Romain Privat, Jean-Noe1l Jaubert,* and Fabrice Mutelet

Transcription

1 Ind. Eng. Chem. Res. 28, 47, Addition of the Nitrogen Group to the PPR78 Model (Predictive 1978, Peng Robinson EOS with Temperature-Dependent k ij Calculated through a Group Contribution Method) Romain Privat, Jean-Noe1l Jaubert,* and Fabrice Mutelet Laboratoire de Thermodynamique des Milieux Polyphasés, Nancy-UniVersité, 1 rue GrandVille, B.P. 2451, F-541 Nancy Cedex, France In 24, we started to develop a group contribution method aimed at estimating the temperature-dependent binary interaction parameters (k ij (T)) for the widely used Peng-Robinson equation of state (EOS). This model was called PPR78 (predictive 1978, Peng Robinson EOS), because it relies on the Peng-Robinson EOS as published by Peng and Robinson in 1978 and because the addition of a group contribution method to estimate the k ij value makes it predictive. In our previous papers, 12 groups were defined: CH 3,CH 2, CH, C, CH 4 (methane), C 2 H 6 (ethane), CH aro,c aro,c fused aromatic rings,ch 2,cyclic,CH cyclic ) C cyclic, and CO 2. Thus, it was possible to estimate the k ij value for any mixture that contains alkanes, aromatics, naphthenes, and CO 2, regardless of the temperature. In this study, the PPR78 model is extended to systems that contain nitrogen. To do so, the group N 2 was added. Introduction Nitrogen is a major component of petroleum fluids. Moreover, the injection of N 2 into oil reservoirs is a currently used oil recovery technique. To simulate and design the processes that involve N 2, it is necessary to predict the phase equilibrium of mixtures that contain N 2 in both the subcritical and critical regions. To meet these requirements, Jaubert and co-workers 1-7 developed a group contribution method that allowed estimation of the temperature-dependent binary interaction parameters (k ij (T)) for the widely used Peng-Robinson equation of state (EOS). Because their model relies on the Peng-Robinson EOS as published by Peng and Robinson 8 in 1978, and because the addition of a group contribution method to estimate the k ij value makes it predictive, Jaubert et al. decided to call this new model PPR78 (predictive 1978, Peng-Robinson EOS). In our previous papers, groups were defined: CH 3, CH 2, CH, C, CH 4 (methane), C 2 H 6 (ethane), CH aro, C aro, C fused aromatic rings,ch 2,cyclic,CH cyclic ) C cyclic, and CO 2. Thus, it was possible to estimate the k ij value for any mixture that contained saturated hydrocarbons (n-alkanes and branched alkanes), aromatic hydrocarbons, cyclic hydrocarbons (naphthenes), and carbon dioxide, regardless of the temperature. In this study, the PPR78 model is extended to systems that contain nitrogen. To do so, the N 2 group was added. The interactions between this new group and the 12 groups previously defined (a total of 24 parameters) are determined. Today, it is thus possible to estimate, at any temperature, the k ij value between two components in any mixture that contains paraffins, naphthenes, aromatics, CO 2, and N 2. Difficulties in Predicting the Phase Behavior of the N 2 + Hydrocarbon Binary Mixtures All binary N 2 + hydrocarbon systems develop, except for methane, Type III phase diagrams in the classification scheme * Author to whom correspondence should be addressed. Fax: addresss: jean-noel.jaubert@ensic.inpl-nancy.fr. of van Konynenburg and Scott. 9 Such systems are known to be extremely difficult to predict with a cubic EOS. Another major difficulty in the modeling of binary systems that contain N 2 with a cubic EOS comes from the unusual shape of the isothermal (P,x,y) diagrams for such systems. Indeed, as shown in Figure 1a for the N 2 + n-hexane system at T ) K, in the vicinity of the critical point, the experimentally determined diagram becomes very flat (in a large composition range around the critical composition, the slope of the bubble and dew curves is maintained low). Using a cubic EOS, such behavior is impossible to reproduce and the slope of the bubble and dew curves in the vicinity of the critical composition will always be much steeper than that which is observed experimentally. This last point remains true regardless of the alpha function used (Soave, Twu Bluck Cunningham Coon,...). Therefore, the choice of the best k ij value for such systems becomes an issue. If we select, as in Figure 1b, a k ij value that allows one to perfectly reproduce the critical pressure (in the present case, k ij )-.3), the dew curve also will be accurately reproduced, but huge deviations will appear on the bubble curve, because, in a large composition range around the critical point, the calculated shape of the phase diagram is not correct. The only way to better predict the bubble curve is to increase the k ij value. By doing so (see Figure 1c, 1d, 1e), we increase the critical pressure and we increase the deviations on the dew compositions. Figure 1 also clearly shows that, regardless of the k ij value, the calculated critical composition is more or less always the same and always much higher than the experimental value. This means that it is impossible to find a k ij value that would lead to a correct critical composition. As a conclusion, cubic EOS are unable to accurately reproduce the experimental shape of the isothermal (P,x,y) diagrams for binary systems that contain N 2. In this study, we decided to define a compromise between an accurate critical pressure and an accurate bubble composition. As an example, Figure 1d shows the prediction obtained with the PPR78 model (k ij ).2). However, we are conscious that this k ij value does not lead to very accurate results, but no k ij value is able to do a better job! 1.121/ie71524b CCC: $ American Chemical Society Published on Web 2/27/28

2 234 Ind. Eng. Chem. Res., Vol. 47, No. 6, 28 The PPR78 Model The Equation of State. In 1978, Peng and Robinson 8 published an improved version of their well-known EOS, noted as PR78 in this paper. For a pure component, the PR78 EOS is with P ) RT a i (T) - V-b i V(V+b i ) + b i (V-b i ) R ) J mol -1 K -1 b i ) ( RT c,i P c,i ) where P is the pressure, R the ideal gas constant, T the temperature, V the molar volume, T c the critical temperature, P c the critical pressure, and ω the acentric factor. In this paper, the PR78 EOS is used. To apply such an EOS to mixtures, mixing rules are used to calculate the a and b values of the mixtures. Classical mixing rules are used in this study: where z k represents the mole fraction of component k in a mixture, and N is the number of components in the mixture. The term k ij (T) is the so-called binary interaction parameter which characterizes molecular interactions between molecules i and j. In this paper, to obtain a predictive model and to define the PPR78 model (predictive 1978, PR EOS), k ij, which is dependent on temperature, is calculated by a group contribution method through the following expression: More information on eq 4 may be found in our first article. 1 The PPR78 model is thus defined by eqs 1-4. In eq 4, T is the temperature and the parameters a i and b i are simply calculated by eq 2. N g is the number of different groups defined by the method (for the time being, 13 groups are defined and N g ) 13). The parameter R ik 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). A kl () A lk ) and B kl () B lk ) (where k and l are two different groups) are constant parameters determined either in this study or in our previous papers 1-4 (A kk ) B kk ) ). For the new group )[ 1 + m i( 1 - T 2 T c,i)] (1) (2a) (2b) a i ) ( R2 2 T c,i (2c) P { c,i m 2 i ) ω i ω i (if ω i e.491) m i ) ω i ω 2 i + k ij (T) ).16666ω i 3 2[ {- 1 N g k)1 (if ω i >.491) } (2d) N N a ) i)1 z i z j a i a j (1 - k ij (T)) j)1 N b ) z i b i i)1 N g (R -R ik jk )(R il -R jl kl( )A K l)1 T ) ( a i (T) b i )2 a j (T) - b j (3a) (3b) (B kl /A kl )-1] - a i (T)a j (T) }/[2 (4) b i b j ] added in this paper (group 13 ) N 2 ), we must estimate the interactions between this new group and the 12 groups previously defined. Therefore, we must estimate 24 parameters (12 A kl values and 12 B kl values). These parameters have been determined to minimize the deviations between calculated and experimental VLE data from an extended database. The corresponding A kl and B kl values (expressed in MPa) are summarized in Table 1. An example of k ij calculation may be found in our first article. 1 Database and Reduction Procedure. Table 2 presents the list of pure components used in this study. The pure fluid physical properties (T c, P c, and ω) used in this study originate from Poling et al. 1 Table 3 details the sources of the binary experimental data used in our evaluations, along with the temperature, pressure, and composition range for each binary system. Most of the data available in the open literature (3915 bubble points dew points + 87 mixture critical points) have been collected. Our database includes VLE data on 36 binary systems. The 24 parameters (12 A kl and 12 B kl ) determined in this study (see Table 1) are those that minimize the following objective function: where with with with F obj ) F obj,bubble + F obj,dew + F obj,crit. comp + F obj,crit. pressure n bubble + n dew + n crit + n crit (5) n bubble F obj,bubble ) 1.5( x + x i)1 x 1,exp x 2,exp)i x ) x 1,exp - x 1,cal ) x 2,exp - x 2,cal n dew F obj,dew ) 1.5( y + y i)1 y 1,exp y 2,exp)i y ) y 1,exp - y 1,cal ) y 2,exp - y 2,cal n crit F obj,crit. comp ) 1.5( x c + i)1 x c1,exp x c x c2,exp)i x c ) x c1,exp - x c1,cal ) x c2,exp - x c2,cal n crit ( F obj,crit. pressure ) 1 P cm,exp - P cm,cal i)1 P cm,exp )i (5a) (5b) (5c) (5d) The parameters n bubble, n dew, and n crit are the number of bubble points, dew points, and mixture critical points, respectively; x 1 is the mole fraction in the liquid phase of the most volatile component, and x 2 the mole fraction of the heaviest component (it is obvious that x 2 ) 1- x 1 ). Similarly, y 1 is the mole fraction in the gas phase of the most volatile component, and y 2 is the mole fraction of the heaviest component (it is obvious that y 2 ) 1 - y 1 ); x c1 is the critical mole fraction of the most volatile

3 Ind. Eng. Chem. Res., Vol. 47, No. 6, Figure 1. Isothermal dew and bubble curves for the N 2 (1) + n-hexane (2) binary system at T ) K, calculated with the Peng-Robinson equation of state (EOS), giving different k ij values: (+) experimental bubble points, (*) experimental dew points, and (O) experimental critical points. Solid lines represent calculated curves. Panel a shows the experimental data points, panel b shows data for k ij )-.3, panel c shows data for k ij )., panel d shows data for k ij ).2, and panel e shows data for k ij ).6. component, and x c2 the critical mole fraction of the heaviest component. P cm is the binary critical pressure. Results and Discussion For all of the 815 data points included in our database, the objective function defined by eq 5 is F obj ) 8.7%. The value of the objective function for each binary system is given in Table 3. The average overall deviation on the liquid-phase composition is x 1 ) x 2 ) n bubble ( x - x 1,exp 1,cal ) i i)1 ).25 n bubble and The average overall deviation on the gas-phase composition is and x% ) x 1 % + x 2 % ) F obj,bubble ) 1.8% 2 n bubble y 1 ) y 2 ) n dew ( y - y 1,exp 1,cal ) i i)1 ).12 n dew

4 236 Ind. Eng. Chem. Res., Vol. 47, No. 6, 28 N2 (group 13) y% ) y 1 % + y 2 % ) F obj,dew ) 7.42% 2 n dew Table 1. Group Interaction Parameters Akl () Alk) and Bkl () Blk) (Both Given in Units of MPa) a CO2 (group 12) CHcyclic or Ccyclic (group 11) CH2,cyclic (group 1) Cfused aromatic rings (group 9) Caro (group 8) CHaro (group 7) C2H6 (group 6) CH4 (group 5) C (group 4) CH (group 3) CH2 (group 2) CH3 (group 1) CH3 (group 1) CH2 A12 ) (group 2) B12 ) CH A13 ) A23 ) (group 3) B13 ) B23 ) C A14 ) A24 ) A34 )-35.7 (group 4) B14 ) 84.3 B24 ) 315. B34 )-25.8 CH4 A15 ) A25 ) A35 ) A45 ) (group 5) B15 )-35. B25 ) 18.4 B35 ) 31.6 B45 ) C2H6 A16 ) A26 ) A36 ) A46 ) A56 ) 13.4 (group 6) B16 ) B26 ) B36 ) B46 ) 23.8 B56 ) CHaro A17 ) 9.25 A27 ) A37 ) 13.3 A47 ) A57 ) A67 ) (group 7) B17 ) B27 ) B37 ) B47 ) B57 ) B67 ) 5.79 Caro A18 ) 62.8 A28 ) A38 ) A48 ) A58 ) A68 )-3.88 A78 ) (group 8) B18 ) B28 ) B38 ) B48 )-326. B58 ) B68 ) 13.4 B78 ) 2.25 Cfused aromatic rings A19 ) 62.8 A29 ) A39 ) A49 ) A59 ) A69 )-3.88 A79 ) A89 ). (group 9) B19 ) B29 ) B39 ) B49 )-326. B59 ) B69 ) 13.4 B79 ) 2.25 B89 ). CH2,cyclic A1-1 ) 4.38 A2-1 ) A3-1 ) 11.9 A4-1 ) A5-1 ) A6-1 ) A7-1 ) A8-1 ) A9-1 ) (group 1) B1-1 ) 95.9 B2-1 ) B3-1 )-9.93 B4-1 ) 61.9 B5-1 ) B6-1 ) B7-1 ) B8-1 ) B9-1 ) CHcyclic or Ccyclic A1-11 ) A2-11 )-54.9 A3-11 ) A4-11 ) A5-11 ) 4.15 A6-11 ) 1.29 A7-11 ) A8-11 )-15.7 A9-11 )-15.7 A1-11 )-5.1 (group 11) B1-11 ) B2-11 ) B3-11 ) B4-11 )-19.5 B5-11 ) B6-11 ) B7-11 ) B8-11 ) B9-11 ) B1-11 ) CO2 A1-12 ) 164. A2-12 ) A3-12 ) A4-12 ) A5-12 ) A6-12 ) A7-12 ) 12.6 A8-12 ) 11.1 A9-12 ) A1-12 ) 13.1 A11-12 ) (group 12) B1-12 ) 269. B2-12 ) B3-12 ) B4-12 ) B5-12 ) B6-12 ) B7-12 ) B8-12 ) B9-12 ) B1-12 ) B11-12 ) 82.1 N2 A1-13 ) A2-13 ) A3-13 ) A4-13 ) A5-13 ) 37.9 A6-13 ) A7-13 ) A8-13 ) 284. A9-13 ) A1-13 ) A11-13 ) 1.9 A12-13 ) (group 13) B1-13 ) B2-13 ) 22.8 B3-13 ) B4-13 ) B5-13 ) 37.2 B6-13 ) B7-13 ) 49.6 B8-13 ) 1892 B9-13 ) 1892 B1-13 ) B11-13 ) B12-13 ) a Only the last line of this table, relative to N2, was determined in this study; the first 12 lines of this table were determined from our previous work. 1-4 and The average overall deviation on the critical composition is The average overall deviation on the binary critical pressure is and x c1 ) x c2 ) n crit ( x - x c1,exp c1,cal ) i i)1 ).33 n crit x c % ) x c1 % + x c2 % ) F obj,crit. comp ) 9.1% 2 n crit P c ) n crit ( P - P cm,exp cm,cal ) i i)1 n crit ) 2.5 bar P c % ) F obj,crit. pressure n crit ) 6.68% These results indicate that the PPR78 model remains an accurate predictive model, even if the deviations observed in this study are higher than those observed with hydrocarbons 1-3 or with CO 24 (for all the systems studied in our previous papers 1-4 (i.e., for >5 data points), the objective function is F obj ) 5.86%). As discussed at the beginning of this paper, in this study, it was necessary to find a compromise between a small deviation on the liquid-phase composition and a small deviation on the critical pressure. Indeed, a k ij value that is able to simultaneously Table 2. List of the 37 Pure Components Used in This Study component abbreviation component abbreviation nitrogen N 2 n-hexadecane 16 carbon dioxide CO 2 n-eicosane 2 methane 1 benzene B ethane 2 methyl benzene (toluene) mb propane 3 1,4-dimethyl benzene 14mB (para-xylene) 2-methyl 2m3 1,3-dimethyl benzene 13mB propane (meta-xylene) n-butane 4 n-propyl benzene prb 2,2-dimethyl 22m3 1,3,5-trimethyl benzene 135mB propane 2-methyl 2m4 naphthalene BB butane n-pentane 5 tertiobutyl benzene tbub n-hexane 6 1-methyl naphthalene 1mBB n-heptane 7 cyclopentane C5 2,2,4-trimethyl 224m5 cyclohexane C6 pentane n-octane 8 methyl cyclohexane mc6 2,2,5-trimethyl 225m6 ethyl cyclohexane ec6 hexane n-nonane 9 n-propyl cyclohexane prc6 n-decane 1 tetralin (1,2,3,4-tetrahydro tet naphthalene) n-dodecane 12 trans decalin tcc6 (trans-decahydro naphthalene) n-tetradecane 14

5 Ind. Eng. Chem. Res., Vol. 47, No. 6, Table 3. Binary Systems Database binary system a temperature range (K) pressure range (bar) x1 range (liquid mole fraction of first compound) y1 range (gas mole fraction of first compound) number of bubble points (T, P,x) number of dew points (T, P, y) number of binary critical points (Tcm, Pcm, xc) Fobj (from eq 5) for each binary system (%) reference(s) N2-CO N N , 3, 31, 34, 44, 45, 47, 5-59 N , 3, 5, 6-64 N2-2m , N , 6, N2-22m N2-2m N N ,83 N N2-224m , 95, 96 N , 95, 97, 98 N2-225m N , 91, 1 N , 96, 99, N , 99, N N N N2-B , N2-mB , 96, N2-14mB N2-13mB , 125 N2-prB N2-135mB N2-BB , 12 N2-tbuB N2-1mBB , 127 N2-C N2-C , 129, 13 N2-mC , 89, 131, 132 N2-eC N2-prC N2-tet N2-tCC total number of points: Fhobj ) 8.7% a Given in the following format: first compound-second compound.

6 238 Ind. Eng. Chem. Res., Vol. 47, No. 6, 28 Figure 2. Prediction of the corresponding critical locus of isothermal dew and bubble curves for two binary systems that contain N 2 and an n-alkane using the PPR78 model: (+) experimental bubble points, (*) experimental dew points, and (O) experimental critical points. Solid line represents predicted curves with the PPR78 model, and the dashed lines represent the vaporization curves of the pure compounds. Panel a shows data for the N 2 (1)/methane (2) system at six different temperatures (T 1 ) 9.68 K (k ij ).314), T 2 ) K (k ij ).326), T 3 ) 13. K (k ij ).338), T 4 ) 15. K (k ij ).349), T 5 ) 17. K (k ij ).36), and T 6 ) K (k ij ).367). Panel b shows data for the critical locus of the N 2/methane system. Panel c shows data for the N 2 (1)/ethane (2) system at two different temperatures (T 1 ) K (k ij ).535), and T 2 ) 23. K (k ij ).362)). Panel d shows data for the N 2 (1)/ethane (2) system at two different temperatures (T 1 ) K (k ij ).453), and T 2 ) 29. K (k ij ).278). Panel e shows the critical locus of the N 2/ethane system. predict the liquid-phase composition and the critical pressure does not exist. To illustrate the accuracy and the limitations of the proposed model, it was decided that several families of binary systems would be defined. It is indeed impossible to show the results for all the studied systems. Results for Mixtures of Nitrogen + n-alkanes. The binary system N 2 + methane exhibits Type I phase behavior in the classification scheme of van Konynenburg and Scott. 9 As a consequence, 1-4 the PPR78 model is able to reproduce the phase behavior of this system perfectly, whatever the temperature (see Figure 2a and 2b). For this system, the binary interaction

7 Ind. Eng. Chem. Res., Vol. 47, No. 6, Figure 3. Prediction of the corresponding critical locus of isothermal dew and bubble curves for two binary systems that contain N 2 and a n-alkane, using the PPR78 model: (+) experimental bubble points, (*) experimental dew points, (O) experimental critical points. Solid lines represent predicted curves with the PPR78 model, and the dashed lines represent the vaporization curves of the pure compounds. Panel a shows data for the N 2 (1)/n-pentane (2) system at two different temperatures (T 1 ) K (k ij ).557) and T 2 ) K (k ij )-.511)). Panel b shows data for the N 2 (1)/n-pentane (2) system at two different temperatures: T 1 ) K (k ij ).154) and T 2 ) K (k ij )-.235). Panel c shows data for the critical locus of the N 2/n-pentane system. Panel d shows data for the N 2 (1)/n-hexane (2) system at two different temperatures (T 1 ) K (k ij ).33), T 2 ) K (k ij )-.474)). Panel e shows data for the N 2 (1)/n-hexane (2) system at two different temperatures (T 1 ) K (k ij ).2), T 2 ) K (k ij )-.27)). Panel f shows data for the critical locus of the N 2/n-hexane system. parameter (k ij ) increases slightly with temperature. All the other binary mixtures of the N 2 + n-alkane system exhibit Type III phase behavior. From our experience, 1-4 it is thus very difficult to predict accurately (see Figures 2-4) the phase behavior of such systems with a cubic equation of state even with temperature-dependent k ij values. For all these other systems, the k ij value decreases with temperature. Moreover, regardless of the length of the n-alkane, the accuracy of the PPR78 is constant. As can be seen in Figures 2e, 3c, 3f, and 4c, the PPR78 predicts (with an acceptable accuracy) the critical loci of these binary systems. In return, the liquid-phase composition generally is systematically overestimated. We believe that the inevitable

8 24 Ind. Eng. Chem. Res., Vol. 47, No. 6, 28 Figure 4. Prediction of the corresponding critical locus of isothermal dew and bubble curves for two binary systems that contain N 2 and a n-alkane, using the PPR78 model: (+) experimental bubble points, (*) experimental dew points, and (O) experimental critical points. Solid lines represent predicted curves with the PPR78 model, and the dashed lines represent the vaporization curves of the pure compounds. Panel a shows data for the N 2 (1)/n-heptane (2) system at two different temperatures (T 1 ) K (k ij ).658), T 2 ) K (k ij ).853)). Panel b shows data for the N 2 (1)/n-heptane (2) system at two different temperatures (T 1 ) K (k ij ).362), T 2 ) K (k ij )-.168)). Panel c shows data for the critical locus of the N 2/n-heptane system. Panel d shows data for the N 2 (1)/n-hexadecane (2) system at two different temperatures (T 1 ) K (k ij ).11), T 2 ) K (k ij ).665)). Panel e shows data for the N 2 (1)/n-hexadecane (2) system at two different temperatures (T 1 ) K (k ij ).894), T 2 ) 73.4 K (k ij ).466)). Panel f shows data for the critical locus of the N 2/n-hexadecane system. compromise between a correct critical pressure and an accurate liquid-phase composition has been properly determined in the PPR78 model. Results for Mixtures of Nitrogen + Branched Alkanes. Our databank (see Table 3) contains VLE data for only five binary mixtures that contain nitrogen and a branched alkane. All these systems exhibit Type III phase behavior. Consequently (see Figure 5), the critical pressure is always overestimated and the liquid-phase composition is not very accurately predicted. As shown in Figure 5f, the overestimation of the critical pressure is generally not too high (15 bar on average). For all these systems, the k ij value is a monotonous decreasing function of temperature. Results for Mixtures of Nitrogen + Aromatic Compounds. VLE data are only known for nine binary systems that contain N 2 and an aromatic compound. The 916 experimental data points available for these systems unfortunately do not contain any critical points. Moreover, VLE data are generally only available

9 Ind. Eng. Chem. Res., Vol. 47, No. 6, Figure 5. Prediction of isothermal dew and bubble curves for three binary systems that contain N 2 and a branched alkane, using the PPR78 model (prediction of the critical locus for one system): (+) experimental bubble points, (*) experimental dew points, and (O) experimental critical points. Solid lines represent predicted curves with the PPR78 model, and the dashed lines represent the vaporization curves of the pure compounds. Panel a shows data for the N 2 (1)/2-methyl propane (2) system at three different temperatures (T 1 ) K (k ij ).113), T 2 ) K (k ij ).15), T 3 ) K (k ij ).993)). Panel b shows data for the N 2 (1)/2-methyl propane (2) system at three different temperatures (T 1 ) K (k ij ).19), T 2 ) K (k ij ).12), T 3 ) K (k ij ).964)). Panel c shows data for the N 2 (1)/2-methyl butane (2) system at two different temperatures (T 1 ) K (k ij ).956), T 2 ) K (k ij ).837)). Panel d shows data for the N 2 (1)/2,2,4-trimethyl pentane (2) system at T ) K (k ij ).887). Panel e shows data for the N 2 (1)/2,2,4-trimethyl pentane (2) system at T ) K (k ij ).86). Panel f shows data for the critical locus of the N 2/2,2-dimethyl propane (22m3) system. at low pressure, and finding the six parameters (three A kl and three B kl ) that better correlate the entire data is not an easy task. As can be seen in Figure 6, where four aromatic molecules were selected, the PPR78 model predicts the systems that contain an aromatic compound less accurately than those which contain an alkane. The predicted phase diagrams have the same drawbacks as those previously shown: the liquid-phase composition is not accurately predicted and the shape of the

10 242 Ind. Eng. Chem. Res., Vol. 47, No. 6, 28 Figure 6. Prediction of isothermal dew and bubble curves for four binary systems that contain N 2 and an aromatic compound, using the PPR78 model: (+) experimental bubble points, (*) experimental dew points. Solid lines represent predicted curves with the PPR78 model. Panel a shows data for the N 2 (1)/benzene (2) system at two different temperatures (T 1 ) K (k ij ).612), T 2 ) K (k ij ).358)). Panel b shows data for the N 2 (1)/benzene (2) system at two different temperatures (T 1 ) K (k ij ).314), T 2 ) K (k ij )-.23)). Panel c shows data for the N 2 (1)/toluene (2) system at two different temperatures (T 1 ) K (k ij )-.696), T 2 ) K (k ij )-.123)). Panel d shows data for the N 2 (1)/toluene (2) system at two different temperatures (T 1 ) K (k ij )-.86), T 2 ) K (k ij )-.125)). Panel e shows data for the N 2 (1)/meta-xylene (2) system at two different temperatures (T 1 ) K (k ij )-.643), T 2 ) K (k ij )-.14)). Panel f shows data for the N 2 (1)/1-methyl naphthalene (2) system at two different temperatures (T 1 ) 624. K (k ij )-.82), T 2 ) 73.3 K (k ij )-.144)). calculated diagram in the critical region is not similar to the experimental diagram. Once again, all these systems exhibit Type III phase behavior, and, once again, the k ij is a monotonous decreasing function of temperature. Generally, the k ij value is positive at low temperature and becomes negative at higher temperature.

11 Ind. Eng. Chem. Res., Vol. 47, No. 6, Figure 7. Prediction of isothermal dew and bubble curves for five binary systems that contain N 2 and a naphthenic compound, using the PPR78 model: (+) experimental bubble points, (*) experimental dew points. Solid lines represent predicted curves with the PPR78 model. Panel a shows data for the N 2 (1)/cyclopentane (2) system at two different temperatures (T 1 ) K (k ij ).733), T 2 ) 41.2 K (k ij ).183)). Panel b shows data for the N 2 (1)/methyl cyclohexane (2) system at two different temperatures (T 1 ) K (k ij ).118), T 2 ) K (k ij ).185)). Panel c shows data for the N 2 (1)/methyl cyclohexane (2) system at two different temperatures (T 1 ) K (k ij ).914), T 2 ) K (k ij )-.19)). Panel d shows data for the N 2 (1)/ethyl cyclohexane (2) system at two different temperatures (T 1 ) K (k ij ).11), T 2 ) K (k ij ).286)). Panel f shows data for the N 2 (1)/n-propyl cyclohexane (2) system at two different temperatures (T 1 ) K (k ij ).16), T 2 ) K (k ij ).384)). Panel f shows data for the N 2 (1)/tetralin (2) system at two different temperatures (T 1 ) 544. K (k ij )-.144), T 2 ) K (k ij )-.253)). Results for Mixtures of Nitrogen + Naphthenic Compounds (Also Called Naphthenes or Cycloparaffins). Our databank (see Table 3) contains VLE data for seven binary mixtures that contain nitrogen and a naphthene. The 539 experimental data points available for these systems unfortunately do not contain any critical points. Figure 7 shows predicted phase diagrams with the PPR78 model for five binary systems. The accuracy of our model is similar to that observed with paraffins and aromatics. All these systems exhibit Type III phase behavior. As a consequence, the calculated critical

12 244 Ind. Eng. Chem. Res., Vol. 47, No. 6, 28 Figure 8. Prediction of isothermal dew and bubble curves, prediction of the critical locus, and temperature dependence of k ij for the binary system N 2 + CO 2, using the PPR78 model: (+) experimental bubble points, (*) experimental dew points, and (O) experimental critical points. Solid lines represent predicted curves with the PPR78 model, and the dashed lines represent the vaporization curves of the pure compounds. Panel a shows data for T 1 ) K(k ij )-.856) and T 2 ) K (k ij )-.325). Panel b shows data for T 1 ) K (k ij )-.194) and T 2 ) K (k ij )-.437). Panel c shows data for T 1 ) 24. K (k ij )-.242) and T 2 ) K (k ij )-.514). Panel d shows data for T 1 ) K (k ij )-.294) and T 2 ) K(k ij )-.564). Panel e shows data for the critical locus. Panel f shows a graph of k ij vs T (the square indicates the temperature at which k ij ) ). pressure is often >2 bar (see Figures 7b and 7e). For all these systems, k ij is a monotonous decreasing function of temperature. Results for Mixtures of Nitrogen + Carbon Dioxide. Mixtures of nitrogen and carbon dioxide have been measured extensively (see Table 3), and there is a vast amount of reliable experimental phase equilibria and critical data (593 VLE data points were determined for this system). Although it exhibits Type III behavior (see Figure 8e), the PPR78 model is able to predict, with high accuracy, the phase behavior of this system. A few examples may be seen in Figure 8. For this system, the objective function defined by eq 5 is F obj ) 4.41%, which is smaller than the objective function obtained for the entire database (by a factor of 2). In the vicinity of the T c value for carbon dioxide, the critical locus is perfectly predicted with the PPR78 model. By decreasing the temperature, our model has a tendency to overestimate the critical pressure. Once again, the binary interaction parameter is a decreasing function of the temperature (see Figure 8f); k ij is positive at temperatures of <28 K and negative at temperatures of >28 K.

13 Ind. Eng. Chem. Res., Vol. 47, No. 6, Conclusion In two of our previous papers, 3,4 we concluded that, even with a temperature-dependent k ij expression, the Peng-Robinson equation of state (EOS) was not able to predict the critical loci of Type III systems accurately, according to the classification scheme of van Konynenburg and Scott. 9 This was particularly true at low temperature (in the vicinity of the upper critical end point), where the slope of the critical curve is often very steep (a small change of the temperature induces a large change of pressure). This paper has shown that the phase behavior of all binary N 2 + hydrocarbon fluid mixtures develop, except for methane, Type III phase diagrams. Therefore, it is not amazing that the results obtained in this paper are less accurate than those previously published. 1-4 This paper also gives proof that the N 2 + hydrocarbon binary systems do not behave classically. Because of the fact that, in a large composition range around the critical point, the slopes of the dew curve and the bubble curve remain low, the PPR78 model overestimates the liquidphase composition and the critical pressure. However, an objective function of <1% clearly indicates that the obtained results are quite good. Here, it is important to notice that many of the binary N 2 + hydrocarbon vapor-liquid equilibrium (VLE) data reported in the literature are generally not internally consistent and are mutually conflicting (i.e., there is a great deal of scatter among the experimental points). It is thus impossible to find a model able to simultaneously predict accurately all the available data. This paper allows one to conclude that, for all the N 2 + hydrocarbon systems (except methane), k ij is a decreasing function of temperature. Finally, with the group interactions determined in this study, today, it is possible to estimate the k ij for any mixture that contained N 2,CO 2, alkanes, aromatics, and naphthenes, regardless of the temperature. Nomenclature a(t) ) temperature-dependent function of the equation of state A kl, B kl ) constant parameters allowing the calculation of the binary interaction parameters b ) covolume k ij ) binary interaction parameter m ) shape parameter P ) pressure P c ) critical pressure R ) ideal gas constant T ) temperature T c ) critical temperature V)volume x i, y i, z i ) mole fractions Greek Letters ω ) acentric factor R ik ) fraction occupied by group k in molecule i Acknowledgment The French Petroleum Company TOTAL and, more particularly, Dr. François Montel and Dr. Pierre Duchet-Suchaux are gratefully acknowledged for sponsoring this research. Dr. Fernando García-Sánchez (Instituto Mexicano del Petróleo) is also gratefully acknowledged for sending us, two years before publication, much very accurate VLE data that he measured in his laboratory. Literature Cited (1) Jaubert, J. N.; Mutelet, F. VLE predictions with the Peng-Robinson equation of state and temperature dependent k ij calculated through a group contribution method. Fluid Phase Equilib. 24, 224 (2), (2) Jaubert, J. N.; Vitu, S.; Mutelet, F.; Corriou, J. P. Extension of the PPR78 model (Predictive 1978, Peng Robinson EOS with temperature dependent k ij calculated through a group contribution method) to systems containing aromatic compounds. Fluid Phase Equilib. 25, 237 (1-2), (3) Vitu, S.; Jaubert, J. N.; Mutelet, F. Extension of the PPR78 model (Predictive 1978, Peng Robinson EOS with temperature dependent k ij calculated through a group contribution method) to systems containing naphtenic compounds. Fluid Phase Equilib. 26, 243, (4) Vitu, S.; Privat, R.; Jaubert, J. N.; Mutelet, F. Predicting the phase equilibria of CO 2 + hydrocarbon systems with the PPR78 model (PR EOS and k ij calculated through a group contribution method). J. Supercrit. Fluids, in press (doi:1.116/j.supflu ). (5) Mutelet, F.; Vitu, S.; Privat, R.; Jaubert, J. N. Solubility of CO 2 in branched alkanes in order to extend the PPR78 model (Predictive 1978, Peng Robinson EOS with temperature dependent k ij calculated through a group contribution method) to such systems. Fluid Phase Equilib. 25, 238 (2), (6) 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. 27, 52 (5), (7) Vitu, S.; Jaubert, J.-N.; Pauly, J.; Daridon, J.-L.; Barth, D. Phase equilibria measurements of CO 2 + methyl cyclopentane and CO 2 + isopropyl cyclohexane binary mixtures at elevated pressures. J. Supercrit. Fluids 28, 44 (2), (8) Robinson, D. B.; Peng, D. Y. The characterization of the heptanes and heavier fractions for the GPA Peng-Robinson programs, Research Report RR-28, Gas Processors Association, Tulsa, OK, (9) 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 198, 298, (1) Poling, B. E.; Prausnitz, J. M.; O Connell, J. P. The Properties of Gases and Liquids, 5th Edition; McGraw-Hill: New York, 2. (11) Yucelen, B.; Kidnay, A. J. Vapor-Liquid Equilibria in the Nitrogen + Carbon Dioxide + Propane System from 24 to 33 K at Pressures to 15 MPa. J. Chem. Eng. Data 1999, 44 (5), (12) Brown, T. S.; Niesen, V. G.; Sloan, E. D.; Sloan, E. D.; Kidnay, A. J. Vapor-liquid equilibria for the binary systems of nitrogen, carbon dioxide, and n-butane at temperatures from 22 to 344 K. Fluid Phase Equilib. 1989, 53, (13) Brown, T. S.; Sloan, E. D.; Kidnay, A. J. Vapor-liquid equilibria in the nitrogen + carbon dioxide + ethane system. Fluid Phase Equilib. 1989, 51, (14) Zenner, G. H.; Dana, L. I. Liquid-vapor equilibrium compositions of carbon dioxide-oxygen-nitrogen mixtures. Chem. Eng. Prog. Symp. Ser. 1963, 59, (15) Al-Wakeel, I. M. Experimentelle und analytische Bestimmung von binaeren und ternaeren Dampf-Fluessig-Gleichgewichtsdaten der Stoffe Difluordichlormethan-Kohlendioxyd-Stickstoff im Bereich hoher Druecke und tiefer Temperaturen. Ph.D. Thesis, TU Berlin, Berlin, Germany, (16) Muirbrook, N. K.; Prausnitz, J. M. Multicomponent vapor-liquid equilibriums at high pressures. I. Experimental study of the nitrogen-oxygencarbon dioxide system at C. AIChE J. 1965, 11 (6), (17) Weber, W.; Zeck, S.; Knapp, H. Gas solubilities in liquid solvents at high pressures: apparatus and results for binary and ternary systems of nitrogen, carbon dioxide, and methanol. Fluid Phase Equilib. 1984, 18 (3), (18) Arai, Y.; Kaminishi, G. I.; Saito, S. Experimental determination of the P-V-T-X [pressure-volume-temperature-composition] relations for the carbon dioxide-nitrogen and the carbon dioxide-methane systems. J. Chem. Eng. Jpn. 1971, 4 (2), (19) Somait, F. A.; Kidnay, A. J.; Arthur, J. Liquid-vapor equilibriums at 27. K for systems containing nitrogen, methane, and carbon dioxide. J. Chem. Eng. Data 1978, 23 (4), (2) Al-Sahhaf, T. A.; Kidnay, A. J.; Sloan, E. D. Liquid + vapor equilibriums in the nitrogen + carbon dioxide + methane system. Ind. Eng. Chem. Fundam. 1983, 22 (4),

14 246 Ind. Eng. Chem. Res., Vol. 47, No. 6, 28 (21) Al-Sahhaf, T. A. Vapor-liquid equilibria for the ternary system nitrogen + carbon dioxide + methane at 23 and 25 K. Fluid Phase Equilib. 199, 55 (1-2), (22) Xu, N.; Dong, J.; Wang, Y.; Shi, J. Vapor-liquid equilibria for nitrogen-methane-carbon dioxide system near critical region. Huagong Xuebao 1992, 43 (5), (23) Xu, N.; Dong, J.; Wang, Y.; Shi, J. High pressure vapor liquid equilibria at 293 K for systems containing nitrogen, methane and carbon dioxide. Fluid Phase Equilib. 1992, 81, (24) Krichevskii, I. R.; Khazanova, N. E. Liquid-gas equilibrium in the nitrogen-carbon dioxide system under elevated pressures. Khim. Promst. (Moscow) 1962, (25) Yorizane, M.; Yoshimura, S.; Masuoka, H.; Miyano, Y.; Kakimoto, Y. New procedure for vapor-liquid equilibria. Nitrogen + carbon dioxide, methane + Freon 22, and methane + Freon 12. J. Chem. Eng. Data 1985, 3 (2), (26) Yorizane, M.; Yoshimura, S.; Masuoka, H.; Nakamura, M. Prediction of high-pressure vapor-liquid equilibriums for multicomponent systems by the BWR [Benedict-Webb-Rubin] equation of state. J. Chem. Eng. Jpn. 1971, 4 (1), (27) Yorizane, M. Determination of vapor-liquid equilibrium data at high pressure and low temperature. Kenkyu HokokusAsahi Garasu Kogyo Gijutsu Shoreikai 1971, 18, (28) Bian, B. Ph.D. Thesis, University of Nanjing, Nanjing, PRC, (29) Zhang, Z.; Guo, L.; Yang, X.; Knapp, H. Vapor and liquid equilibrium for nitrogen-ethane-carbon dioxide ternary system. Huagong Xuebao 1999, 5 (3), (3) Rozhnov, M. S.; Kozya, V. G.; Zhdanov, V. I. Phase ratios in twocomponent systems of C1-3 hydrocarbons and nitrogen. Khim. Promst. (Moscow). 1988, 11, (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), (32) Cines, M. R.; Roach, J. T.; Hogan, R. J.; Roland, C. H. Nitrogen- Methane Vapor-Liquid Equilibria. Chem. Eng. Prog. Symp. Ser. 1953, 49 (6), 1-1. (33) Bloomer, O. T.; Parent, J. D. Liquid-Vapor Phase Behavior of the Methane-Nitrogen System. Chem. Eng. Prog. Symp. Ser. 1953, 49 (6), (34) Hiza, M. J.; Haynes, W. M.; Parrish, W. R. Orthobaric liquid densities and excess volumes for binary mixtures of low molar-mass alkanes and nitrogen between 15 and 14 K. J. Chem. Thermodyn. 1977, 9 (9), (35) Skripka, V. G.; Nikitina, I. E.; Zhdanovich, L. A.; Sirotin, A. G.; Ben yaminovich, O. A. Liquid-vapor phase equilibriums at low temperatures in binary systems formed by components of natural gas. GazoV. Promst. 197, 15 (12), (36) Fuks, S.; Bellemans, A. Excess free energies and volumes of twosimple binary liquid mixtures: methane-krypton and nitrogen-methane. Bull. Soc. Chim. Belg. 1967, 76 (5-6), (37) McClure, D. W.; Lewis, K. L.; Miller, R. C.; Staveley, L. A. K. Excess enthalpies and Gibbs free energies for nitrogen + methane at temperatures below the critical point of nitrogen. J. Chem. Thermodyn. 1976, 8 (8), (38) Sprow, F. B.; Prausnitz, J. M. Vapor-Liquid equilibria for five cryogenic mixtures. AIChE J. 1966, 12 (4), (39) Parrish, W. R.; Hiza, M. J. Liquid-vapor equilibriums in the nitrogen-methane system between 95 and 12 deg K. AdV. Cryog. Eng. 1974, 19, (4) Stryjek, R.; Chappelear, P. S.; Kobayashi, R. Low-temperature vapor-liquid equilibriums of nitrogen-methane system. J. Chem. Eng. Data 1974, 19 (4), (41) Kidnay, A. J.; Miller, R. C.; Parrish, W. R.; Hiza, M. J. Liquidvapor phase equilibriums in the molecular nitrogen-methane system from 13 to 18 deg K. Cryogenics 1975, 15 (9), (42) Miller, R. C.; Kidnay, A. J.; Hiza, M. J. Liquid-vapor equilibria at 112. K for systems containing nitrogen, argon, and methane. AIChE J. 1973, 19 (1), (43) Fastovskii, V. G.; Petrovskii, Yu. V. Liquid and vapor equilibriums in the nitrogen-methane system. Zh. Fiz. Khim. 1957, 31, (44) Ellington, R. T.; Eakin, B. E.; Parent, J. D.; Gami, D. C.; Bloomer, O. T. Vapor-liquid phase equilibriums in the binary systems of CH 4,C 2H 6, and N 2. In Thermodynamic and Transport Properties of Gases, Liquids, and Solids, Papers Presented at the Symposium on Thermal Properties, February 23-26, 1959, Lafayette, IN: American Society of Mechanical Engineers (ASME): New York, 1959: pp (45) Cheung, H.; Wang, D. I. J. Solubility of Volatile Gases in Hydrocarbon Solvents at Cryogenic Temperatures. Ind. Eng. Chem. Fundam. 1964, 3 (4), (46) Kremer, H. Experimentelle Untersuchung und Berechnung von Hochdruck-Fluessigkeits-Dampf Gleichgewichten fuer tiefsiedende Gemische. Ph.D. Thesis, TU Berlin, Berlin, Germany, (47) Wilson, G. M. Vapor-liquid equilibria of nitrogen, methane, ethane, and propane binary mixtures at LNG temperatures from total pressure measurements. AdV. Cryog. Eng. 1975, 2, (48) Brandt, L. W.; Stroud, L. Phase equilibria in natural gas systemsapparatus with windowed cell for 8 pounds per square inch gauge and temperatures to -32 F. J. Ind. Eng. Chem. 1958, 5, (49) Kremer, H.; Knapp, H. Vapor-liquid equilibriums in ternary mixtures of hydrogen, nitrogen, carbon monoxide, and methane. Fluid Phase Equilib. 1983, 11 (3), (5) Grauso, L.; Fredenslund, A.; Mollerup, J. Vapor-Liquid Equilibrium Data for the Systems C 2H 6 + N 2,C 2H 4 + N 2,C 3H 8 + N 2, and C 3H 6 + N 2. Fluid Phase Equilib. 1977, 1 (1), (51) Stryjek, R.; Chappelear, P. S.; Kobayashi, R. Low-temperature vapor-liquid equilibriums of nitrogen-ethane system. J. Chem. Eng. Data 1974, 19 (4), (52) Eakin, B. E.; Ellington, R. T.; Gami, D. C. Physical-chemical properties of ethane-nitrogen mixtures. Inst. Gas Technol. Res. Bull. 1955, 26. (53) 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), (54) Kremer, H.; Knapp, H. Three-phase conditions [during gas processing] are predictable. Hydrocarbon Process. 1983, 62 (4), (55) Guedes, H. J. R.; Zollweg, J. A.; John, A.; Filipe, E. J. M.; Martins, L. F. G.; Calado, J. C. G. Thermodynamics of liquid (nitrogen + ethane). J. Chem. Thermodyn. 22, 34 (5), (56) Raabe, G.; Kohler, J. Phase equilibria in the system nitrogen-ethane and their prediction using cubic equations of state with different types of mixing rules. Fluid Phase Equilib. 24, , 3-9. (57) Gupta, M. K.; Gardner, G. C.; Hegarty, M. J.; Kidnay, A. J. Liquid- Vapor Equilibria for the N 2 + CH 4 + C 2H 6 System from 26 to 28 K. J. Chem. Eng. Data 198, 25 (4), (58) Zeck, S.; Knapp, H. Vapor-liquid and vapor-liquid-liquid phase equilibria for binary and ternary systems for nitrogen, ethane and methanol: Experiment and data reduction. Fluid Phase Equilib. 1986, 25 (3), (59) Raabe, G.; Janisch, J.; Koehler, J. Experimental studies of phase equilibria in mixtures relevant for the description of natural gases. Fluid Phase Equilib. 21, 185 (1-2), (6) Hudziak, J. A.; Kahvand, H.; Yassaie, M.; Leipziger, S. Dew point measurements for nitrogen-propane and nitrogen-butane mixtures. J. Chem. Eng. Data 1984, 29 (3), (61) Schindler, D. L.; Swift, G. W.; Kurata, F. More Low Temperature V-L Design Data. Hydrocarbon Process. 1966, 45 (11), (62) Bol shakov, P. E. et al. Solubility of a 1:3 nitrogen-hydrogen mixture in liquid ammonia at high pressures. Tr. Gos. Nauchno Issled. Proektn. Inst. Azotn. Promst. Prod. Org. Sin. 1954, 4, (63) Roof, J. G.; Baron, J. D. Critical loci of binary mixtures of propane with methane, carbon dioxide, and nitrogen. J. Chem. Eng. Data 1967, 12 (3), (64) Yorizane, M.; Sadamoto, S.; Yoshimura, S.; Masuoka, H.; Shiki, N.; Kimura, T.; Toyama, A. Low temperature vapor-liquid equilibriums. Nitrogen-propylene and carbon monoxide-methane systems. Kagaku Kogaku 1968, 32 (3), (65) Kalra, H.; Ng, H. J.; Miranda, R. D.; Robinson, D. B. Equilibrium Phase Properties of the Nitrogen-Isobutane System. J. Chem. Eng. Data 1978, 23 (4), (66) Robinson, D. B.; Kalra, H. The Equilibrium Phase Properties of Selected Binary Systems: n-heptane-hydrogen Sulfide, n-heptane- Carbon Dioxide and i-butane-nitrogen, Research Report RR-18, Gas Processors Association, Tulsa, OK, (67) Chen, G.; Knapp, H.; Hou, Y. Vapor-liquid equilibria for the nitrogen-isobutane system. J. Solution Chem. 1997, 26 (8), (68) Akers, W. W.; Attwell, L. L.; Robinson, J. A. Volumetric and phase behavior of nitrogen-hydrocarbon systems. Nitrogen-butane system. J. Ind. Eng. Chem. 1954, 46, (69) Roberts, L. R.; McKetta, J. J. Vapor-liquid equilibrium in the butane-nitrogen system. AIChE J. 1961, 7, (7) Shibata, S. K.; Sandler, S. I. High-pressure vapor-liquid equilibria involving mixtures of nitrogen, carbon dioxide, and n-butane. J. Chem. Eng. Data 1989, 34 (3), (71) Sauer, R. N. Ph.D. Thesis, University of Texas, Austin, TX, (72) Steinbach, H. G.; Steinbrecher, M. Solubility of nitrogen C 4- liquefied gases. Chem. Tech. (Leipzig, Ger.) 1966, 18 (1), 633.

15 Ind. Eng. Chem. Res., Vol. 47, No. 6, (73) Malewski, M. K. F.; Sandler, S. I. High-pressure vapor-liquid equilibria of the binary mixtures nitrogen + n-butane and argon + n-butane. J. Chem. Eng. Data 1989, 34 (4), (74) Lehigh, W. R.; McKetta, J. J. Vapor-Liquid Equilibrium in the Ethane-n-Nitrogen System. J. Chem. Eng. Data 1966, 11 (2), (75) Skripka, V. G.; Barsuk, S. D.; Nikitina, I. E.; Gubkina, G. F.; Benyaminovich, O. A. Liquid-vapor equilibriums in a nitrogen-n-butane system. GazoV. Promst. 1969, 14 (4), (76) Reisig, H.; Schneider, G. M. Fluid-phase and crystallization equilibria of the binary system nitrogen + dimethylpropane between 19 and 3 K and at pressures up to 2 MPa. Fluid Phase Equilib. 1989, 45 (1), (77) Krishnan, T. R.; Kalra, H.; Robinson, D. B. The Equilibrium Phase Properties of the Nitrogen-Isopentane System. J. Chem. Eng. Data 1977, 22 (3), (78) Wisotzki, K. D.; Schneider, G. M. Fluid phase equilibria of the binary systems molecular nitrogen + ethane and molecular nitrogen + pentane between 88 K and 313 K and at pressures up to 2 MPa. Ber. Bunsen-Ges. 1985, 89 (1), (79) Kalra, H.; Robinson, D. B.; Besserer, G. J. The equilibrium phase properties of the nitrogen-n-pentane system. J. Chem. Eng. Data. 1977, 22 (2), (8) Kurata, F.; Swift, G. W. Experimental Measurements of Vapor- Liquid Equilibrium Data for the Ethane-Carbon Dioxide and Nitrogenn-Pentane Binary Systems, Research Report RR-5, Gas Processors Association, Tulsa, OK, (81) Silva-Oliver, G.; Eliosa-Jimenez, G.; García-Sánchez, F.; Avendano- Gomez, J. R. High-pressure vapor-liquid equilibria in the nitrogen-npentane system. Fluid Phase Equilib. 26, 25 (1-2), (82) Eliosa-Jimenez, G.; Silva-Oliver, G.; García-Sánchez, F.; De Ita de la Torre, A. High-Pressure Vapor-Liquid Equilibria in the Nitrogen + n-hexane System. J. Chem. Eng. Data 27, 52 (2), (83) Poston, R. S.; McKetta, J. J. Vapor-Liquid Equilibrium in the n-hexane-nitrogen System. J. Chem. Eng. Data 1966, 11 (3), (84) Peter, S.; Eicke, H. F. Phase equilibrium in the systems nitrogenn-heptane, nitrogen-2,2,4-trimethylpentane, and nitrogen-methylcyclohexane at higher pressures and temperatures. Ber. Bunsen-Ges. 197, 74 (3), (85) García-Sánchez, F.; Eliosa-Jimenez, G.; Silva-Oliver, G.; Godinez- Silva, A. High-pressure (vapor + liquid) equilibria in the (nitrogen + n-heptane) system. J. Chem. Thermodyn. 27, 39 (6), (86) Akers, W. W.; Kehn, D. M.; Kilgore, C. H. Volumetric and phase behavior of nitrogen-hydrocarbon systems. Nitrogen-heptane system. J. Ind. Eng. Chem. 1954, 46, (87) Figuiere, P.; Hom, J. F.; Laugier, S.; Renon, H.; Richon, D.; Szwarc, H. Vapor-liquid equilibria up to 4, KPa and 4 C: A new static method. AIChE J. 198, 26 (5), (88) Llave, F. M.; Chung, T. H. Vapor-liquid equilibria of nitrogenhydrocarbon systems at elevated pressures. J. Chem. Eng. Data 1988, 33 (2), (89) Brunner, G.; Peter, S.; Wenzel, H. Phase equilibrium in the systems n-heptane-nitrogen, methylcyclohexane-nitrogen, and n-heptane-methylcyclohexane-nitrogen at high pressures. Chem. Eng. J. 1974, 7 (2), (9) Boomer, E. H.; Johnson, C. A.; Piercey, A. G. A. Equilibria in two-phase, gas-liquid hydrocarbon systems. IV. Methane and heptane. Can. J. Res. 1938, 16, (91) Schlichting, H. Experimentelle Bestimmung und Korrelierung der Loeslichkeit verschiedener Loesungsmittel in Hochdruckgasen, Ph.D. Thesis, TU Berlin, Berlin, Germany, (92) Cohen, A.; Richon, D. New apparatus for simultaneous determination of phase equilibria and rheological properties of fluids at high pressures: its application to coal pastes studies up to 773 K and 3 MPa. ReV. Sci. Instrum. 1986, 57 (6), (93) Waeterling, U.; Zheng, D.; Knapp, H. Vapor-liquid equilibria at high temperatures and pressures in binary mixtures containing hydrogen, methane, and carbon dioxide with high boiling hydrocarbons: experimental equipment and results. Chem. Eng. Process. 1991, 29 (3), (94) Legret, D.; Richon, D.; Renon, H. Vapor liquid equilibria up to 1 MPa: a new apparatus. AIChE J. 1981, 27 (2), (95) Graham, E. B.; Weale, K. E. The solubility of compressed gases in nonpolar liquids. In Progress in International Research on Thermodynamics of Transport Properties, ASME Proceedings from the 2nd Symposium on Thermophysical Properties, Princeton, NJ, 1962; American Society of Mechanical Engineers (ASME): New York, 1962; pp (96) Prausnitz, J. M.; Benson, P. R. Solubility of liquids in compressed hydrogen, nitrogen, and carbon dioxide. AIChE J. 1959, 5, (97) García-Sánchez, F. Personal communication, 27. (98) Daridon, J. L.; Lagourette, B.; Xans, P. Thermodynamic properties of liquid mixtures containing gas under pressure based on ultrasonic measurements. Fluid Phase Equilib. 1994, 1, (99) D Avila, S. G.; Kaul, B. K.; Prausnitz, J. M. Solubilities of heavy hydrocarbons in compressed methane and nitrogen. J. Chem. Eng. Data 1976, 21 (4), (1) Silva-Oliver, G.; Eliosa-Jimenez, G.; García-Sánchez, F.; Avendano-Gomez, J. R. High-pressure vapor-liquid equilibria in the nitrogenn-nonane system. J. Supercrit. Fluids 27, 42 (1), (11) Ghanem, G.; Tagand, G.; Loiseleur, H.; Ingrain, D.; Jose, J. Determination of the solubility of liquid tetrahydrothiophene in the principal constituents of natural gas (CH 4,CO 2, and N 2) by a dynamic device with vapor-phase chromatography analysis. J. Chim. Phys. Phys. Chim. Biol. 1998, 95 (5), (12) Azarnoosh, A.; McKetta, J. J. Nitrogen-n-Decane System in the Two-Phase Region. J. Chem. Eng. Data 1963, 8 (4), (13) Tong, J.; Gao, W.; Robinson, R. L.; Gasem, K. A. M. Solubilities of Nitrogen in Heavy Normal Paraffins from 323 to 423 K at Pressures to 18. MPa. J. Chem. Eng. Data 1999, 44 (4), (14) Srinivasan, R. Ph.D. Thesis, Illinois Institute of Technology, Chicago, (15) Pearce, D. L.; Peters, C. J.; De Swaan Arons, J. Measurement of the gas phase solubility of decane in nitrogen. Fluid Phase Equilib. 1993, 89 (2), (16) Wilcock, R. J.; Battino, R.; Danforth, W. F.; Wilhelm, E. Solubilities of gases in liquids. II. The solubilities of He, Ne, Ar, Kr, O 2, N 2, CO, CO 2,CH 4,CF 4, and SF 6 in n-octane 1-octanol, n-decane, and 1-decanol. J. Chem. Thermodyn. 1978, 1 (9), (17) Ampueda Ramos, F. Ph.D. Thesis, Universit de Lyon, Lyon, France, (18) Rupprecht, S. D.; Faeth, G. M. Investigation of air solubility in jet A fuel at high pressures, Report Contract No. 3422, National Aeronautics and Space Administration (NASA), (19) Gao, W.; Robinson, R. L.; Gasem, K. A. M. High-Pressure Solubilities of Hydrogen, Nitrogen, and Carbon Monoxide in Dodecane from 344 to 41 K at Pressures to 13.2 MPa. J. Chem. Eng. Data 1999, 44 (1), (11) de Leeuw, V. V.; de Loos, T. W.; Kooijman, H. A.; de Swaan Arons, J. The experimental determination and modeling of VLE for binary subsystems of the quaternary system nitrogen + methane + butane + tetradecane up to 1 bar and 44 K. Fluid Phase Equilib. 1992, 73 (3), (111) Sultanov, R. G.; Skripka, V. G.; Namiot, A. Yu. Phase equilibriums of methane and nitrogen with high-boiling hydrocarbons. GazoV. Delo 1972, 1, (112) Lin, H. M.; Kim, H.; Chao, K. C. Gas-liquid equilibriums in nitrogen + n-hexadecane mixtures at elevated temperatures and pressures. Fluid Phase Equilib. 1981, 7 (2), (113) Sultanov, R. G.; Skripka, V. G.; Namiot, A. Yu. Phase equilibriums in methane-n-hexadecane and nitrogen-n-hexadecane systems at high temperatures and pressures. Zh. Fiz. Khim. 1971, 45 (7), (114) Coan, C. R.; King, A. D. Second cross virial coefficients of benzene-gas mixtures from high-pressure solubility measurements. Comparison with gas-chromatographic values. J. Chromatogr. 1969, 44 (3-4), (115) Krichevskii, I.; Gamburg, D. Solubility of liquids in compressed gases-solubility of benzene in compressed nitrogen. Acta Physicochim. URSS 1942, 16, (116) Krichevskii, I.; Efremova, G. D. Phase and volume relations in liquid-gas systems at high pressures. Zh. Fiz. Khim. 1948, 22, (117) Miller, P.; Dodge, B. F. The system benzene-nitrogen. Liquidvapor phase equilibria at elevated pressures. J. Ind. Eng. Chem. 194, 32, (118) Lewis, W. K.; Luke, C. D. Vapor-liquid equilibria of hydrocarbons at high pressures. J. Ind. Eng. Chem. 1933, 25, (119) Gao, W.; Gasem, K. A. M.; Robinson, R. L. Solubilities of Nitrogen in Selected Naphthenic and Aromatic Hydrocarbons at Temperatures from 344 to 433 K and Pressures to 22.8 MPa. J. Chem. Eng. Data 1999, 44 (2), (12) de Leeuw, V. V.; Poot, W.; de Loos, T. W.; de Swaan Arons, J. High pressure phase equilibria of the binary systems nitrogen + benzene, nitrogen + p-xylene and nitrogen + naphthalene. Fluid Phase Equilib. 1989, 49, (121) Richon, D.; Laugier, S.; Renon, H. High-pressure vapor-liquid equilibrium data for binary mixtures containing molecular nitrogen, carbon dioxide, hydrogen sulfide and an aromatic hydrocarbon or propylcyclohexane in the range K. J. Chem. Eng. Data 1992, 37 (2),