Ind. Eng. Chem. Res. 2008, 47, 7483–7489
7483
RESEARCH NOTES Use of the PPR78 Model To Predict New Equilibrium Data of Binary Systems Involving Hydrocarbons and Nitrogen. Comparison with Other GCEOS Romain Privat, Jean-Noe¨l Jaubert,* and Fabrice Mutelet Laboratoire de Thermodynamique des Milieux Polyphase´s, Nancy-UniVersite´ 1 rue GrandVille, B.P. 20451, F-54001 Nancy Cedex, France
Very recently, Privat et al. decided to add the nitrogen group to the PPR78 model. However, during the writing of their paper, new VLE data were published on three binary systems containing nitrogen: N2 + methane, N2 + ethane, N2 + and n-decane (new data on the ethane + methane system were also published). In this research note, the capability of the PPR78 model to predict these data along with two ternary systems involving nitrogen, methane, ethane, and n-decane is checked. Comparison with two other predictive models, VTPR and PSRK, is also performed. Introduction 1-10
is a group contribution method aimed The PPR78 model at estimating the binary interaction parameters of the well-known Peng-Robinson equation of state.11 A few months ago, the nitrogen group (N2) was added to the PPR78 model.5 To do so, most of the available VLE data of binary systems containing nitrogen were collected in the open literature. These data were used to fit the parameters of the model. However, during the publishing procedure of this extension of the PPR78 model, new VLE data on systems containing nitrogen were published. Janisch et al.12 studied the binary systems N2 + methane and N2 + ethane (they also measured the methane + ethane system). Garcı´a-Sa´nchez et al.13 focused on the system N2 + n-decane. In addition, Janisch et al.12 correlated their new data with the VTPR14-16 model (volume translated Peng-Robinson equation of state) and the PSRK17-19 model (predictive Soave-RedlichKwong equation of state). In this research note, the PPR78 model is used to predict these data and a comparison between the three predictive models, PPR78, VTPR, and PSRK, is proposed. In addition, the predictive PPR78 model is used to represent the VLE experimental data of two ternary systems involving nitrogen, methane, ethane, and n-decane. Short Presentation of the PPR78 Model
{
The PPR78 model is based on the Peng-Robinson equation of state (EOS)11 with classical van der Waals mixing rules: P)
a(T) RT V - b V(V + b) + b(V - b) N
a(T) )
N
∑ ∑ z z √a a [1 - k (T)] i j
i)1 j)1
i j
ij
(1)
N
b)
∑zb
i i
i)1
where P is the pressure, R the ideal gas constant, T the temperature, V the molar volume, and zk the mole fraction of component k. The parameters ak and bk are those of the pure component k. In the PPR78 model, the binary interaction * To whom the correspondence should be addressed. E-mail:
[email protected]. Fax: +33 3 83 17 51 52.
parameters kij(T), depend on temperature and are calculated by a group contribution method through the following equation: kij(T) ) -
1 2
[
Ng
Ng
( ) ( 298.15 T⁄K ) Bkl
∑ ∑ (R
ik - Rjk)(Ril - Rjl)Akl ·
k)1 l)1
2
Akl
√ai(T) · aj(T)
-1
]
-
(
√ai(T) - √aj(T) bi
bj
)
2
bi · bj
(2)
In eq 2, Ng is the number of different groups defined by the method (for the time being, 15 groups are defined and Ng ) 15). Rik is the fraction of molecule i occupied by group k (occurrence of group k in molecule i divided by the total number of groups present in molecule i). Akl ) Alk and Bkl ) Blk (where k and l are two different groups) are constant parameters determined in our previous papers.1-6 Ability of the PPR78 Model To Predict the New Binary VLE Data Data from Janisch et al. The data by Janisch et al.12 can be seen on Figure 1a and b for the systems N2 + methane and N2 + ethane. The experimental data points shown on Figure 1 are identical to those shown by Janisch et al.12 in their own paper and include data from other authors.20-22 This allows us to compare the different models used to predict the VLE data. By looking at Figure 1a, it is obvious that the PPR78 model is able to predict with high accuracy the behavior of the N2(1) + methane(2) system. The paper by Janisch et al.12 shows that the VTPR and PSRK models are equivalent and lead, as PPR78, to excellent results. This is confirmed by the relative average deviation of bubble pressures (∆P%) and the absolute average deviation of vapor composition (∆y1) given in Table 1 for the three group contribution equations of state (GCEOS). The N2 + methane system exhibits type I phase behavior in the classification scheme of van Konynenburg and Scott,23 and we know from our experience that cubic GCEOS are generally able to reproduce type I behavior accurately. That is why small deviations are observed in the present case. The results for the system methane(1) + ethane(2), also studied by Janisch et al.,12 are also given in Table 1. For this system, the PPR78 model is twice as accurate as the PSRK model.
10.1021/ie800636h CCC: $40.75 2008 American Chemical Society Published on Web 08/26/2008
7484 Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008
Figure 1. Prediction of isothermal dew and bubble curves for the two systems nitrogen(1)/methane(2) and nitrogen(1)/ethane(2) using the PPR78 model. Solid lines: predicted curves with the PPR78 model. (a) System nitrogen(1)/methane(2) at four different temperatures: T1 ) 130.00 K (kij ) 0.0338), T2 ) 150.00 K (kij ) 0.0349), T3 ) 160.00 K (kij ) 0.0354), and T4 ) 170.00 K (kij ) 0.0360). (+) Experimental points from Kidnay et al.20 and (O) experimental points from Janisch et al.12 (b) System nitrogen(1)/ethane(2) at two different temperatures: T1 ) 170.00 K (kij ) 0.0456) and T2 ) 270.00 K (kij ) 0.0305). (+) Experimental points from Gupta et al.21 and Brown et al.;20 (O) experimental points from Janisch et al.12 Table 1. Comparison of the Ability of Three Models (PPR78, PSRK, VTPR) To Predict VLE Data PPR78 ∆P% N2 + CH4 N2 + C2H6 CH4 + C2H6
1.5 8.2a 1.8a
PSRK ∆P%
∆y1 a
0.004 0.006a 0.004a
a
1.1 11.2 3.7
VTPR
∆y1
∆P%
∆y1
0.005 0.011 0.008
1.2 9.4 2.2
0.005 0.009 0.006
a The values in boldface type correspond to the smallest deviations (in pressure and vapor composition) for the considered system.
Let us now turn to the system N2(1) + ethane(2), which exhibits a type III phase behavior5 according to the classification of Van Konynenburg and Scott.23 We know5 that it is extremely difficult to fit the parameters of a cubic GCEOS in order to predict type III phase behavior. This is why (see Figure 1b and Table 1) the deviations observed for this system are higher than those observed previously for the N2 + CH4 system. This is particularly true in the critical region where the calculated dew and bubble pressures are systematically higher than the experimental values (see Figure 1b). From Table 1 and from the comparison of Figure 1b with figures published by Janisch et al.,12 it is clear that the PPR78 model is more accurate (especially in the critical region) than the VTPR and PSRK models. Data from Garcı´a-Sa´nchez et al. Professor F. Garcı´aSa´nchez, who is well-known for his accurate measurements on systems containing N2,24-27 recently sent us some not yet published VLE data on the binary system N2(1) + n-decane(2). These data cover the temperature range 344-563 K and describe nearly the whole composition range. The parameters of the PPR78 model were obviously not fitted on these experimental data points. It is thus extremely interesting to test the prediction ability of our model on such data. Indeed, these new data cover a temperature range much higher than the one used to fit the parameters of the PPR78 model. The results are presented in Figures 2 and 3. The N2 + n-decane system exhibits type III phase behavior. It is thus not amazing that the predicted curves remain above the experimental ones in the critical area. In order to evaluate the ability of the PPR78 model to predict the behavior of the N2(1) + n-decane(2) system, the same objective function as the one defined in our previous papers (see, for example, eq 5 in ref 5) was used. This function takes into account the
relative deviations on the liquid phase composition, on the vapor-phase composition, on the critical mole fraction, and on the binary critical pressure. For the N2(1) + n-decane(2) system, the value of the objective function is Fobj ) 8.79%. In our previous study,5 a similar value (8.70%) was obtained by considering the whole database (nitrogen + paraffins, aromatics, naphthenes and CO2). A comparison between PPR78 and the predictive model PSRK was also performed (see Figures 2 and 3). To compare these two models, we define the average overall deviation on the liquid-phase composition nbubble
∑ (|x
1,exp - x1,cal|)i
∆x1 ) ∆x2 )
i)1
nbubble
(3)
the average overall deviation on the gas-phase composition ndew
∑ (|y
1,exp - y1,cal|)i
∆y1 ) ∆y2 )
i)1
ndew
(4)
the average overall deviation on the critical composition ncrit
∑ (|x
c1,exp - xc1,cal|)i
∆xc1 ) ∆xc2 )
i)1
ncrit
(5)
the average overall deviation on the binary critical pressure ncrit
∑ (|P
cm,exp - Pcm,cal|)i
∆Pc )
i)1
ncrit
(6)
The numerical values of these quantities for both models are reported in Table 2. By looking at Figures 2 and 3, one can notice that the models PPR78 and PSRK represent the VLE data with a similar accuracy. Their main difference essentially lies in the representation of the critical region and those of the bubble points. More explicitly, PSRK and PPR78 both illustrate the problem of cubic EOS for properly representing the supercritical systems:
Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008 7485
Figure 2. Prediction of isothermal dew and bubble curves for the nitrogen(1)/n-decane(2) system using the PPR78 model. Solid lines: predicted curves with the PPR78 model. Dashed lines: predicted curves with the PSRK model. (+) Experimental bubble points, (/) experimental dew points, and (O) experimental critical points from Garcia Sanchez et al. (a) T1 ) 344.60 K (kij ) 0.0878), (b) T2 ) 377.40 K (kij ) 0.0751), (c) T3 ) 410.90 K (kij ) 0.0633), (d) T4 ) 463.70 K (kij ) 0.0463), (e) T5 ) 503.00 K (kij ) 0.0341), (f) T6 ) 533.50 K (kij ) 0.0246), and (g) T7 ) 563.10 K (kij ) 0.0153).
N2 + n-alkanes (n g 2). Because the shape of the isothermal and isobaric phase diagrams of such systems is quite unusual within the critical region (i.e., very flattened experimental bubble
and dew curves in the vicinity of the critical point), predictive cubic EOS cannot perfectly restitute such a behavior (this issue is discussed with more details in ref 5).
7486 Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008
Figure 3. Prediction of the critical locus for the nitrogen(1)/n-decane(2) system. Solid lines: predicted curves with the PPR78 model. Dashed lines: predicted curves with the PSRK model. (O) Experimental critical points from Garcia Sanchez et al. (a) Critical pressure versus critical temperature. (b) Critical temperature versus nitrogen critical composition. Table 2. Comparison of the Ability of Two Models (PPR78 and PSRK) To Represent VLE Data of the Binary System Nitrogen(1)/n-Decane(2) models
∆x1
∆y1
∆xc1
∆Pc /bar
PPR78 PSRK
0.0354 0.0159
0.0099 0.0100
0.0563 0.0598
86.2 116
As a consequence, when one wants to develop a predictive model from a cubic EOS for supercritical systems containing N2 + n-alkanes, a real dilemma arises. If special attention is paid to critical points for improving their prediction, the predicted bubble curve is systematically more poorly resti-
tuted than when the attention is focused on bubble and dew experimental points. Conversely, when the bubble curve is well reproduced, the critical region is always very badly represented. These problems are essentially met in the area of the (pressure, temperature) diagram in which the critical locus of the binary mixture becomes nearly vertical (very high values of the slope dPc /dT). To sum up, either the critical region is satisfactorily represented (and, in that case, the representation of the bubble
Figure 4. Prediction VLE phase diagrams for the ternary system N2(1) + methane(2) + ethane(3). Solid green lines: predicted curves with the PPR78 model. Solid red lines bounded by two circles: experimental liquid-vapor tie lines. (0) Predicted critical point of the mixture. (a) at T ) 160 K and P ) 20 bar, (b) at T ) 140 K and P ) 20 bar, (c) at T ) 200 K and P ) 40 bar, and (d) at T ) 200 K and P ) 80 bar.
Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008 7487 Table 3. Ability of the PPR78 Model To Represent VLE Data on Two Ternary Systems Containing Nitrogen ternary system
∆x1
∆x2
∆x3
∆y1 >
∆y2
∆y3
number of bubble points
number of dew points
N2(1) + CH4(2) + C2H6(3) CH4(1) + N2(2) + n-decane(3)
0.0123 0.0137
0.0499 0.0080
0.0549 0.0111
0.0061 0.0041
0.0057 0.0064
0.0085 0.0068
346 174
346 174
points is less effective), either the bubble points are perfectly reproduced (and, in that case, the critical points are badly calculated). As can be seen in Figures 2 and 3, developers of the PSRK method chose to reproduce the bubble curve with quite good accuracy though the calculated critical points are far from the experimental values, whereas for the PPR78 method, we decided to find a compromise between perfectly representing the bubble curve and restituting the critical points (see ref 5). These remarks are in accordance with the numerical values presented in Table 2. In conclusion, it is extremely interesting to see that the PPR78 GCEOS predicts these new data with an accuracy similar to the one observed on the binary systems used to determine the parameters of the model.
PPR78. For the second ternary system, 174 bubble and dew points35 were used. For calculating the deviations between the PPR78 model and the experimental points, we used a flash calculation performed for each couple of bubble and dew points at the same temperature and pressure as the experimental data but with an overall composition equal to the average composition between the bubble and the dew compositions. Then, the bubble and dew compositions calculated by the flash algorithm can be compared to the experimental ones. By doing so, we defined the following quantities: the average overall deviations on the liquid-phase composition nbubble
Ability of the PPR78 Model To Predict Ternary VLE Data We have considered two ternary systems containing nitrogen for testing the predictive ability of the PPR78 method: the N2(1) + methane(2) + ethane(3) and the methane(1) + N2(2) + n-decane(3) systems. Regarding the first ternary system, 346 experimental couples of bubble and dew points stemming from the open literature28-34 were compared to those calculated by
∆x1 )
∑
nbubble
(|x1,exp - x1,cal|)i
i)1
nbubble
∑ (|x
2,exp - x2,cal|)i
,
∆x2 )
i)1
nbubble
,
nbubble
∑ (|x
3,exp - x3,cal|)i
∆x3 )
i)1
nbubble
(7)
the average overall deviations on the gas-phase composition
Figure 5. Prediction VLE phase diagrams for the ternary system methane(1) + N2(2) + n-decane(3). Solid green lines: predicted curves with the PPR78 model. Solid red lines bounded by two circles: experimental liquid-vapor tie lines. (a) at T ) 310.93 K and P ) 68.95 bar, (b) at T ) 344.26 K and P ) 137.90 bar, (c) at T ) 377.59 K and P ) 206.84 bar, and (d) at T ) 377.59 K and P ) 344.74 bar.
7488 Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008 ndew
ndew
∑ (|y
1,exp - y1,cal|)i
∆y1 )
i)1
ndew
∑ (|y
2,exp - y2,cal|)i
,
∆y2 )
i)1
,
ndew ndew
∑ (|y
3,exp - y3,cal|)i
∆y3 )
i)1
ndew
(8)
The numerical values of these deviations for the two considered ternary systems are reported in Table 3. As can be observed, these are nearly all weaker than 1% except for the liquid-phase compositions of the ternary system N2(1) + methane(2) + ethane(3) for which the deviations are ∼5%. Figures 4 and 5 illustrate the results by representing some bubble and dew VLE ternary data points in equilateral triangles. From qualitative and quantitative points of view, the studied ternary systems are well predicted by the PPR78 model. Indeed, the deviations generally remain below 1% concerning the vapor phase and below 5% for the liquid phase. Conclusion The phase behavior prediction of systems containing alkanes and nitrogen is a challenging task. Except the binary system N2 + methane, which exhibits a type I phase behavior in the classification scheme of van Konynenburg and Scott,23 all the other alkanes mixed with nitrogen exhibit a type III phase behavior. In the present paper, a comparison between the three predictive equations of state PPR78, VTPR, and PSRK were carried out. As a conclusion, all of them are nearly equivalent for representing the system N2(1) + methane(2) but behave differently in representing the system N2(1) + ethane(2). In this case, the PPR78 GCEOS leads to the most satisfying results. The ability of the PPR78 model to predict new data was also tested on the binary system N2(1) + n-decane(2). Such type III systems are not very accurately predicted by a GC approach with cubic EOS, but our model remains efficient and can pretend to represent the binary with an overall deviation lower than 10%. Regarding ternary systems involving nitrogen and alkane compounds, PPR78 seems to be able to predict their behavior with a satisfying accuracy. Acknowledgment Dr. Fernando Garcı´a-Sa´nchez is gratefully acknowledged for sending us many accurate experimental data before having published them. Dr. Gabriele Raabe is also warmly acknowledged for sending us many details on the work described in her last paper. Literature Cited (1) Jaubert, J. N.; Mutelet, F. VLE predictions with the Peng-Robinson equation of state and temperature dependent kij calculated through a group contribution method. Fluid Phase Equilib. 2004, 224 (2), 285–304. (2) Jaubert, J. N.; Vitu, S.; Mutelet, F.; Corriou, J. P. Extension of the PPR78 model (Predictive 1978 Peng Robinson EOS with temperature dependent kij calculated through a group contribution method) to systems containing aromatic compounds. Fluid Phase Equilib. 2005, 237 (1-2), 193–211. (3) Vitu, S.; Jaubert, J. N.; Mutelet, F. Extension of the PPR78 model (Predictive 1978, Peng Robinson EOS with temperature dependent kij calculated through a group contribution method) to systems containing naphtenic compounds. Fluid Phase Equilib. 2006, 243, 9–28. (4) Vitu, S.; Privat, R.; Jaubert, J. N.; Mutelet, F. Predicting the phase equilibria of CO2 + hydrocarbon systems with the PPR78 model (PR EOS
and kij calculated through a group contribution method). J. Supercrit. Fluids 2008, 45 (1), 1–26. (5) Privat, R.; Jaubert, J. N.; Mutelet, F. Addition of the nitrogen group to the PPR78 model (Predictive 1978 Peng Robinson EOS with temperaturedependent kij calculated through a group contribution method). Ind. Eng. Chem. Res. 2008, 47 (6), 2033–2048. (6) Privat, R.; Jaubert, J. N.; Mutelet, F. Addition of thesulfhydryl group (-SH) to the PPR78 model (Predictive 1978, Peng-Robinson EOS with temperature dependent kij calculated through a group contribution method). J. Chem. Thermodyn. 2008, 40 (9), 1331–1341. (7) Mutelet, F.; Vitu, S.; Privat, R.; Jaubert, J. N. Solubility of CO2 in branched alkanes in order to extend the PPR78 model (Predictive 1978, Peng Robinson EOS with temperature dependent kij calculated through a group contribution method) to such systems. Fluid Phase Equilib. 2005, 238 (2), 157–168. (8) Vitu, S.; Jaubert, J. N.; Pauly, J.; Daridon, J. L.; Barth, D. Bubble and Dew Points of Carbon Dioxide + a Five-Component Synthetic Mixture: Experimental Data and Modeling with the PPR78 Model. J. Chem. Eng. Data 2007, 52 (5), 1851–1855. (9) Vitu, S.; Jaubert, J. N.; Pauly, J.; Daridon, J. L.; Barth, D. Phase equilibria measurements of CO2 + methyl cyclopentane and CO2 + isopropyl cyclohexane binary mixtures at elevated pressures. J. Supercrit. Fluids 2008, 44 (2), 155–163. (10) Vitu, S.; Jaubert, J. N.; Pauly, J.; Daridon, J. L. High-pressure phase behaviour of the binary system (CO2 + cis-decalin) from 292.75 to 373.75 K. J. Chem. Thermodyn. 2008, 40 (9), 1358–1363. (11) Robinson, D. B.; Peng, D. Y. The characterization of the heptanes and heavier fractions for the GPA Peng-Robinson programs, Gas Processors Association, Research Report RR-28, 1978. (12) Janisch, J.; Raabe, G.; Ko¨hler, J. Vapor-liquid equilibria and saturated liquid densities in binary mixtures of nitrogen, methane, and ethane and their correlation using the VTPR and PSRK GCEOS. J. Chem. Eng. Data 2007, 52, 1897–1903. (13) Garcı´a-Sa´nchez, F. Personal communication. (14) Ahlers, J.; Gmehling, J. Development of a universal group contribution equation of state. I. Prediction of liquid densities for pure compounds with a volume translated Peng-Robinson equation of state. Fluid Phase Equilib. 2001, 191, 177–188. (15) Ahlers, J.; Gmehling, J. Development of a Universal Group Contribution Equation of State. 2. Prediction of Vapor-Liquid Equilibria for Asymmetric Systems. Ind. Eng. Chem. Res. 2002, 41, 3489–3498. (16) Ahlers, J., III. Prediction of Vapor-Liquid Equilibria, Excess Enthalpies, and Activity Coefficients at Infinite Dilution with the VTPR Model. Ind. Eng. Chem. Res. 2002, 41, 5890–5899. (17) Holderbaum, T.; Gmehling, J. PSRK: A Group Contribution Equation of State Based on UNIFAC. Fluid Phase Equilib. 1991, 70, 251– 265. (18) Fischer, K.; Gmehling, J. Further development. Status and results of the PSRK method for the prediction of vapor-liquid equilibria and gas solubilities. Fluid Phase Equilib. 1996, 121, 185–206. (19) Horstmann, S.; Jabloniec, A.; Krafczyk, J.; Fischer, K.; Gmehling, J. PSRK: group contribution equation of state: comprehensive revision and extension IV, including critical constants and R-function parameters for 1000 components. Fluid Phase Equilib. 2005, 227, 157–164. (20) Kidnay, A. J.; Miller, R. C.; Parrish, W. R.; Hiza, M. J. Liquidvapor phase equilibriums in the molecular nitrogen-methane system from 130 to 180.deg.K. Cryogenics 1975, 15 (9), 531–540. (21) Gupta, M. K.; Gardner, G. C.; Hegarty, M. J.; Kidnay, A. J. LiquidVapor Equilibria for the N2 + CH4 + C2H6 System from 260 to 280 K. J. Chem. Eng. Data 1980, 25 (4), 313–318. (22) Brown, T. S.; Sloan, E. D.; Kidnay, A. J. Vapor-liquid equilibria in the nitrogen + carbon dioxide + ethane system. Fluid Phase Equilib. 1989, 51, 299–313. (23) Van Konynenburg, P. H.; Scott, R. L. Critical lines and phase equilibriums in binary Van der Waals mixtures. Philos. Trans. R. Soc. London, Ser. A. 1980, 298, 495–540. (24) Silva-Oliver, G.; Eliosa-Jimenez, G.; Garcı´a-Sa´nchez, F.; AvendanoGomez, J. R. High-pressure vapor-liquid equilibria in the nitrogen-n-pentane system. Fluid Phase Equilib. 2006, 250 (1-2), 37–48. (25) Eliosa-Jimenez, G.; Silva-Oliver, G.; Garcı´a-Sa´nchez, F.; De Ita de la Torre, A. High-Pressure Vapor-Liquid Equilibria in the Nitrogen + n-Hexane System. J. Chem. Eng. Data 2007, 52 (2), 395–404. (26) Garcı´a-Sa´nchez, F.; Eliosa-Jimenez, G.; Silva-Oliver, G.; GodinezSilva, A. High-pressure (vapor + liquid) equilibria in the (nitrogen + n-heptane) system. J. Chem. Thermodyn. 2007, 39 (6), 893–905. (27) Silva-Oliver, G.; Eliosa-Jimenez, G.; Garcı´a-Sa´nchez, F.; AvendanoGomez, J. R. High-pressure vapor-liquid equilibria in the nitrogen-n-nonane system. J. Supercrit. Fluids 2007, 42 (1), 36–47.
Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008 7489 (28) Lu, B.C. Y.; Yu, P.; Poon, D. P. L. Formation of a Third Liquid Layer in the Nitrogen-Methane-Ethane System. Nature 1969, 222 (5195), 768–769. (29) Yu, P.; Elshayal, I. M.; Lu, B. C. Y. Liquid-liquid-vapor equilibriums in the nitrogen-methane-ethane system. Can. J. Chem. Eng. 1969, 47 (5), 495–498. (30) Gupta, M. K.; Gardner, G. C.; Hegarty, M. J.; Kidnay, A. J. Liquidvapor equilibriums for the N2 + CH4 + C2H6 system from 260 to 280 K. J. Chem. Eng. Data 1980, 25 (4), 313–318. (31) Chang, S.-D.; Lu, B. C. Y. Vapor-liquid equilibriums in the nitrogen-methane-ethane system. Chem. Eng. Prog., Symp. Ser. 1967, 63 (81), 18–27. (32) Cosway, H. F.; Katz, D. L. Low-temperature vapor-liquid equilibrium in ternary and quaternary systems containing hydrogen, nitrogen, methane, and ethane. AIChE J. 1959, 5, 40–50.
(33) Trappehl, G.; Knapp, H. Vapor-liquid equilibria in the ternary mixtures nitrogen-methane-ethane and nitrogen-ethane-propane. Cryogenics 1987, 27 (12), 696–716. (34) Barsuk, S. D.; Ben’yaminovich, O. A. Liquid-vapor equilibrium in a nitrogen-methane-ethane mixture. GazoVaya Promyshlennost. 1973, 12, 38–39. (35) Azarnoosh, A.; McKetta, J. J. Vapor-liquid equilibrium in the methane-n-decane-nitrogen system. J. Chem. Eng. Data 1963, 8 (4), 513– 519.
ReceiVed for reView April 19, 2008 ReVised manuscript receiVed July 10, 2008 Accepted August 4, 2008 IE800636H
