Addition of the Sulfur Dioxide Group (SO2), the Oxygen Group (O2

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Addition of the sulfur dioxide group (SO2), the oxygen group (O2) and the nitric oxide group (NO) to the E-PPR78 model Xiaochun Xu, Romain Privat, and Jean-Noel Jaubert Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.5b02639 • Publication Date (Web): 25 Aug 2015 Downloaded from http://pubs.acs.org on September 2, 2015

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Industrial & Engineering Chemistry Research

Table of Contents (TOC) Graphic

SO2

PPR78

O2

Group − Contribution Equation of State

KEEPS GROWING NO

Addition of the sulfur dioxide group (SO2), the oxygen group (O2) and the nitric oxide group (NO) to the E-PPR78 model

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Xiaochun XU, Romain PRIVAT and Jean-Noël JAUBERT(*) Université de Lorraine, Ecole Nationale Supérieure des Industries Chimiques, Laboratoire Réactions et Génie des Procédés (UMR CNRS 7274), 1 rue Grandville, 54000 Nancy, France.

E-mail: [email protected] – Phone: +33 3 83 17 50 81 – Fax: +33 3 83 17 51 52 (*) author to whom the correspondence should be addressed.

Abstract The E-PPR78 model is a predictive version of the widely used Peng-Robinson equation of state in which the binary interaction parameters are estimated by a group-contribution method. With the 24 groups available before the writing of this paper, such a model could be used to predict fluid phase equilibrium of systems containing hydrocarbons, permanent gases (CO2, N2, H2S, H2, CO, He and Ar), mercaptans, alkenes and water. During the process of the Carbon dioxide Capture and Storage (CCS), it is often necessary to know thermodynamic properties of mixtures containing carbon dioxide, water, hydrocarbons and trace gases, such as nitrogen, argon, hydrogen, carbon monoxide, sulfur dioxide, oxygen or nitric oxide. Basically, except sulfur dioxide, oxygen and nitric oxide, most components encountered in systems regarding CCS processes could be modeled with the E-PPR78 model. So in order to predict the phase behavior and estimate energetic properties (e.g. enthalpy or heat capacity changes on mixing) of such systems, the applicability range of the E-PPR78 model is extended through the addition of three new groups: “SO2”, “O2” and “NO”.

Keywords: E-PPR78, predictive equation of state, Peng-Robinson, CCS, binary interaction parameters.


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1. Introduction The Carbon dioxide Capture and Storage (CCS), which is one of the options for reducing atmospheric emissions of CO2 from human activities (such as burning of fossil fuels), involves the capture, the transport and the storage into underground formations like deep saline aquifers or depleted oil and gas fields1. Depending on the CO2 origin, the composition of gases accompanying CO2 (also called impurities) can vary considerably. Indeed, along with CO2 and water, many other compounds such as O2, N2, Ar, SOx, NOx, H2 and CO can be present at different levels of concentration in flue gases1-4. To understand the role played by these impurities during the processes of CCS, it is essential to know the thermodynamic properties of such gas mixtures under the conditions of CO2 capture, transport and storage. Considering the variety of composition of these gas mixtures, it is necessary to develop suitable models for predicting their thermodynamic properties. It is indeed almost impossible to get all thermodynamic properties from experimental measurements. The PPR78 (Predictive 1978, Peng-Robinson equation of state) model, which was originally proposed by Jaubert and co-workers5, has been shown to be accurate and reliable for the phase equilibrium prediction in mixtures containing hydrocarbons5-8, permanent gases9-13, sulfur compounds14-16, water17 and even esters18, 19. The PPR78 model also has been successfully applied to phase envelope prediction of petroleum fluids20, 21. Recently, Qian et al.22 published predictions of enthalpy and heat capacity changes on mixing with the PPR78 model. They concluded that predictions of properties changes on mixing could be highly improved by simultaneously fitting the group-interaction parameters on vapor-liquid equilibrium, enthalpy and heat capacity changes on mixing data. Such a work was performed by Qian during his thesis22 and the resulting model was called E-PPR78 (Enhanced Predictive Peng-Robinson, 1978). Until now, except sulfur dioxide, oxygen and nitric oxide, most components encountered in systems regarding CCS processes could be predicted with the E-PPR78 model. In this work, in order to complete the capacity of such a model to predict the thermodynamic behavior of gas mixtures regarding CCS processes, three new groups: sulfur dioxide (SO2), oxygen (O2) and nitric oxide (NO) are added.


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2. The E-PPR78 model In 1978, Peng and Robinson published an improved version of their well–known equation of state, referred to as PR78 in this paper. For a pure component, the PR78 EoS is: P=

RT a i (T) − v − bi v(v + bi ) + bi (v − bi )

(1)

and

R = 8.314472 J ⋅ mol−1 ⋅ K −1   −1 + 3 6 2 + 8 − 3 6 2 − 8 ≈ 0.253076587 X = 3   RTc,i X with: Ωb = ≈ 0.0777960739  bi = Ω b Pc,i X+3   2    R 2Tc,i 8 ( 5X + 1) T a = Ω α(T) with: Ωa = ≈ 0.457235529 and α(T) = 1 + mi 1 − i a   Pc,i 49 − 37X Tc,i    if ω ≤ 0.491 m = 0.37464 + 1.54226ω − 0.26992ω2 i i i  i if ωi > 0.491 mi = 0.379642 + 1.48503ωi − 0.164423ωi2 + 0.016666ω3i

(2)     

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where P is the pressure, R is the gas constant, T is the temperature, ai and bi are the cohesive parameter and molar covolume of pure component i, v is the molar volume, Tc,i is the critical temperature, Pc,i is the critical pressure and ωi is the acentric factor of pure i. To apply this 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 are used in the PPR78 model: N N  a(T , z ) = zi z j a i (T) ⋅ a j (T) 1 − k ij (T)  ∑∑   i =1 j=1  N b(z) = z b ∑ i i  i =1

(3)

where zi represents the mole fraction of component i and N is the number of components in the mixture. The kij(T) parameter, whose estimation is difficult even for the simplest systems, is the so–called binary interaction parameter (BIP) characterizing the molecular interactions between molecules i and j. Although the common practice is to fit kij to reproduce the vapor–liquid equilibrium data of the mixture under consideration, the predictive PPR78 model calculates the kij value, which is temperature–dependent, with a group contribution method5-26 using the following expression: Addition of the sulfur dioxide group (SO2), the oxygen group (O2) and the nitric oxide group (NO) to the E-PPR78 model

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N 1 g − ∑ 2 k =1  kij (T ) =

 Bkl  −1  

Ng

 298.15  Akl (α ik − α jk )(α il − α jl )Akl ⋅  ∑  l =1  T K 

2   −  ai (T ) − a j (T )    b bj  i   

ai (T ) ⋅ a j (T )

2

(4)

bi ⋅ b j

In Eq. (4), T is the temperature. The ai and bi values are given in Eq. (2). The Ng variable is the number of different groups defined by the group-contribution method (for the time being, twenty seven groups are defined, and Ng = 27). The αik variable 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). The group-interaction parameters, Akl = Alk and Bkl = Blk (where k and l are two different groups), were determined in our previous papers (Akk = Bkk = 0)13, 23. For the groups added in this paper (group 25: “SO2”, group 26: “O2”, group 27: “NO”), 54 group-interaction parameters (27 Akl and 27 Bkl values) were estimated. The corresponding Akl and Bkl values (expressed in MPa) are summarized in Table S1 of Supporting Information. To be really exhaustive, let us recall that the E-PPR78 model can also be seen as the combination of the PR EoS with a Van Laar type activity coefficient (gE) model under infinite pressure. Indeed, as explained by Jaubert and Privat20, the well–established Huron–Vidal mixing rules: p  a(T , z ) a (T ) G E  = zi i − bi CEoS  b(z ) i =1  p  b(z ) = zi bi  i =1   2 ln(1 + 2) for the PR EoS CEoS =  2

∑

∑

(5)

are rigorously equivalent to the Van der Waals one−fluid mixing rules with temperature–dependent kij if a Van–Laar type excess function: p

E GVan Laar

C EoS

=

1 ⋅ 2

p

∑∑ zi z jbi b jEij (T) i =1 j=1

p

(6)

∑ b jz j j=1

is used in Eq. (5). The mathematical relation between kij(T) [Eq. (3)] and the interaction parameter of the Van–Laar gE model [Eij(T) in Eq. (6)] is: Addition of the sulfur dioxide group (SO2), the oxygen group (O2) and the nitric oxide group (NO) to the E-PPR78 model

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k ij (T) =

Eij (T) − (δi − δ j )2 2δ i δ j

with δi =

ai bi

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(7)

Furthermore, the PR2SRK model27 makes it possible to deduce the kij of any EoS (like the SRK EoS) knowing those of the PR EoS. In other words, the group–interaction parameters (Akl and Bkl) initially developed for the PR EoS can be used to predict the kij of any other cubic EoS combined with any alpha function. As an example, BIPs for the SRK EoS are given by:  − δSRK ESRK (T) − (δSRK )2 ij i j  k SRK (T) = ij 2δSRK δSRK  i j  SRK  E ij (T) = ξ ⋅ E ijPPR 78 (T)  ξ ≈ 0.807341

(8)

Note that the value of the ξ parameter is theoretically justified in the original paper presenting the PR2SRK model27.


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3 Database and reduction procedure Table 1 lists the 23 pure components involved in this study. The pure fluid physical properties (Tc,

Pc and ω) that were used in this study, originate from Poling et al..28 Table 2 details the sources of the binary experimental data4, 29-76 used in our evaluations, along with the temperature, pressure and composition ranges for each binary system. Most of data available in the open literature were collected. Our database includes experimental data for 31 binary systems. The 54 parameters (27 Akl and 27 Bkl) determined in this study, were obtained by minimizing the following objective function: Fobj =

Fobj, bubble + Fobj, dew + Fobj, crit.comp + Fobj, crit.pressure + Fobj, az.comp + Fobj, az.pressure + Fobj, mix,enthalpy nbubble + ndew + 2ncrit + 2naz + nmix,enthalpy

nbubble   ∆x ∆x   Fobj, bubble = 100 ∑ 0.5  +  with ∆x = x1, exp − x1, cal = x2, exp − x2, cal   i =1  x1, exp x2, exp i  ndew  ∆y ∆y   +  with ∆y = y1, exp − y1, cal = y2, exp − y2, cal  Fobj, dew = 100∑ 0.5  i =1  y1, exp y2, exp i   ncrit  ∆xc ∆xc  F = + 100 0. 5   with ∆xc = xc1, exp − xc1, cal = xc2, exp − xc2, cal ∑ obj, crit, comp x  xc2, exp  i =1 c1, exp  i  (9) ncrit  P   − P cm, exp cm, cal    Fobj, crit, pressure = 100∑   P i = 1 cm, exp   i  naz  ∆xaz ∆xaz  F = 100 0.5  +  with ∆xaz = xaz1, exp − xaz1, cal = xaz2, exp − xaz2, cal ∑ obj, az, comp x  xaz2, exp  i =1 az1, exp  i   naz  P − Paz, cal   Fobj, az, pressure = 100∑  az, exp     Paz, exp i =1  i  nmix ,enthalpy   ∆h M  M M M  Fobj, mix, enthalpy = 100 ∑  M  with ∆h = hexp − hexp   h i = 1   exp i

where nbubble, ndew, ncrit, naz and nmix,enthalpy are the number of bubble points, dew points, mixture critical points, azeotropic points, and enthalpy change on mixing points, respectively. The variable, x1, is the mole fraction of the most volatile component in the liquid phase, and x2 is the mole fraction of the heaviest component (x2 = 1 - x1) at a fixed temperature and pressure. Similarly, y1 is the mole fraction of the most volatile component in the gas phase, and y2 is the mole fraction of the heaviest component (y2 = 1 - y1) at a fixed temperature and pressure. The variable xc1 is the critical mole fraction of the most volatile component, and xc2 is the critical mole fraction of the heaviest component at a fixed temperature. Pcm is the binary critical pressure at a fixed temperature. The variable xaz1 is the Addition of the sulfur dioxide group (SO2), the oxygen group (O2) and the nitric oxide group (NO) to the E-PPR78 model

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azeotropic mole fraction of the most volatile component, and xaz2 is the azeotropic mole fraction of the heaviest component at a fixed temperature. Paz is the azeotropic pressure at a fixed temperature. hM is the enthalpy change on mixing at fixed temperature, pressure and composition.


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4. Extension of E-PPR78 model to SO2, O2 and NO

4.1 Addition of group “SO2” For all the binary data points included in our database and involving sulfur dioxide (718 points), the objective function defined by Eq. (9) is Fobj = 9.33%. The values of the objective function for each binary system are listed in Table 2. The average overall deviations on the liquid phase composition ( ∆x1 = ∆x2 , ∆x% ), the gas phase composition ( ∆y1 = ∆y2 , ∆y% ), the azeotropic composition ( ∆xaz1 = ∆xaz 2 , ∆xaz % ), the azeotropic pressure ( ∆paz , ∆paz % ), the binary critical composition ( ∆xc1 = ∆xc2 , ∆xc % ) and the binary critical pressure ( ∆pcm , ∆pcm % ) are listed in Table 3. These results indicate that the E-PPR78 model remains an accurate predictive model for binary system involving SO2, even if the deviations observed in this study are higher than those observed with hydrocarbons5-7 or with CO29. Two reasons can explain this higher objective function value. The first reason is the presence of many azeotropes in the studied systems, such as, propane + sulfur dioxide, sulfur dioxide + n-butane and sulfur dioxide + alkenes systems. Indeed, as explained by Privat et al.16, the presence of an azeotropic point makes increase “artificially” the value of the objective function in comparison to phase diagrams without azeotrope. The second reason is that, the vapor composition of (SO2 + aromatic compound) systems at high pressures is often close to pure SO2. As explained by Plee et al.13, in this case, a very small absolute difference between the calculated and the experimental value leads to a high relative deviation that is to a high value of the objective function. Due to the lack of experimental data, it was not possible to determine the interactions between group 25 (SO2) and groups 4 (C), 6 (C2H6), 9 (Cfused aromatic rings), 10 (CH2,cyclic), 11 (CHcyclic/Ccyclic), 14 (H2S), 15 (SH), 17 (C2H4), 20 (CHcycloalkenic/Ccycloalkenic), 21 (H2), 22 (CO) and 23 (He). In order to have a fair idea of the accuracy of the proposed model, isothermal (P,x1,y1) and isobaric (T,x1,y1) phase diagrams were predicted at the temperatures and pressures where experimental data were available. Such diagrams, built with an easy to handle algorithm77, can be seen in Figures 1-5. As shown in Figures 1 and 2, except the methane + SO2 system which exhibits a type III phase behavior, the other studied binary systems containing alkanes or alkenes exhibit a type I (or II) phase Addition of the sulfur dioxide group (SO2), the oxygen group (O2) and the nitric oxide group (NO) to the E-PPR78 model

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behavior in the classification scheme of Van Konynenburg and Scott (VKS)78,79. The phase equilibrium behaviors of these systems, especially the azeotropic behaviors, are accurately predicted. As mentioned in former section, the values of the objective function of these systems are often higher than the average value, due to the presence of many azeotropes in these systems. Figures 3a, 3b, 3c and 3d show phase diagrams for mixtures containing SO2 and an aromatic compound. A satisfactory agreement is observed between model prediction and experimental data. It is however noticeable that, the values of the objective function for these systems are high. As explained in former section, this is because the SO2 mole fraction in the gas phase is very close to 1. The prediction results for mixtures containing SO2 and three other permanent gases (CO2, Ar and N2) are presented in Figures 4a, 4b, 4c and 4d, together with experimental data. The group–interaction parameters A12-25 and B12-25 between “CO2” and “SO2” were determined by correlating recently reported vapor-liquid equilibrium (VLE) data4. The CO2 + SO2 system exhibits a type I phase behavior, and the corresponding objective function value is low. Both (Ar + SO2) and (N2 + SO2) systems exhibit a type III phase behavior. As shown in Figures 3b, 3c and 3d, the phase equilibrium behavior of both systems can be reliably predicted with the E-PPR78 model over a wide range of temperature. Figure 5 shows the prediction of phase behavior for the SO2 + H2O system at different temperatures. The E-PPR78 model predicts a type II phase behavior for this system. It is worth mentioning that only the VLE data35 – where the dissociation of sulfur dioxide in the liquid phase was taken into account – were used for regressing parameters A16-25 and B16-25. An interesting feature of the E-PPR78 model is its capability to accurately predict the 3-phase line location of this system at different temperatures.

4.2 Addition of group “O2” For all the binary data points included in our database and involving oxygen (2754 points), the objective function defined by Eq. (9) is Fobj = 5.95%. The average overall deviations on the liquid phase composition ( ∆x1 = ∆x2 , ∆x% ), the gas phase composition ( ∆y1 = ∆y2 , ∆y% ), the binary critical composition ( ∆xc1 = ∆xc2 , ∆xc % ), the binary critical pressure ( ∆pcm , ∆pcm % ) and the enthalpy change on mixing ( ∆h M % ) are listed in Table 3. The value of the objective function is quite low. As seen in Table 2, the values of the objective function Addition of the sulfur dioxide group (SO2), the oxygen group (O2) and the nitric oxide group (NO) to the E-PPR78 model

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(Fobj) for most studied systems (except O2 + H2O system) are very low. It indicates that, the phase equilibrium properties of binary systems containing O2 can be accurately predicted with the E-PPR78 model. Due to a lack of experimental data, it was not possible to determine the interactions between group 26 (O2) and groups 3 (CH), 4 (C), 5 (CH4), 6 (C2H6), 9 (Cfused aromatic rings), 14 (H2S), 15 (SH), 17 (C2H4), 18 (CH2,alkenic/CHalkenic), 19 (Calkenic), 20 (CHcycloalkenic/Ccycloalkenic), 21 (H2), 22 (CO) and 23 (He). Several phase diagrams predicted with the E-PPR78 model are visible in Figures 6-12. As seen in Figure 6, the phase behavior of three binary systems containing O2 and an alkane are well described with the E-PPR78 model. They exhibit a type III phase behavior in the classification scheme of Van Konynenburg and Scott. The phase diagrams for (O2 + benzene) and (O2 + methylbenzene) systems are shown in Figure 7, together with experimental VLE data. For both systems, which exhibit a type III phase behavior, the mole fraction of O2 in the liquid phase is quite low. The results for binary systems containing O2 and a naphthenic compound are presented in Figure 8. For such systems, experimental phase equilibrium data are quite scarce. For the moment, it is not possible to determine the group–interaction parameters between group 26 (O2) and group 11 (CHcyclic/Ccyclic), and the determination of the group–interaction parameters A10-26 and B10-26 (between group O2 and group CH2,cyclic) are based on very limited sets of experimental data available within a narrow range of temperature and pressure. The results for mixtures containing O2 and two gases (CO2 and SO2) are shown in Figures 9a-9d. Both systems exhibit a type III phase behavior. As shown in Figures 9a-9c, the E-PPR78 model slightly overestimates the critical pressures for the system O2 + CO2. However, outside the critical region, quite accurate results are obtained. The phase equilibrium of the O2 + SO2 system could also be well predicted within a wide range of temperature and pressure. The next two figures show results for (N2 + O2) and (Ar + O2) systems. Both systems exhibit a type I phase behavior, and binary interaction parameters remain small regardless of the temperature. It is observed that the bubble and dew points are predicted with a high accuracy. As shown in Figure 11e, the few hM data points available in the open literature for the Ar + O2 system are also well reproduced.


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The O2 + H2O system depicted in Figure 12 exhibits a type III phase behavior. The group–interaction parameters between groups O2 and H2O were determined by correlating experimental data in a wide range of temperature and pressure. For this system, at temperatures lower than but close to the critical temperature of H2O, two critical points can be found at the same temperature. As evidenced in Figure 12c, the E-PPR78 model is able to predict a temperature minimum on the critical locus, however the corresponding calculated temperature is a little higher than the experimental value.

4.3 Addition of group “NO” For all the binary data points included in our database and involving nitric oxide (164 points), the objective function defined by Eq. (9) is Fobj = 6.17%. The average overall deviations on the liquid phase composition ( ∆x1 = ∆x2 , ∆x% ), the gas phase composition ( ∆y1 = ∆y2 , ∆y% ), the binary critical composition ( ∆xc1 = ∆xc2 , ∆xc % ) and the binary critical pressure ( ∆pcm , ∆pcm % ) are listed in Table 3. The experimental or simulated phase equilibrium data for binary systems containing NO are very scarce, and to the best our knowledge, only data for four systems are available in the open literature. For these systems, the values of the objective function are quite low, as seen in Table 2, and their phase diagrams predicted with the E-PPR78 model are shown in Figures 13 and 14. It can be found that, the phase behavior of NO + cyclohexane system can be well predicted with the E-PPR78 model. The model predicts a type V phase behavior for this system. Such a behavior can however not be confirmed by the few available experimental data. The results of the NO + CO2 and NO + SO2 are presented in Figures 14a and 14b respectively. As seen in Figures, the prediction results of the E-PPR78 model are satisfactorily consistent with experimental data and with results of Monte Carlo simulations. Both systems exhibit a type III phase behavior. Figures 14c, 14d and 14e present the result of N2 + NO system. The dew points of this system could be well reproduced with the E-PPR78 model. The mole fractions of N2 in liquid phase at high pressures are however overestimated. The N2 + NO system exhibits a type II phase behavior.


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5 Conclusions In this paper, three new groups: “SO2”, “O2”, and “NO” were added to the E-PPR78 model in order to make possible the prediction of the phase behavior for systems involved in the process of Carbon dioxide Capture and Storage. Such new groups may also be useful to design Enhanced Oil recovery (EoR) processes80-81. The new group–interaction parameters of the E-PPR78 model were determined by correlating most experimental data available in the open literature. As introduced in the previous sections, most of studied systems exhibit a type III phase behavior in the classification scheme of Van Konynenburg and Scott. In this study, accurate fluid phase equilibrium predictions were obtained in large temperature, pressure and composition ranges.

Acknowledgements This study was financially supported by French National Agency for Research (ANR) through the SIGARRR project.

Supporting Information Group–interaction parameters: (Akl = Alk)/MPa and (Bkl = Blk)/MPa. This information is available free of charge via the Internet at http://pubs.acs.org/.


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References (1) El Ahmar, E.; Boonaert, E.; Coquelet, C. Thermodynamic study of mixtures of compounds present during the carbon dioxide capture, transport and storage. Energy Procedia 2013, 36, 702-706. (2) Sterpenich, J.; Dubessy, J.; Pironon, J.; Renard, S.; Caumon, M.-C.; Randi, A.; Jaubert, J.-N.; Favre, E.; Roizard, D.; Parmentier, M.; Azaroual, M.; Lachet, V.; Creton, B.; Parra, T.; El Ahmar, E.; Coquelet, C.; Lagneau, V.; Corvisier, J.; Chiquet, P. Role of Impurities on CO2 Injection: Experimental and Numerical Simulations of Thermodynamic Properties of Water-salt-gas Mixtures (CO2 + Co-injected Gases) Under Geological Storage Conditions. Energy Procedia 2013, 37, 3638-3645. (3) Corvisier, J.; El Ahmar, E.; Coquelet, C.; Sterpenich, J.; Privat, R.; Jaubert, J. N.; Ballerat-Busserolles, K.; Coxam, J. Y.; Cezac, P.; Contamine, F.; Serin, J. P.; Lachet, V.; Creton, B.; Parmentier, M.; Blanc, P.; Andre, L.; de Lary, L.; Gaucher, E. C. Simulations of the Impact of Co-injected Gases on CO2 Storage, the SIGARRR Project: First Results on Water-gas Interactions Modeling. Energy Procedia 2014, 63, (12th International Conference on Greenhouse Gas Control Technologies, GHGT-12), 3160-3171. (4) Coquelet, C.; Valtz, A.; Arpentinier, P. Thermodynamic study of binary and ternary systems containing CO2 + impurities in the context of CO2 transportation. Fluid Phase Equilib. 2014, 382, 205-211. (5) 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. (6) 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. (7) 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 naphthenic compounds. Fluid Phase Equilib. 2006, 243, (1-2), 9-28. (8) Qian, J.-W.; Jaubert, J.-N.; Privat, R. Prediction of the phase behavior of alkene-containing binary systems with the PPR78 model. Fluid Phase Equilib. 2013, 354, 212-235. (9) 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 Addition of the sulfur dioxide group (SO2), the oxygen group (O2) and the nitric oxide group (NO) to the E-PPR78 model

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Chem. Res. 2008, 47, (19), 7483-7489. (12) Qian, J.-W.; Jaubert, J.-N.; Privat, R. Phase equilibria in hydrogen-containing binary systems modeled with the Peng-Robinson equation of state and temperature-dependent binary interaction parameters calculated through a group-contribution method. J. Supercrit. Fluids 2013, 75, 58-71. (13) Plee, V.; Jaubert, J.-N.; Privat, R.; Arpentinier, P. Extension of the E-PPR78 equation of state to predict fluid phase equilibria of natural gases containing carbon monoxide, helium-4 and argon. J. Pet.

Sci. Eng., 2015, DOI:10.1016/j.petrol.2015.03.025. (14) Privat, R.; Jaubert, J.-N.; Mutelet, F. Addition of the sulfhydryl 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. (15) Privat, R.; Jaubert, J.-N. Addition of the sulfhydryl group (SH) to the PPR78 model: Estimation of missing group-interaction parameters for systems containing mercaptans and carbon dioxide or nitrogen or methane, from newly published data. Fluid Phase Equilib. 2012, 334, 197-203. (16) Privat, R.; Mutelet, F.; Jaubert, J.-N. Addition of the Hydrogen Sulfide Group to the PPR78 Model (Predictive 1978, Peng-Robinson Equation of State with Temperature Dependent kij Calculated through a Group Contribution Method). Ind. Eng. Chem. Res. 2008, 47, (24), 10041-10052. (17) Qian, J.-W.; Privat, R.; Jaubert, J.-N. Predicting the Phase Equilibria, Critical Phenomena, and Mixing Enthalpies of Binary Aqueous Systems Containing Alkanes, Cycloalkanes, Aromatics, Alkenes, and Gases (N2, CO2, H2S, H2) with the PPR78 Equation of State. Ind. Eng. Chem. Res. 2013,

52, (46), 16457-16490. (18) 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, 3162–3171. Addition of the sulfur dioxide group (SO2), the oxygen group (O2) and the nitric oxide group (NO) to the E-PPR78 model

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Fuels 2013, 27, (11), 7150-7178. (23) Qian, J.-W. Développement du modèle E-PPR78 pour prédire les équilibres de phases et les grandeurs de mélange de systèmes complexes d'intérêt pétrolier sur de larges gammes de températures et de pressions. Nancy, 2011. (24) 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. (25) 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. (26) 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. (27) 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, (1), 26-37. (28) Poling, B. E.; Prausnitz, J. M.; O'Donnell, J. H. The properties of Gases and Liquids. 5th ed.; McGraw-Hill: New York, 2001. Addition of the sulfur dioxide group (SO2), the oxygen group (O2) and the nitric oxide group (NO) to the E-PPR78 model

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Chem. Soc., Faraday Trans. 1 1975, 71, (11), 2232-50. (34) El Ahmar, E.; Creton, B.; Valtz, A.; Coquelet, C.; Lachet, V.; Richon, D.; Ungerer, P. Thermodynamic study of binary systems containing sulphur dioxide: Measurements and molecular modelling. Fluid Phase Equilib. 2014, 304, (1-2), 21-34. (35) Rumpf, B.; Maurer, G. Solubilities of hydrogen cyanide and sulfur dioxide in water at temperatures from 293.15 to 413.15 K and pressure up to 2.5 MPa. Fluid Phase Equilib. 1992, 81, 241-260. (36) Ayscough, P. B.; Ivin, K. J.; O'Donnell, J. H. Vapor pressure of the system isobutene-sulfur dioxide. Trans. Faraday Soc. 1965, 61, (512), 1601-1607. (37) Brady, B. H. G.; O'Donnell, J. H. Activity coefficients in binary liquid mixtures of 3-methyl-1-butene and sulfur dioxide. Trans. Faraday Soc. 1968, 64, (1), 23-28. (38) El Ahmar, E.; Valtz, A.; Coquelet, C.; Richon, D.; Lagneau, V. VLE study of sulfur dioxide containing binary mixtures. In 24th European Symposium on Applied Thermodynamics, Alberto Arce and Ana Soto: 2009. (39) Houssin-Agbomson, D.; Coquelet, C.; Arpentinier, P.; Delcorso, F.; Richon, D. Equilibrium Data for the Oxygen + Propane Binary System at Temperatures of (110.22, 120.13, 130.58, and 139.95) K. J.

Chem. Eng. Data 2010, 55, (10), 4412-4415. (40) Wilcock, R. J.; Battino, R.; Danforth, W. F.; Wilhelm, E. Solubilities of gases in liquids II. The Addition of the sulfur dioxide group (SO2), the oxygen group (O2) and the nitric oxide group (NO) to the E-PPR78 model

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9, (2), 111-115. (45) Field, L. R.; Wilhelm, E.; Battino, R. Solubility of gases in liquids. 6. Solubility of nitrogen, oxygen, carbon monoxide, carbon dioxide, methane, and carbon tetrafluoride in methylcyclohexane and toluene at 283 to 313 K. J. Chem. Thermodyn. 1974, 6, (3), 237-243. (46) Booth, H. S.; Carter, J. M. The critical constants of carbon dioxide-oxygen mixtures. J. Phys.

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Dana,

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I.

Liquid-vapor

equilibrium

compositions

of

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dioxideoxygen-nitrogen mixtures. Chem. Eng. Prog., Symp. Ser. 1963, 59, 36-41. Addition of the sulfur dioxide group (SO2), the oxygen group (O2) and the nitric oxide group (NO) to the E-PPR78 model

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(64) Baidakov, V. G.; Kaverin, A. M.; Andbaeva, V. N. The liquid-gas interface of oxygen-nitrogen solutions. Fluid Phase Equilib. 2008, 270, (1-2), 116-120. (65) Japas, M. L.; Franck, E. U. High pressure phase equilibria and PVT-data of the water-oxygen system including water-air to 673 K and 250 MPa. Ber. Bunsen-Ges. Phys. Chem. 1985, 89, (12), 1268-1275. (66) Stephan, E. L.; Hatfield, N. S.; Peoples, R. S.; Pray, H. A. H. The solubility of gases in water and in aqueous urany salt solutions at elevated temperatures and pressures. Battelle Mem. Inst. Rep 1956, Jan-47. (67) Bourbo, P.; Ischkin, I. Study of the vapor - liquid equilibrium of the system argon - oxygen. Phys.

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using either the gamma-phi or the phi-phi approach for binary and ternary mixtures. Comput. Chem.

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Res. 1998, 37, 4854–4859.


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Tables and Figures


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Page 23 of 39

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Table 1. List of the 23 pure components used in this study. Component methane propane n-butane n-octane n-decane benzene methylbenzene 1,3-dimethylbenzene 1,3,5-trimethylbenzene 1-butene 2-butene 2-methyl-1-propene 3-methyl-1-butene cyclohexane cyclooctane methylcyclohexane carbon dioxide nitrogen water argon sulfur dioxide oxygen nitric oxide

Short name 1 3 4 8 10 B mB 13mB 135mB t1a4 t2a4 2ma3 3ma4 C6 C8 mC6 CO2 N2 H2 O Ar SO2 O2 NO


23 Environment ACS Paragon Plus


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Table 2. Binary systems database. System (1) + (2) 1 - SO2 3 - SO2 SO2 - 4 SO2 - B SO2 - mB SO2 – 13mB SO2 - 135mB CO2 - SO2 N2 - SO2

T range (K)

P range (bar)

x1 range

y1 range

nbubble

ndew

241.09-301.48 323.15-363.15 238.15-276.15 255.37 227.60-249.80 227.60-249.90 227.60-250.00 263.15-333.21 241.09-413.15

0.0152-0.0348 0.3608-0.793 0.5950-0.6440 0.3400-0.9650 0.0762-0.8812 0.0779-0.8760 0.1004-0.9012 0.0296-0.8970 0.0030-0.1740

0.708-0.987 0.3608-0.793

5 7

5 7

0.969-0.999 0.9410-1.0000 0.9740-1.0000 0.9770-1.0000 0.2080-0.9853 0.023-0.989

19 27 27 27 22 51

19 26 21 8 22 51

SO2 - H2O SO2 – t1a4 SO2 – t2a4 SO2 - 2ma3 SO2 – 3ma4 Ar – SO2

293.15-393.33 257.15-276.15 244.15-276.15 243.15-283.15 289.15-313.15 323.45-413.41

O2 - 3 O2 - 8 O2 - 10

110.22-120.13 283.31-348.31 283.15-313.48

17.17-35.51 13.40-43.83 0.48-2.69 0.27-0.69 0.01-0.48 0.01-0.48 0.009-0.50 3.55-87.85 15.51-235.3 0 0.36-25.09 1.00-2.40 0.47-2.07 0.47-2.75 1.66-6.47 23.67-234.7 8 2.69-24.35 1.01-89.671 1.01

O2 - B

302.85-332.63

0.27-4.25

O2- mB O2 - C8

298.43-348.29 289.18-313.53

1.09-91.67 1.013

O2 – mC6

284.15-313.26

1.013

O2 - CO2 N2-O2 O2 - H2O O2 - Ar

213.10-298.15 63.14-132.0 373.15-663.00 82.09-123.17

9.31-149.96 0.029-30.11 17.2-2606.0 0.41-14.25

O2 - SO2

323.15-413.15

NO – C6

283.16-313.16

42.27-199.6 7 0.20-1.31

NO - CO2

232.93-273.02

N2 - NO NO – SO2

113.83-119.56 324.43-345.07

10.10-114.8 6 4.63-21.91 3.23-37.81

0.0035-0.0889 0.583-0.593 0.675-0.723 0.07-0.938 0.101-0.95 0.011-0.185

ncrit

naz

Nmix,enthalpy

Fobj (%) 3.89 11.63 12.24 8.31 10.29 17.63 17.89 1.80 6.14

ref

7.88 16.33 7.58 11.58 18.54 4.46

35 31 31 31, 36 37 38

20 43 3

5.21 1.58 0.92

39 40, 41 40

18

1.18

42

91 3

5.13 0.47

41, 43 44

3

0.21

45

5.61 4.08 15.89 6.93 3.42

46-51 52-64 65, 66 60, 63, 67-73 34

1.43

74

4.85

4

10.85 6.23

75 76

1 7

63 0.583-0.593 0.675-0.723

0.1075-0.8836

56 62 28

2 4 6 29

0.0266-0.4190 0.0021-0.1863 0.00217-0.002 2 0.00008-0.003 25 0.0009-0.1028 0.001069-0.00 11003 0.0014072-0.0 014966 0.0040-0.6000 0.0022-0.9887 0.0002-0.1010 0.0322-0.9604

0.0810-0.8530 0.0059-0.9962 0.2040-0.9420 0.0457-0.9634

128 672 171 366

135 603 59 346

0.0220-0.1510

0.1490-0.8800

26

28

0.00025-0.002 37 0.0157-0.4194

0.1656-0.761

29

29

0.0380-0.9510 0.0174-0.5767 6

0.8920-0.9776 0.3380-0.8538 4

13 18

27 20

5 8 29

24

2

29 30 31 32 33 33 33 4 29, 34

nbubble = number of bubble points; ndew = number of dew points; ncrit = number of critical points; naz = number of azeotropic points; nmix, enthalpy = number of enthalpy change on mixing points; Fobj = objective function.


24


Page 25 of 39

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Table 3. Average overall deviations for the 3 new groups. Group SO2 O2 NO

∆x1 = ∆x2

∆x% 9.07 6.31 6.12

0.0194 0.0106 0.0166

∆y1 = ∆y2

∆y%

∆xaz1 = ∆xaz 2

∆xaz %

0.0096 0.0141 0.0147

9.17 5.34 5.40

0.0734

15.31

∆paz / bar ∆paz % 0.2694

nbubble

∑

∆x1 = ∆x2 =

i

nbubble

; ∆x% =

Fobj, bubble nbubble

; ∆y1 = ∆y2 =

∆h M % =

10.33 10.02 10.33

∆pcm / bar ∆pcm % 114.85 13.46 114.85

33.01 10.65 33.01

∆h M %

11.61

∑ y1,exp − y1,cal i i =1

ndew

i =1

naz

xc1,exp − xc1,cal

i =1

ncrit

; ∆y% =

Fobj, dew ndew

naz

; ∆xaz % =

Fobj, az, comp naz

; ∆paz =

ncrit

∆xc1 = ∆xc2 =

0.0507 0.0351 0.0507

8.26

naz

∑ xaz1,exp − xaz1,cal i

∑

∆xc %

ndew

x1,exp − x1,cal

i =1

∆xaz1 = ∆xaz 2 =

∆xc1 = ∆xc2

∑ paz,exp − paz,cal i i =1

naz

; ∆paz % =

Fobj, az, pressure naz

ncrit i

; ∆xc % =

Fobj, crit, comp ncrit

; ∆pcm =

∑ pcm,exp − pcm,cal i i =1

ncrit

; ∆pcm % =

Fobj, crit, pressure ncrit

Fobj, mix, enthalpy nmix, enthalpy


25



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

50.0

Page 26 of 39

50.0 (a)

(b)

P / bar

P / bar

T1 = 241.09 K, k12 = 0.135238 T2 = 301.48 K, k12 = 0.138901

25.0

25.0

T1 = 323.15 K, k12 = 0.161688 T2 = 363.15 K, k12 = 0.194841

x1, y1 0.0 0.0

0.5

0.0 0.0

1.0

0.5

x1, y1 1.0

100.0 (c)

P / bar

50.0 azeotropic line

T/K 0.0 100.0

300.0

Figure 1. Isothermal phase diagrams and critical locus predicted with the E-PPR78 model for binary systems containing SO2 and a n-alkane: (a) methane (1) + SO2 (2); (b) propane (1) + SO2 (2); (c) SO2 (1) + n-butane (2). (+) experimental bubble points, (*) experimental dew points, (◊) experimental azeotropic points.


26


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80.0

(a)

(b)

P / bar

P / bar

2.5 T1 = 253.15 K k12 = 0.019635 T2 = 258.15 K k12 = 0.022161 T3 = 263.15 K k12 = 0.024669 T4 = 268.15 K k12 = 0.027162 T5 = 273.15 K k12 = 0.029642 T6 = 278.15 K k12 = 0.032112 T7 = 283.15 K k12 = 0.034573

1.5

T/K

x1, y1 0.5 0.0

0.5

azeotropic line

40.0

0.0 160.0

1.0

360.0

(c)

P / bar

6.0 T1 = 289.15 K k12 = 0.060467 T2 = 293.15 K k12 = 0.061672 T3 = 297.15 K k12 = 0.062811 T4 = 301.15 K k12 = 0.063880 T5 = 305.15 K k12 = 0.064877 T6 = 309.15 K k12 = 0.065799 T7 = 313.15 K k12 = 0.066642

4.0

2.0

x1, y1 0.0 0.0

0.5

1.0

Figure 2. Isothermal phase diagrams and critical locus predicted with the E-PPR78 model for binary systems containing SO2 and an alkene: (a, b) SO2 (1) + 2-methyl-1-propene (2); (c) SO2 (1) + 3-methyl-1-butene. (+) experimental bubble points, (◊) experimental azeotropic points.


27



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0.8

Page 28 of 39

0.6

(a)

(b)

P / bar

P / bar

T1 = 227.60 K, k12 = -0.025662 T2 = 237.40 K, k12 = -0.022278 T3 = 249.80 K, k12 = -0.017988

T1 = 255.37 K, k12 = 0.003819

0.4

0.4

0.2

x1, y1 0.0 0.0

0.5

x1, y1 0.0 0.0

1.0

0.6

0.5

1.0

0.6

(c)

(d)

P / bar

P / bar

T1 = 227.60 K, k12 = -0.055749 T2 = 237.40 K, k12 = -0.050613 T3 = 250.00 K, k12 = -0.044139

T1 = 227.60 K, k12 = -0.043219 T2 = 237.40 K, k12 = -0.038800 T3 = 249.90 K, k12 = -0.033231

0.4

0.4

0.2

0.2

x1, y1 0.0 0.0

x1, y1 0.0

0.5

1.0

0.0

0.5

1.0

Figure 3. Isothermal phase diagrams predicted with the E-PPR78 model for binary systems containing SO2 and an aromatic compound: (a) SO2 (1) + benzene (2); (b) SO2 (1) + methylbenzene (2); (c) SO2 (1) + 1,3-dimethylbenzene (2); (d) SO2 (1) + 1,3,5-trimethylbenzene. (+) experimental bubble points, (*) experimental dew points.


28


Page 29 of 39

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100.0

800.0

(a)

(b)

P / bar

P / bar

T1 = 323.45 K, k12 = 0.222764 T2 = 343.45 K, k12 = 0.208541 T3 = 374.07 K, k12 = 0.190035 T4 = 413.41 K, k12 = 0.170795

T1 = 263.15 K, k12 = 0.024956 T2 = 333.21 K, k12 = 0.025076

50.0

400.0

x1, y1

x1, y1

0.0

0.0

0.0

0.5

1.0

100.0

0.0

0.5

1.0

(d) P / bar 2000.0 T1 = 323.15 K, k12 = 0.083002

(c)

P / bar

T2 = 343.15 K, k12 = 0.086010 T3 = 373.15 K, k12 = 0.096213 T4 = 413.15 K, k12 = 0.099666

T1 = 241.09 K, k12 = 0.075000 T2 = 301.48 K, k12 = 0.080194

50.0

1000.0

x1, y1 0.0

x1, y1 0.0 0.0

0.0

0.5

0.5

1.0

1.0

Figure 4. Isothermal phase diagrams predicted with the E-PPR78 model for binary systems containing SO2 and another gas: (a) CO2 (1) + SO2 (2); (b) Ar (1) + SO2 (2); (c, d) N2 (1) + SO2 (2). (+) experimental bubble points, (*) experimental dew points.


29



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 39

10.0

5.0 (a)

(b)

P / bar

P / bar

5.0

2.5

T1 = 313 K, k12 = -0.078917

T1 = 293 K, k12 = -0.086774

x1, y1

x1, y1

0.0 0.0

0.0 0.0

0.5

1.0

0.5

1.0

20.0

15.0 (c)

(d)

P / bar

P / bar

10.0

10.0

5.0

T1 = 333 K, k12 = -0.070768

T1 = 343 K, k12 = -0.066567

x1, y1 0.0 0.0

0.5

x1, y1 0.0 0.0

1.0

0.5

1.0

50.0

30.0 (e)

(f)

P / bar

P / bar

20.0

25.0

10.0

T1 = 393 K, k12 = -0.044420

T1 = 363 K, k12 = -0.057963

x1, y1 0.0 0.0

0.5

x1, y1 0.0 0.0

1.0

0.5

1.0

Figure 5. Isothermal phase diagrams predicted with the E-PPR78 model for the SO2 (1) + H2O (2) system. (+) experimental bubble points.


30


Page 31 of 39

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400.0

50.0

(b)

(a)

T/K

P / bar

T1 = 110.22 K, k12 = 0.118550 T2 = 120.13 K, k12 = 0.116250 T3 = 130.58 K, k12 = 0.114376 T4 = 139.95 K, k12 = 0.113081

300.0

25.0

200.0

P1 = 1.01 bar

x1, y1 0.0 0.0

0.5

100.0 0.0

1.0

0.5

x1, y1 1.0

1500.0

200.0 (c)

(d)

P / bar

P / bar

1000.0

100.0

500.0

T1 = 298.42 K, k12 = 0.156701

0.0 0.0

0.5

T1 = 323.30 K, k12 = 0.155592

x1, y1

0.0 0.0

1.0

1200.0

0.5

x1, y1 1.0

500.0

(e)

(f)

P / bar

T/K

800.0

300.0

400.0

T1 = 348.31 K, k12 = 0.155121

0.0 0.0

0.5

P1 = 1.01 bar

x1, y1 100.0 0.0

1.0

0.5

x1, y1 1.0

Figure 6. Isothermal and isobaric phase diagrams predicted with the E-PPR78 model for binary systems containing O2 and an alkane: (a) O2 (1) + propane (2); (b-e) O2 (1) + n-octane (2); (f) O2 (1) + n-decane (2). (+) experimental bubble points. Addition of the sulfur dioxide group (SO2), the oxygen group (O2) and the nitric oxide group (NO) to the E-PPR78 model

31



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

10.0

10.0

5.0

(a)

10.0

(b)

P / bar

ZOOM

P / bar

ZOOM

5.0

2.5

5.0

Page 32 of 39

0.0 0.000

0.005

5.0

0.0 0.000

0.015

T1 = 283.45 K, k12 = 0.303772 T2 = 313.15 K, k12 = 0.218488 T3 = 323.15 K, k12 = 0.208845 T4 = 333.15 K, k12 = 0.202581 T5 = 353.15 K, k12 = 0.195234 T6 = 373.15 K, k12 = 0.191099 T7 = 393.15 K, k12 = 0.188371

T1 = 302.85 K, k12 = 0.253178 T2 = 317.71 K, k12 = 0.249054 T3 = 332.63 K, k12 = 0.245256

x1, y1 0.0 0.0

0.5

x1, y1 0.0 0.0

1.0

100.0

0.5

1.0

100.0

(c)

P / bar

ZOOM

50.0

0.0 0.0

0.15

50.0

T1 = 298.43 K, k12 = 0.244610 T2 = 323.30 K, k12 = 0.208731 T3 = 348.29 K, k12 = 0.196611

x1, y1 0.0 0.0

0.5

1.0

Figure 7. Isothermal phase diagrams predicted with the E-PPR78 model for binary systems containing O2 and an aromatic compound: (a) O2 (1) + benzene (2); (b, c) O2 (1) + methylbenzene (2). (+) experimental bubble points.


32


Page 33 of 39

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400.0

500.0 (a)

(b)

T/K

T/K

400.0

300.0

300.0

P1 = 1.01 bar

200.0 0.0

0.5

P1 = 1.01 bar

x1, y1 1.0

200.0 0.0

0.5

x1, y1 1.0

Figure 8. Isobaric phase diagram predicted with the E-PPR78 model for binary systems containing O2 and a naphthenic compound: (a) O2 (1) + cyclooctane (2); (b) O2 (1) + methyl-cyclohexane (2). (+) experimental bubble points.


33



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

200.0

200.0

T1 = 218.15 K, k12 = 0.09632 (a) T2 = 223.15 K, k12 = 0.09899 T5 = 253.15 K, k12 = 0.11483 T3 = 232.85 K, k12 = 0.10399 T6 = 263.15 K, k12 = 0.12029 T4 = 243.15 K, k12 = 0.10945

P / bar

100.0

Page 34 of 39

(b) T1 = 223.75 K, k12 = 0.09922 T2 = 233.15 K, k12 = 0.10414 T5 = 288.15 K, k12 = 0.13433 T3 = 273.15 K, k12 = 0.12584 T6 = 298.15 K, k12 = 0.14011 T4 = 283.15 K, k12 = 0.13147

100.0

x1, y1 0.0 0.0

0.5

x1, y1 0.0 0.0

1.0

0.5

1.0

400.0

1000.0 (c)

(d)

P / bar

200.0

500.0

P / bar

T1 = 323.15 K k12 = 0.230089 T2 = 343.15 K k12 = 0.221343 T3 = 373.15 K k12 = 0.210226 T4 = 413.15 K k12 = 0.198413

x1, y1

T/K 0.0 100.0

P / bar

0.0 0.0

300.0

0.5

1.0

Figure 9. Isothermal phase diagrams and critical locus predicted with the E-PPR78 model for binary systems containing O2 and another gas: (a-c) O2 (1) + CO2 (2); (d) O2 (1) + SO2 (2). (+) experimental bubble points, (*) experimental dew points, (○) experimental critical points.


34


Page 35 of 39

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130.0

140.0

(a)

(b)

T/K

T/K

110.0

120.0

P1 = 12.16 bar P2 = 14.19 bar P3 = 16.21 bar P4 = 18.24 bar P5 = 20.27 bar P6 = 23.30 bar P7 = 26.34 bar

90.0 P1 = 1.01 bar P5 = 6.08 bar P2 = 1.33 bar P6 = 8.11 bar P3 = 2.03 bar P7 = 10.13 bar P4 = 4.05 bar

70.0 0.0

0.5

x1, y1 100.0 0.0

1.0

x1, y1 0.5

1.0

40.0

1.5 (c)

T1 = 83.82 K, k12 = -0.014869 T2 = 90.53 K, k12 = -0.015111 T3 = 99.94 K, k12 = -0.015448 T4 = 110.05 K, k12 = -0.015809 T5 = 119.91 K, k12 = -0.016159 T6 = 124.97 K, k12 = -0.016339

P / bar

T1 = 63.14 K, k12 = -0.014106 T2 = 65.00 K, k12 = -0.014176 T3 = 70.00 K, k12 = -0.014362 T4 = 74.70 K, k12 = -0.014536 T5 = 77.50 K, k12 = -0.014639 T6 = 79.07 K, k12 = -0.014696

1.0

(d)

P / bar

20.0

0.5

x1, y1

x1, y1 0.0 0.0

0.0 0.0

0.5

1.0

40.0

40.0 (e)

P / bar

T1 = 100.11 K, k12 = -0.015454 T2 = 110.02 K, k12 = -0.015808 T3 = 120.62 K, k12 = -0.016185 T4 = 122.70 K, k12 = -0.016259 T5 = 125.00 K, k12 = -0.016340

20.0

0.5

T1 = 105.00 K, k12 = -0.015629 T2 = 110.00 K, k12 = -0.015807 T3 = 115.00 K, k12 = -0.015985 T4 = 120.00 K, k12 = -0.016163 T5 = 124.00 K, k12 = -0.016305

(f)

P / bar

20.0

T6 = 128.00 K, k12 = -0.016447 T7 = 132.00 K, k12 = -0.016589

x1, y1 0.0 0.0

1.0

0.5

0.0 0.0

1.0

0.5

x1, y1

1.0

Figure 10. Isobaric and isothermal phase diagrams predicted with the E-PPR78 model for the binary systems N2 (1) + O2 (2). (+) experimental bubble points, (*) experimental dew points. Addition of the sulfur dioxide group (SO2), the oxygen group (O2) and the nitric oxide group (NO) to the E-PPR78 model

35



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1.6

(a)

T/K

Page 36 of 39

(b)

P / bar

T1 = 82.09 K, k12 = 0.011666 T2 = 83.82 K, k12 = 0.011576 T3 = 87.00 K, k12 = 0.011419 T4 = 89.57 K, k12 = 0.011300 T5 = 90.52 K, k12 = 0.011257

96.0 1.2

92.0 0.8 P1 = 1.22 bar P2 = 1.52 bar P3 = 1.72 bar P4 = 2.03 bar

88.0 0.0

x1, y1 0.5

x1, y1 0.4 0.0

1.0

7.0

1.0

(d)

(c)

5.0

0.5

P / bar

P / bar T1 = 90.00 K, k12 = 0.011280 T2 = 95.00 K, k12 = 0.011068 T3 = 100.00 K, k12 = 0.010877 T4 = 105.00 K, k12 = 0.010703 T5 = 110.00 K, k12 = 0.010546

12.5 T1 = 101.80 K, k12 = 0.010812 T2 = 104.51 K, k12 = 0.010720 T3 = 110.01 K, k12 = 0.010546 T4 = 112.86 K, k12 = 0.010462 T5 = 120.02 K, k12 = 0.010271 T6 = 123.17 K, k12 = 0.010195

7.5 3.0

x1, y1

x1, y1 1.0 0.0

0.5

2.5 0.0

1.0

0.5

(e)

1.0

hM / (J/mol)

60.0

40.0

20.0 T1 = 84.0 K, k12 = 0.011567 T2 = 86.0 K, k12 = 0.011467 T3 = 86.6 K, k12 = 0.011438

x1

0.0 0.0

0.5

1.0

Figure 11. Phase diagrams and enthalpy changes on mixing predicted with the E-PPR78 model for the binary system Ar (1) + O2 (2). (+) experimental bubble points, (*) experimental dew points, (×) experimental enthalpy changes on mixing. Addition of the sulfur dioxide group (SO2), the oxygen group (O2) and the nitric oxide group (NO) to the E-PPR78 model

36


Page 37 of 39

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3000.0

(a)

(b)

P / bar

200.0

200.0 100.0

0.0 0.00

T1 = 373.15 K k12 = 0.099011 T2 = 408.15 K k12 = 0.123911 2000.0 T3 = 435.93 K k12 = 0.145165 T4 = 477.59 K k12 = 0.179660 T5 = 533.15 K k12 = 0.230975 T6 = 560.93 K 1000.0 k12 = 0.259124

ZOOM

0.01

100.0

P / bar

T1 = 523.00 K, k12 = 0.221188 T2 = 563.00 K, k12 = 0.261293 T3 = 583.00 K, k12 = 0.282772 T4 = 603.00 K, k12 = 0.305243 T5 = 623.00 K, k12 = 0.328755 T6 = 628.50 K, k12 = 0.335411

x1, y1

0.0 0.0

0.5

x 1 , y1 0.0 0.0

1.0

0.5

1.0

4000.0 P / bar

(c)

2000.0

T/K 0.0 100.0

300.0

500.0

700.0

Figure 12. Isothermal phase diagrams (a, b) and critical locus (c) predicted with the E-PPR78 model for the binary system O2 (1) + H2O (2). (+) experimental bubble points, (*) experimental dew points, (○) experimental critical points.


37



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1.2

1.2

P / bar 0.8

0.4

ZOOM

0.8 0.0 0.0

0.005

0.4

0.0

T2 = 293.16 K, k12 = -0.10132 T1 = 283.16 K, k12 = -0.08557 T3 = 313.16 K, k12 = -0.13933

0.0

0.5

x1, y1

1.0

Figure 13. Isothermal phase diagrams predicted with the E-PPR78 model for the binary system NO (1) + C6 (2). (+) experimental bubble points.


38


Page 38 of 39

Page 39 of 39

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


150.0

600.0 (a)

(b)

P / bar

P / bar

T1 = 324.43 K, k12 = -0.128747 T2 = 345.07 K, k12 = -0.223493

100.0

400.0

50.0

200.0

0.0 0.0

T1 = 232.93 K, k12 = -0.011314 T2 = 252.98 K, k12 = -0.047399 T3 = 273.02 K, k12 = -0.077487

0.5

x1, y1

x1, y1 0.0 0.0

1.0

0.5

1.0

20.0

20.0 (c)

(d)

P / bar

T1 = 113.83 K, k12 = 0.019608

P / bar

T1 = 114.68 K, k12 = 0.021751

10.0

10.0

x1, y1

x1, y1 0.0 0.0

0.5

0.0 0.0

1.0

0.5

(e)

1.0

P / bar

T1 = 119.56 K, k12 = 0.034149

20.0

10.0

x1, y1 0.0 0.0

0.5

1.0

Figure 14. Isothermal phase diagrams predicted with the E-PPR78 model for binary systems: (a) NO (1) + CO2 (2); (b) NO (1) + SO2 (2); (c-e) N2 (1) + NO (2). (+) experimental bubble points, (*) experimental dew points, (×) bubble points from Monte-Carlo simulations76, (□) dew points from Monte-Carlo simulation76, (○) critical points from Monte-Carlo simulation76. Addition of the sulfur dioxide group (SO2), the oxygen group (O2) and the nitric oxide group (NO) to the E-PPR78 model

39


Addition of the Sulfur Dioxide Group (SO2), the Oxygen Group (O2

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