Fluid Phase Equilibria Correlation for Carbon Dioxide +1-Heptanol

Research Note pubs.acs.org/IECR

Fluid Phase Equilibria Correlation for Carbon Dioxide +1-Heptanol System with Cubic Equations of State Catinca Secuianu,†,‡ Junwei Qian,§ Romain Privat,§ and Jean-Noel̈ Jaubert*,§ †

Department of Inorganic Chemistry, Physical Chemistry and Electrochemistry, Faculty of Applied Chemistry and Materials Science, Politehnica University of Bucharest, 1-7 Gh. Polizu Street, S1, 011061 Bucharest, Romania ‡ Department of Chemical Engineering, Imperial College London, South Kensington Campus, SW7 2AZ, London, United Kingdom § Laboratoire Réactions et Génie des Procédés (UPR CNRS 3349), École Nationale Supérieure des Industries Chimiques, Université de Lorraine, 1 rue Grandville, 54000 Nancy, France ABSTRACT: The purpose of this paper is to compare three thermodynamic models to correlate the phase behavior of the highly polar system: carbon dioxide +1-heptanol. These three models rely either on the Peng−Robinson (PR) or on the Soave− Redlich−Kwong (SRK) equations of state and are all coupled with classical van der Waals one-fluid mixing rules. For the two first models, noted SRK/2PCMR and PR/2PCMR, where 2PCMR means two-parameter conventional mixing rule, a single set of temperature-independent binary parameters (kij and lij) was considered. The third model is the well-established PPR78 model also based on the PR equation of state (1978 version). In such a model, lij = 0 but the second binary interaction parameter (kij) is temperature-dependent and predicted by a group-contribution method. All available literature data in a wide range of pressures and temperatures and the global phase equilibrium diagram of the system were calculated with the three aforementioned models. Although the models used are simple, they are able to represent reasonably well the complex phase behavior of the system studied in this work. used as cosolvents.29 Comparison with PR/2PCMR and SRK/ 2PCMR8−10 models is also given. In the carbon dioxide + 1-alcohol series, the carbon dioxide + 1-heptanol system is exhibiting type III phase behavior, according to the classification of Van Konynenburg and Scott.30 In the P−T diagram,31 this type is characterized by a three-phase liquid−liquid−vapor (LLV) line and two critical lines. The occurring three-phase LLV line is terminated by an upper critical end point (UCEP) of the nature L + L = V. A liquid−vapor critical line (L = V) connects this UCEP with the vapor−liquid critical point of the more volatile component (carbon dioxide). Another critical line L = V emerges from the critical point of the less volatile component (1-heptanol), shows a maximum and a minimum in pressure, and gradually changes in nature into L = L, toward higher pressures. The high-pressure L = L critical curve, and partially the L = V critical curve toward 1-heptanol were measured by Scheidgen32 between 285.67 and 389.93 K and up to 99.51 MPa. Several points on the L = V critical curve were also reported by Elizalde-Solis et al.33 at temperatures from 313.14 to 411.99 K and pressures from 11.709 to 21.509 MPa. The liquid−liquid phase compositions along the threephase LLV line are available from Secuianu et al.34 The temperature and pressure of the UCEP were both measured by Lam et al.35 and by Secuianu et al.34 The P−T data along

1. INTRODUCTION The knowledge of high-pressure phase behavior of carbon dioxide comprising mixtures is of interest in a variety of processes.1−4 The proper operating conditions for such processes are determined by direct measurement of phase equilibria and/or by using thermodynamic models over a wide range of pressures and temperatures. As the experiments are usually expensive and very time-consuming, equation of state (EoS) models are the most common approach for the correlation and prediction of phase equilibria and properties of the mixtures. Although accurate results5,6 may be obtained by fitting the binary interaction parameters kij and/or lij, modern process design requires models in which such parameters can be predicted using, for example, the group-contribution concept. One of the most severe tests for a model lies in its implementation for mixtures of polar compounds, where strong associative interactions are present.7 The capabilities of different thermodynamic models for accurately predicting the phase equilibrium of high-pressure asymmetric mixtures containing carbon dioxide have been investigated recently in several papers.5,8−19 Among them, a model developed by Jaubert and co-workers,20−28 called PPR78 (predictive 1978, Peng−Robinson EoS), proved to quite accurately predict the phase behavior of a range of systems including complex mixtures like petroleum fluids.7 In this paper the prediction of the carbon dioxide +1heptanol system by the PPR78 approach is shown, as the carbon dioxide + alkanols mixtures at high-pressures are of a particular importance in the design, simulation, and optimization of extraction processes, where the alcohols are commonly © 2012 American Chemical Society

Received: Revised: Accepted: Published: 11284

June 8, 2012 July 6, 2012 August 2, 2012 August 2, 2012 dx.doi.org/10.1021/ie3015186 | Ind. Eng. Chem. Res. 2012, 51, 11284−11293

Industrial & Engineering Chemistry Research

Research Note

Table 1. Critical Parameters and Acentric Factor of Pure Carbon Dioxide41 and 1-Heptanol.41 substance

Tc (K)

Pc (MPa)

ω

carbon dioxide 1-heptanol

304.21 610.30

7.383 3.417

0.22362 0.57635

the LLV line are available from Elizalde-Solis et al.33 and Secuianu et al.34 Isothermal vapor−liquid equilibrium (VLE) data were measured at (292, 298, 316, and 393) K by Scheidgen,32 who also measured isobaric VLE at (0.64, 0.72 and 0.80) MPa. ElizaldeSolis et al.33 measured VLE data at (313.14, 333.16, 373.32, 411.99, and 431.54) K. Secuianu et al.29,34 measured vapor− liquid−liquid and vapor−liquid equilibria at (293.15, 298.15, 303.15, 313.15, 316.15, 333.15, and 353.15) K. Figure 1. Temperature dependence of the binary interaction parameter (kij) as predicted by the PPR78 model for the carbon dioxide + 1-heptanol system.

2. MODELING The phase behavior (critical curve, LLV line, isothermal VLE, LLE, and VLLE, isobaric VLE and LLE) of the carbon dioxide + 1-heptanol system was modeled using both the Soave−Redlich−Kwong36 (SRK) and the Peng−Robinson37 (PR) EoS coupled with classical van der Waals one-fluid mixing rules. Three different models: PPR78, PR/2PCMR, and SRK/2PCMR were considered. The predictive PPR787,20−28 model relies on the Peng−Robinson equation of state as published by Peng and Robinson38 in 1978 and on a group-contribution method to estimate the kij value which is temperature dependent.20 In the last years,7,20−28 several groups were defined: CH3, CH2, CH, C, CH4 (methane), C2H6 (ethane), CHaro, Caro, Cfused_aromatic_rings, CH2,cyclic, CHcyclic or Ccyclic, CO2, N2, H2S, and -SH and it is thus possible to predict the kij for any mixture containing alkanes, aromatics, naphthenes, CO2, N2, H2S, and mercaptans. Recently, the model was used to predict the phase behavior of synthetic petroleum fluids containing components of different volatilities.7 The many comparisons between calculated and experimental data on natural gases, crude oils,39 and gas condensates proved that the PPR78 approach is a successful model for phase-equilibrium calculations of this kind of mixtures. Therefore, in this study the model was tested for an asymmetric, highly nonideal system consisting of carbon dioxide and one medium chained alcohol, as it is known that accurate modeling of this type of systems, using equations of state can be a very difficult and challenging task.19 So that the PPR78 model could be used for the CO2 + 1-heptanol system, it was decided to define the 1-heptanol molecule as a new group and to determine the interaction parameters between this new group and group CO2. This is indeed a preliminary step before adding the hydroxyl (−OH) group to the model. Addition of a new group is indeed a huge work needing thousands of data and a complex methodology to determine the best group-interaction parameters. Such an addition will be performed whether accurate resultsat least as accurate as those obtained by using both a constant kij and a constant lijcan be obtained in large ranges of temperature and pressure on the binary system studied in this paper. For a pure component, the 1978 Peng−Robinson EoS on which the PPR78 model relies is ai(T ) RT P= − V − bi V (V + bi) + bi(V − bi)

with ⎧ R = 8.314472 J·mol−1·K−1 ⎪ ⎪ 3 3 ⎪ X = −1 + 6 2 + 8 − 6 2 − 8 ⎪ 3 ⎪ ≈ 0.253076587 ⎪ RTc, i X ⎪ with Ωb = ≈ 0.0777960739 ⎪bi = Ωb P X +3 c, i ⎪ ⎪ 2 ⎛ ⎞⎤ ⎪ R2Tc, i 2 ⎡ T ⎪ ⎢ ⎥ ⎟ 1 + mi⎜⎜1 − with ⎨ ai = Ωa Pc, i ⎢⎣ Tc, i ⎟⎠⎥⎦ ⎝ ⎪ ⎪ 8(5X + 1) ≈ 0.457235529 ⎪ Ωa = 49 − 37X ⎪ ⎪ ⎪ if ωi ≤ 0.491 ⎪ mi = 0.37464 + 1.54226ωi − 0.26992ωi 2 ⎪ ⎪ if ωi > 0.491 ⎪ 2 ⎪ mi = 0.379642 + 1.48503ωi − 0.164423ωi ⎪ + 0.016666ω 3 ⎩ i

(2)

where P is the pressure, R is the ideal-gas constant, T is the temperature, and a and b are EoS parameters, V is the molar volume, Tc is the critical temperature, Pc is the critical pressure, and ω is the acentric factor. To apply an EoS to a mixture, mixing rules are necessary to calculate the values of a and b of the mixture. Classical van der Waals one-fluid mixing rules, recalled in eqs 3 and 4, are used in the PPR78 model. N

a=

N

∑ ∑ zizj

aiaj [1 − kij(T )] (3)

i=1 j=1 N

b=

N

∑ ∑ zizj

bi + bj

i=1 j=1

2

(1 − lij) (4)

However, in such a model the lij interaction parameter is set to zero so that eq 4 reduces to N

bPPR78 =

(1)

∑ zibi i=1

11285

(5)

dx.doi.org/10.1021/ie3015186 | Ind. Eng. Chem. Res. 2012, 51, 11284−11293


Research Note

Figure 2. P−T fluid phase diagram of carbon dioxide + 1-heptanol system: (red ○) experimental critical curve; (red +) experimental critical points of pure components; (blue △) experimental UCEP; (blue ○) experimental LLV line; (---) calculated vapor pressure curves of pure components; (blue ▲) calculated UCEP; () calculated critical curves and LLV lines by the three considered models, (a) PPR78, (b) SRK/2PCMR, and (c) PR/ 2PCMR.

When i = j, kij = 0. Although the common practice is to fit kij so as to represent the vapor−liquid equilibrium data of the mixture under consideration, the predictive PPR78 model calculates the kij, which is temperature-dependent, by a group-contribution method through the following expression:

In the previous equations, zk represents the mole fraction of component k in a mixture, and N is the number of components in the mixture. In eqs 3 to 5, the summations are over all chemical species. kij(T), whose choice is difficult even for the simplest systems, is the so-called binary−interaction parameter characterizing molecular interactions between molecules i and j.

kij(T ) =

1⎡ N N − 2 ⎢∑k =g 1 ∑l =g 1 (αik ⎣

− αjk)(αil − αjl)A kl · 2

(

298.15 T/K

(Bkl / Akl − 1) ⎤

)

⎛ ⎥−⎜ ⎦ ⎝

ai(T ) bi

−

aj(T ) bj

⎞2 ⎟ ⎠

ai(T )·aj(T ) bi·bj

(6)

and SRK EoSs coupled with classical van der Waals one-fluid mixing rules (see eqs 3 and 4) were also used to calculate the critical curves, the LLV line, isothermal VLE, LLE, and VLLE and isobaric VLE and LLE of the carbon dioxide +1-heptanol binary system. In this paper, such mixing rules are noted 2PCMR which means two parameter conventional mixing rules to highlight that two parameters per binary system (kij and lij) are needed. For each equation of state, one set of temperature-independent parameters was used to correlate the phase behavior.40 The original Peng−Robinson37 EoS (1976 version) on which the PR/2PCMR model relies is identical to the 1978 version described by eq 2 but the mi

In eq 6, T is the temperature. Ng is the number of different groups defined by the method. αik 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 the group-interaction parameters (Akk = Bkk = 0). In this study, ACO2/1−heptanol and BCO2/1−heptanol, that is, interactions between groups 1-heptanol and CO2, were determined in order to minimize the deviations between calculated and experimental VLE, LLE, and critical points data. On the basis of previous results5,8−10,13−16,28,33 with mixtures containing carbon dioxide and alcohols, the PR (1976 version) 11286



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Figure 3. P−T and T−xCO2 fluid phase diagrams of carbon dioxide +1-heptanol system with emphasis on the three-phase line: (red +) experimental critical points of pure components; (blue △) experimental UCEP; (blue ○) experimental LLV line; (---) calculated vapor pressure curves of pure components; (blue ▲), calculated UCEP; () calculated critical curves and LLV lines by the three considered models, (a) PPR78, (b) SRK/ 2PCMR, and (c) PR/2PCMR and (d) comparison of the three models in the T−xCO2 plane.

3. RESULTS AND DISCUSSION The critical data and the acentric factors of the pure41 substances used in all the calculations are presented in Table 1. 3.1. Group-Interaction Parameters of the PPR78 Model Fitted to the Experimental Data of the Carbon Dioxide +1-Heptanol Binary System. Our first task was to determine the group-interaction parameters between group 1-heptanol and group CO2. To do that, an objective function taking into account the deviations on the liquid phases, gas phase, and critical compositions was built and minimized. All available literature data for the carbon dioxide +1-heptanol system were considered. The obtained parameters to be used in eq 6 are

parameter is calculatedfor any the acentric factor value by mi ,PR76 = 0.37464 + 1.54226ωi − 0.26992ωi2

(7)

The Soave−Redlich−Kwong36 equation of state on which the SRK/2PCMR model relies, is P=

a i(T ) RT − V − bi V (V + bi)

(8)

with 3 ⎧ RTc, i 2 −1 with Ωb = ≈ 0.08664 ⎪bi = Ωb Pc, i 3 ⎪ ⎪ 2 2 2 ⎡ ⎪ ⎞⎤ ⎛ T ⎟⎥ ⎪ a (T ) = Ω R Tc, i ⎢1 + m ⎜ i ,SRK ⎜1 − a ⎨ i Pc, i ⎢⎣ Tc, i ⎟⎠⎥⎦ ⎝ ⎪ 1 ⎪ ⎪ with Ωa = 9( 3 2 − 1) ≈ 0.42748 ⎪ 2 ⎪m ⎩ i ,SRK = 0.480 + 1.574ωi − 0.176ωi

⎧ A CO2 /1‐heptanol = 110.15 MPa ⎪ ⎨ ⎪ ⎩ BCO2 /1‐heptanol = 325.30 MPa

(10)

The dependence on temperature of the binary interaction parameter kij as predicted by the PPR78 model is illustrated in Figure 1. It can be noticed that such dependence is very strong in the temperature range where experimental data were

(9) 11287



Research Note

Figure 4. Comparison of literature data for the carbon dioxide + 1-heptanol system and correlations by the PPR78, SRK/2PCMR, and PR/ 2PCMR models. Symbols, literature data at (292, 293.15, 298.0, 298.15, 303.15, 313.15) K; lines, PPR78, SRK/2PCMR, and PR/2PCMR models.

measured. The kij value indeed varies from 0.06 to 0.11, that is, is more or less multiplied by a factor of 2, when the temperature rises from (290 to 450) K. We can also notice that

the resulting curve is monotonous and does not comprise a discontinuity at the CO2 critical temperature. Such a discontinuity is however often observed42 when the kij is fitted 11288



Research Note

Figure 5. Comparison of literature data for the carbon dioxide + 1-heptanol system and correlations by the PPR78, SRK/2PCMR, and PR/ 2PCMR models. Symbols, literature data at (316, 316.15, 333.15, 353.15, 374.63, 393.0) K; lines, PPR78, SRK/2PCMR, and PR/2PCMR models.

3.2. kij and lij Values for the SRK/2PCMR and PR/ 2PCMR Approaches Suitable for the Carbon Dioxide +1Heptanol Binary System. As was done in the previous section, an objective function was built and minimized in order

temperature by temperature but is incompatible with the PPR78 model which was built so that continuous phenomena are predicted in the critical region of the less volatile component. 11289



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Figure 6. Comparison of literature data for the carbon dioxide + 1-heptanol system and correlations by the PPR78, SRK/2PCMR, and PR/ 2PCMR models. Symbols, literature data at (411.99, 431.54) K and at (6.4, 7.2, 8.0) MPa; lines, PPR78, SRK/2PCMR, and PR/2PCMR models.

3.3. Results Obtained with the Three Models. All available literature data for the carbon dioxide + 1-heptanol system were calculated with the PPR78, PR/2PCMR and SRK/2PCMR models. The results of calculations by these

to determine the most appropriate binary interaction parameters.40 The sets of optimized binary interaction parameters, to be used in eqs 3 and 4, are, respectively, k12 = 0.089, l12 = −0.049 for SRK/2PCMR and k12 = 0.085, l12 = −0.048 for PR/2PCMR. 11290


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The relative deviation on a fluid-phase composition was calculated by Δx% =

100 ndata

⎛ |Δx | n ∑i =data1 0.5⎜ x 1 + ⎝ 1,exp

|Δx1| ⎞ ⎟ with: x2,exp ⎠ i

= |x1,exp − x1,cal| = |x 2,exp − x 2,cal| where (1) is the CO2 and (2) is the n-heptanol.

approaches are compared with experimental data in Figures 2−6. As a first conclusion we can state that the SRK/2PCMR and PR/2PCMR lead to very similar results. Used with the same mixing rules, the SRK and PR EoS have thus a similar accuracy. The global phase equilibrium diagram of the carbon dioxide +1-heptanol system is presented in Figure 2. As can be seen, the three models are able to reproduce the type III phase behavior. The PPR78 model is able to properly correlate the critical curves (only the minimum part of the L = L critical curve is overpredicted and therefore the maximum of the L = V critical curve is located at a too high pressure) and to perfectly correlate the three-phase LLV line (see Figure 3). Only the UCEP is slightly overestimated. The SRK/2PCMR and PR/ 2PCMR models much better predict the minimum and the L = L part of the critical curve. Such models however underestimate the composition of the two liquid phases along the three-phase line and largely overestimate the coordinates of the UCEP and the pressures along the LLV line. They also predict, at very high pressure, an inflection point along the L = L critical curve. Such an inflection point is however not observed experimentally. In return, the PPR78 correlates very well the slope of the L = L critical line. Such differences may probably be explained by the fitting procedure used in this study. Indeed, parameters with different numerical values can lead to very similar values of the objective function. This is because the models are not able to simultaneously correlate all the experimental data. Among the sets of parameters some are going to better reproduce the critical locus and others the three-phase line. In the present study, the objective function was found to be minimum when the SRK/2PCMR and PR/2PCMR models successfully correlated the critical locus and when the PPR78 model accurately correlated the 3-phase line. In Figure 4 are illustrated the isotherms measured at a temperature below or slightly above the experimental temperature of the UCEP, while Figures 5 and 6 present the isotherms measured above the UCEP, in a wide range. The quality of the data correlation by the various models is very different. At low temperature, the PPR78 model perfectly catches the composition of the gas phase and the composition of the liquid phase rich in CO2 but encounters difficulties to reproduce the composition of the other liquid phase. The pressure of the liquid−liquid critical points are, as previously stated, overestimated. In comparison the SRK/2PCMR and PR/2PCMR much better correlate the bubble-point curve and the composition of the heptanol-rich liquid phase but poor results are obtained in the description of the CO2-rich liquid phase. At (313 and 316) K these two models still predict a three-phase line due to a overestimation of the UCEP temperature. As the temperature increases (see Figures 5 and 6), the PPR78 much better predicts the isothermal phase diagrams including the bubble-point curves, whereas the SRK/2PCMR and PR/ 2PCMR tend to overestimate the bubble-point pressures. The isobaric phase diagrams shown in Figure 6 lead to the same conclusions. The PPR78 model better correlates the liquid phase rich in CO2 and the gas phase composition, whereas the two other models are more accurate to correlate the liquid phase rich in alcohol and the bubble-point pressures. We can thus conclude that none of the three models is able to perfectly correlate such a system but the results are globally accurate. To better quantify the strengths and the weaknesses of each model, it was decided (see Table 2) to calculate the

a

13.2 (3.97%) 6.24 (1.91%) 6.13 (1.83%) 0.004 (8.15%) 0.025 (47.0%) 0.029 (54.6%) 0.001 (0.32%) 0.021 (4.65%) 0.024 (5.27%) 0.34 (0.12%) 1.32 (0.44%) 1.70 (0.57%) 0.010 (21.2%) 0.058 (>100%) 0.073 (>100%) 0.051 (13.5%) 0.022 (5.59%) 0.021 (5.21%) 0.049 (11.8%) 0.052 (13.2%) 0.054 (13.6%)

model

PPR78 SRK/2PCMR PR/2PCMR

0.007 (27.2%) 0.011 (35.3%) 0.007 (32.1%)

deviation on the critical temperature: ΔTc (K) deviation on the heptanol-rich liquid phase composition along the three-phase line: Δx deviation on the CO2-rich liquid phase composition: Δx deviation on the heptanol-rich liquid phase composition: δx deviation on the gas phase composition: δy deviation on the liquid phase composition: δx

LLE data VLE data

Table 2. Accuracy of the Three Models Used in This Studya

deviation on the temperature along the three-phase line: ΔT (K)

three-phase line

deviation on the CO2-rich liquid phase composition along the three-phase line: Δx

critical line


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(6) Jaubert, J.-N.; Coniglio, L. The Group Contribution Concept: A Useful Tool To Correlate Binary Systems and To Predict the Phase Behavior of Multicomponent Systems Involving Supercritical CO2 and Fatty Acids. Ind. Eng. Chem. Res. 1999, 38, 5011. (7) Jaubert, J.-N.; Privat, R.; Mutelet, F. Predicting the Phase Equilibria of Synthetic Petroleum Fluids with the PPR78 Approach. AIChE J. 2010, 56, 3225. (8) Secuianu, C.; Feroiu, V.; Geană, D. Measurements and Modeling of High-Pressure Phase Behavior of the Carbon Dioxide + Pentan-1-ol Binary System. J. Chem. Eng. Data 2011, 56, 5000. (9) Secuianu, C.; Feroiu, V.; Geană, D. Phase equilibria of carbon dioxide +1−nonanol system at high pressures. J. Supercrit. Fluids 2010, 55, 653. (10) Secuianu, C.; Feroiu, V.; Geană, D. High−pressure phase equilibria in the (carbon dioxide + 1−hexanol) system. J. Chem. Thermodyn. 2010, 42, 1286. (11) Cismondi, M.; Mollerup, J. M.; Zabaloy, M. S. Equation of state modeling of the phase equilibria of asymmetric CO2 + n-alkane binary systems using mixing rules cubic with respect to mole fraction. J. Supercrit. Fluids 2010, 55, 671. (12) Jaubert, J.-N.; Privat, R. Relationship between the binary interaction parameters (kij) of the Peng−Robinson and those of the Soave−Redlich−Kwong equations of state: Application to the definition of the PR2SRK model. Fluid Phase Equilib. 2010, 295, 26. (13) Secuianu, C.; Feroiu, V.; Geană, D. Phase equilibria calculations for carbon dioxide + methanol binary mixture with the Huron−Vidal infinite dilution (HVID) mixing rules. Rev. Chim. (Bucharest) 2009, 60, 472. (14) Secuianu, C.; Feroiu, V.; Geană, D. Phase behavior for carbon dioxide + 2-butanol system: Experimental measurements and modeling with cubic equations of state. J. Chem. Eng. Data 2009, 54, 1493. (15) Secuianu, C.; Feroiu, V.; Geană, D. Phase equilibria experiments and calculations for carbon dioxide + methanol binary system. Cent. Eur. J. Chem. 2009, 7, 1. (16) Secuianu, C.; Feroiu, V.; Geană, D. Phase behavior for carbon dioxide + ethanol system: experimental measurements and modeling with a cubic equation of state. J. Supercrit. Fluids 2008, 47, 109. (17) Grenner, A.; Kontogeorgis, G. M.; Von Solms, N.; Michelsen, M. L. Modeling phase equilibria of alkanols with the simplified PCSAFT equation of state and generalized pure compound parameters. Fluid Phase Equilib. 2007, 258, 83. (18) Valderrama, J. O.; Zavaleta, J. Generalized binary interaction parameters in the Wong−Sandler mixing rules for mixtures containing n-alkanols and carbon dioxide. Fluid Phase Equilib. 2005, 234, 136. (19) Polishuk, I.; Wisniak, J.; Segura, H. Simultaneous prediction of the critical and sub-critical phase behavior in mixtures using equation of state I. Carbon dioxide-alkanols. Chem. Eng. Sci. 2001, 56, 6485. (20) 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, 285. (21) 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, 193. (22) Jaubert, J. N.; Coniglio, L.; Denet, F. From the Correlation of Binary Systems Involving Supercritical CO2 and Fatty Acid Esters to the Prediction of (CO2-Fish Oils) Phase Behavior. Ind. Eng. Chem. Res. 1999, 38, 3162. (23) 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. (24) Vitu, S.; Privat, R.; Jaubert, J.-N.; Mutelet, F. Predicting the phase equilibria of CO2 + hydrocarbon systems with the PPR78 model

deviations on different properties like the compositions of the phases in equilibrium (VLE and LLE), the temperatures, and the compositions along the three-phase line and the temperatures along the critical line. Table 2 gives evidence that the SRK/2PCMR model is never the best one (see values in bold in Table 2) and that the PPR78 model is globally better than the PR/2PCMR to correlate the data of the complex system carbon dioxide + 1-heptanol.

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CONCLUSION Hundreds of phase equilibrium data of the carbon dioxide +1heptanol system were correlated with three different thermodynamics models: PPR78, PR/2PCMR, and SRK/2PCMR. All these three models rely on cubic equations of state coupled with classical van der Waals one-fluid mixing rules. While for the PPR78 model a unique temperature-dependent binary interaction parameter (kij) was used, one set of temperatureindependent interaction parameters (kij and lij) was used for the two other models. In the PPR78 model, the kij dependence on temperature is caught with the help of two parameters (Akl and Bkl). We can thus conclude that it is totally fair to compare these three models since two parameters per binary system were fitted on the experimental data for each of them. Overall, correlation of the data with the PPR78 model is better than with the PR/2PCMR and SRK/2PCMR models. We can thus conclude that, at least for the studied system, the use of a temperature-dependent kij can improve the correlation of complex type III systems by contrast with the use of a temperature-independent kij and lij. This is the reason why, it is planned to add the hydroxyl group (−OH) to the PPR78 model (the group-interaction parameters between group −OH and all the groups previously defined in the PPR78 model will be determined).

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +33 3 83 17 50 81. Fax: +33 3 83 17 51 52. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS C. Secuianu is grateful to the National Research Council of Romania (CNCS) and to the Executive Agency for Higher Education Research and Innovation Funding (UEFISCDI) for financial support.

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REFERENCES

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Fluid Phase Equilibria Correlation for Carbon Dioxide +1-Heptanol

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