CORRESPONDENCE pubs.acs.org/IECR
Reply to “Comments on ‘Experimental Measurement of Vapor Pressures and Densities at Saturation of Pure Hexafluoropropylene Oxide: Modeling Using a Crossover Equation of State’” Moussa Dicko, Alain Valtz, and Christophe Coquelet* Mines Paristech, CEP/TEP Centre Energetique et Procedes, 35, rue Saint Honore, 77305 Fontainebleau, France ir: We first want to thank Laugier and Richon1 for considering our work and providing analysis. They are correct. The uncertainty is not well estimated and must be re-evaluated (a maximum of ∼5% for vapor densities). We sincerely apologize, regarding the slight problems that they have found for the lowpressure and low-temperature measurements. We have focused our work on the high-pressure measurements, the modeling work, and the determination of critical properties. In their comments, they have used the following virial equation:
S
Z¼
Pv B C ¼ 1+ + 2 RT v v
ð1Þ
By plotting Z as a function of 1/v, we can effectively check the consistency of the measured data. In parallel, we want to mention that, at 263 K, the interval of molar density represents half that of the interval at 283 K, so the problem is emphasized. Indeed, in the entire domain of pressure, a straight line behavior is expected. It is not the case with our data,2 close to ideal gas behavior. Moreover, this point seems to be strange and we must determine if such behavior can be observed for other data measured using the same technique (Bouchot and Richon3). Therefore, we have checked the representation of Z as a function of 1/v for the data measured by Richon and co-workers (Bouchot,4 Benmansour,5 Rivollet,6 and Richon and co-workers7). We have extrapolated the tendency line to the following coordinates: 1/v = 0, Z = 1. Unfortunately, as can be seen in Figures 14, the same behavior is observed (some data deviate greatly from the expected ideal gas behavior). We can see that the extrapolation of the data leads to the same problem. For some molar density, knowing (Z 1)v = B + C/v, if we consider the plot of (Z 1)v as a function of 1/v, we expect a linear curve. But, as can be seen in Figure 5, this is not the case, particularly at very low pressure. The uncertainties mentioned by the authors are ∼0.05% (Richon and co-workers7). It seems that they also are not correct. Another test has been performed with pure nitrogen. We have reduced the flow to a low value in order to be close to the static behavior. Figure 6 shows the results: we encounter a problem when 1/v is close to zero. Therefore, we can conclude that, because of the inertia of the tube, the vibrating tube densimeter is not appropriate for the determination of the densities of gases (particularly at very low pressure). Now, the question is this: What leads to this problem: the technique or the method of calibration? Bouchot faced the same problems during his thesis and tried to give some explanations.4 Finally, we recommend choosing the gas expansion technique, because the virial equation is used by default.8 r 2011 American Chemical Society
Figure 1. Compressibility factor, as a function of inverse volume at 253.00 K (Fluid: R143a). Absolute uncertainty mentioned by Richon and co-workers:7 3 mol 3 m3.
Figure 2. Compressibility factor, as a function of inverse volume at 263.43 K (System R407C). Maximum estimated uncertainty mentioned by Benmansour and Richon:5 3.5 mol 3 m3. (Legend: (2) experimental value and (;) tendency curve.)
The second point of the comment concerns the density values for pressures higher than the saturating pressure. To determine the density values at saturation, we have only considered the value at the pure component’s vapor pressure. For the four points indicated in Table 2 of the Laugier and Richon’s comments,1 which show a pressure higher than the pure component’s vapor pressure, we can explain it by assuming a metastable state. It can appear if the flow through the vibrating tube is very low. Moreover, we want to Published: July 05, 2011 9476
dx.doi.org/10.1021/ie201274y | Ind. Eng. Chem. Res. 2011, 50, 9476–9477
Industrial & Engineering Chemistry Research
Figure 3. Compressibility factor, as a function of inverse volume at 263.43 K (System H2SC3H8zH2S = 0.038). Relative uncertainty mentioned by Richon and co-workers:7 0.05%. (Legend: (2) experimental value and (;) tendency curve.) The horizontal line corresponds to Z = 1.
CORRESPONDENCE
Figure 6. Compressibility factor of pure nitrogen, as a function of inverse volume at 296.32 K.
the value of B at 263.27 and 273.21 K using our data. With our data, we have determined the following: • At 263.27 K, B = 0.8014 m3 3 kmol1. (Laugier and Richon1 determined a value of 0.8036 m3 3 kmol1.) • At 273.21 K, B = 0.7456 m3 3 kmol1. (Laugier and Richon1 determined a value of 0.7158 m3 3 kmol1.) We can see that the second virial coefficient is a very sensitive variable. It confirms that an adequate experimental method must be used, and, considering vibrating tube densimeter, the uncertainty for the vapor density is ∼5%.
’ AUTHOR INFORMATION Corresponding Author Figure 4. Compressibility factor, as a function of inverse volume at 263.11 K (System H2SC3H8zH2S = 0.2227). Relative uncertainty mentioned by Richon and co-workers:7 0.05%. (Legend: (2) experimental value and (;) tendency curve.)
Figure 5. Plot of (Z 1)v, as a function of inverse volume at 263.43 K (System H2SC3H8zH2S = 0.038). (Experimental data are denoted by solid triangles (2).)
highlight that, since we are close to the pure component’s critical point (TC = 359.3 K), density fluctuations can occur at this temperature. Besides, the value of the universal constant using our data2 was found to be very close to 0.325 (in fact, 0.3253). Finally, we have considered the evolution of the second virial coefficient determined by Laugier and Richon.1 We have calculated
*Phone: +33 1 64694962. Fax: + 33 1 64694968. E-mail:
[email protected].
’ REFERENCES (1) Laugier, S.; Richon, D. Comments on “Experimental Measurement of Vapor Pressures and Densities at Saturation of Pure Hexafluoropropylene Oxide: Modeling Using a Crossover Equation of State”. Ind. Eng. Chem. Res. 2011, 50, DOI: 10.1021/ie2011559. (2) Dicko, M.; Belaribi, G.; Coquelet, C.; Valtz, A.; Belaribi, F.; Naidoo, P.; Ramjugernath, D. Experimental Measurement of Vapor Pressures and Densities of Pure Hexafluoropropylene Oxide: Modeling Using a Crossover Equation of State. Ind. Eng. Chem. Res. 2011, 50, 4761. (3) Bouchot, C.; Richon, D. An enhanced method to calibrate vibrating tube densimeters. Fluid Phase Equilib. 2001, 191, 189. (4) Bouchot, C. Nouvelle methode de mesures simultanees des equilibres et des proprietes volumetriques appliquees aux produits de substitution des CFC. Mesures et representation jusqu’a 200 bar et de 20°C a +60 °C. Ph.D. dissertation, Mines ParisTech, Paris, France, 1996. (5) Benmansour, S.; Richon, D. Vaporliquid equilibria and densities of a difluoromethane (R32, 23 wt %) + pentafluoroethane (R125, 25 wt %) + 1,1,1,2-tetrafluoroethane (R134a, 52 wt %) mixture (R407C) at temperatures between 253 and 333 K and pressures up to 20 MPa (11600 data points). ELDATA: Int. Electron. J. Phys.-Chem. Data 1998, 4, 29. (6) Rivollet, F. etude des proprietes volumetriques (PVT) d’hydrocarbures legers (C1C4), du dioxyde de carbone et du sulfure d’hydrogene—Mesures par densimetrie a tube vibrant et modelisation. Ph.D. dissertation, Mines ParisTech, Paris, France, 2005. (7) Rivollet, F.; Jarne, C.; Richon, D. PFT and VLE for ethane + hydrogen sulfide from (254.05 to 363.21) K at pressure up to 20 MPa. J. Chem. Eng. Data 2005, 50, 1883. (8) Burnett, B. S. Compressibility determinations without volume measurements. J. Appl. Mech. 1936, 58, 136.
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