963) 43–51. [9] Gas Encyclopaedia L’ Air Liquide, Elsevier, Amsterdam, 1976.