Hydrogen Solubility in Heavy Undefined Petroleum Fractions Using Group Contributions Methods
Solubilité de l’hydrogène dans des fractions indéfinies du pétrole lourd à l’aide de la méthode de contribution de groupes
^{1}
Universidad Nacional Autónoma de México (UNAM), Posgrado de Ingeniería, Av. Universidad 3000, Ciudad Universitaria, Deleg. Coyoacan
C.P. 04510 – México
^{2}
Mexican Institute of Petroleum, Department of Reservoir Engineering, Eje Central Lázaro Cárdenas Norte 152, Col. San Bartolo Atepehuacan, Deleg. Gustavo A. Madero, C.P. 07730 – México
email: bcarreon@imp.mx
^{*} Corresponding author
Received:
7
June
2016
Accepted:
28
November
2016
Hydrogen solubility in heavy undefined petroleum fractions is estimated by taking as starting point a method of characterization based on functional groups [ CarreónCalderón et al. (2012) Ind. Eng. Chem. Res. 51, 1418814198 ]. Such method provides properties entering into equations of states and molecular pseudostructures formed by noninteger numbers of functional groups. Using VaporLiquid Equilibria (VLE) data from binary mixtures of known compounds, interaction parameters between hydrogen and the calculated functional groups were estimated. Besides, the incorporation of the hydrogencarbon ratio of the undefined petroleum fractions into the method allows the corresponding hydrogen solubility to be properly estimated. This procedure was tested with seven undefined petroleum fractions from 27 to 6 API over wide ranges of pressure and temperature (323.15 to 623.15 K). The results seem to be in good agreement with experimental data (overall Relative Average Deviation, RAD < 15%).
Résumé
La solubilité de l’hydrogène dans des fractions indéfinies du pétrole lourd est estimée en prenant comme point de départ la méthode de contribution de groupes [CarreónCalderón et al. (2012) Ind. Eng. Chem. Res. 51, 1418814198]. Cette méthode fournit les paramètres d’entrée de l’équation d’état et une pseudostructure moléculaire formée par des nombres non entiers pour les groupes fonctionnels. En utilisant les données de l’équilibre liquidevapeur des mélanges binaires de composants connus, les paramètres d’interaction entre l’hydrogène et les groupes fonctionnels sont déterminés. En plus, l’incorporation du rapport hydrogènecarbone des fractions indéfinies du pétrole dans la méthode décrite permet d’estimer correctement la solubilité de l’hydrogène. Cette méthode a été testée avec sept fractions indéfinies de densité API de 6 à 27, et sur une large plage de pressions et de températures (323.15 à 623.15 K). Les résultats montrent un bon accord avec les données expérimentales (erreur moyenne relative globale < 15 %).
© H. AguilarCisneros et al., published by IFP Energies nouvelles, 2017
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Notation
A : Parameter of the equation of state
A_{1}A_{3}: Coefficients in Equation (5)
a_{1}a_{4}: Coefficients in Equations (11)(14)
B : Parameter of the equation of state
b_{1}b_{4}: Coefficients in Equations (11)(14)
C_{ k }: Carbon number of defined hydrocarbons
c_{1}: Coefficient in Equation (11)
d_{1}: Coefficient in Equation (11)
FG : Number of functional groups types
p_{c}: Contribution to P_{c} by functional groups
R : Universal constant of gases, 8.31441 J/mol K
V_{c}: Critical volume, m^{3}/mol
v_{Ci}: Contribution to V_{c} by functional groups
Greek letters
α : Coefficient in Equation (9)
β : Coefficient in Equation (9)
χ : Coefficient in Equation (9)
Δv : Group volume increment in Equations (4) and (5)
ν : Number of functional groups
Superscripts
Subscripts
i : Functional group i or pure component i
j : Undefined petroleum fractions j or pure component j
Introduction
Hydrogen solubility predictions are essential part in several processes in the petroleum and chemical industries; for instance, hydrocracking and hydrogenation processes are used to transform heavy oil into more valuable products. Hydrogen solubility data are required for designing and operating such processes and it is also needed in the corresponding kinetic models (Saajanlehto et al., 2014). Several authors have pointed out the importance of taking into account VaporLiquid Equilibria (VLE) in reaction modeling and its influence in conversion predictions (Chen et al., 2011; Hook, 1985; Pellegrini et al., 2008). A detailed review about VLE of hydrogen and petroleum fraction systems was presented by Chávez et al. (2014). They presented experimental data and modeling methods, most of which were conducted for systems composed of hydrogen and defined hydrocarbons, with few systems formed by hydrogen and undefined petroleum fractions. This may be attributable to the lack of experimental data, making a hard task to develop accurate prediction methods. Besides, binary systems containing hydrogen all exhibit a type III phase behavior in the classification scheme of Van Konynenburg and Scott (Privat and Jaubert, 2013) which cannot be predicted with cubic equations of state using classical mixing rules because of the quantum nature of hydrogen and the mixture sizeasymmetry (Deiters, 2013). Despite these issues, most methods found in literature use cubic Equations Of State (EOS) because of their mathematical simplicity and their capability of modeling multicomponent mixtures over a wide range of temperatures and pressures. To overcome such limitations several authors have proposed to fit EOS parameters to VLE data (Qian et al., 2013); however, in general, their capability of prediction is reduced with such regressions. New approaches have been suggested in order to preserve the predictive features of cubic equations of state, such as that described by Jaubert et al. (2010). In such approach, binary interaction parameters are predicted by using a group contribution method, where classical cubic equations of state and excess free energy models (EOS/g^{E}) are combined, being applied successfully to binary mixtures of hydrogen with defined hydrocarbons (Qian et al., 2013).
A further challenge is the mathematical characterization of the undefined petroleum fraction; that is, the determination of its physicalchemical properties by mathematical means. In such characterization process, it is important to find a convenient number of pseudocomponents in which the undefined petroleum fraction will be divided. According to Lin et al. (1985), better results are obtained as the number of pseudocomponents increases when VLE of systems formed by hydrogen and undefined fractions are modeled. On the other hand, Chávez concluded that 30 pseudocomponents are enough to obtain good agreement between calculated and experimental data. The characterization procedure also involves estimation of the corresponding critical properties entering into cubic equations of state. These properties are frequently calculated from correlations (Firoozabadi, 1988; Lee and Kesler, 1975; Pedersen et al., 2004), but they do not always lead to the same results, because each one was developed for different sets of fluids at limited conditions. Thus, recently, group contribution methods have been recently extended to pseudocomponents, showing a good performance (CarreónCalderón et al., 2012; Xu et al., 2015).
CarreónCalderón et al. (2012) presented a new characterization procedure based on group contribution methods. They used selected functional groups to assign a hypothetical chemical structure to an undefined petroleum fraction by a minimization process of its corresponding Gibbs free energy. This methodology was applied to simulate VLE of heavy (CarreónCalderón et al., 2014) and light hydrocarbons (UribeVargas et al., 2016). Good results were achieved in both cases without making use of correlations to calculate critical properties or adjusted binary interaction parameters. In particular, they modeled vaporliquid equilibria of heavy petroleum fluids, where no significant differences were shown regardless of the number of pseudocomponents used in modeling. These results show the feasibility of applying this characterization procedure to VLE of hydrogen with heavy undefined petroleum fraction. In this work, we add hydrogen functional group to the set of functional groups original proposed and suggest modifications to the characterization procedure in order to determine the hydrogen solubility properly. The entire methodology was tested with experimental data found in literature: Venezuelan Heavy Coking Gas Oil (HGCO) (Ji et al., 2013), Karamay Atmospheric Residue (KRAR) (Ji et al., 2013), Liaohe Atmospheric Residue (LHAR) (Ji et al., 2013), Venezuelan Atmospheric Residue (VNAR) (Ji et al., 2013), Canadian Light Virgin Gas Oil (CLVGO) (Cai et al., 2001), Canadian Heavy Virgin Gas Oil (CHVGO) (Cai et al., 2001) and Athabasca Bitumen (AB) (Lal et al., 1999).
1 Characterization Procedure
The approach presented by CarreónCalderón et al. (2012) is used to determine the properties of the undefined petroleum fractions. In that methodology, a hypothetical structure is calculated with a set of selected functional groups, which depend on the group contribution method used. CarreónCalderón et al. (2012, 2014) have suggested two group contribution methods; JobackReid (JR) (Joback and Reid, 1987) and MarreroGani (MG) (Marrero and Gani, 2001). JR method was suggested to simulate VLE of light petroleum fluids (UribeVargas et al., 2016), while MG method showed better functionality in heavy petroleum fluids heavier than 14 API (CarreónCalderón et al., 2014). In the latter, the C_{7+} fraction, which has unknown composition, was split in 3, 6 and 9 pseudocomponents, founding no significant difference between calculations and experiments regardless of the fraction splitting. Accordingly, in this work, the undefined petroleum fractions are treated as a single pseudocomponent in order to have a simpler characterization, where their corresponding properties are calculated through MG method.
Table 1 shows the functional groups of the MG method and the equivalent groups of the GCVOL (Elbro et al., 1991; Ihmels and Gmehling, 2003) method for determining liquid densities, as originally proposed by CarreónCalderón et al. (2012). A quick review of these functional groups was made and it was found that the last functional groups are not equivalent each other (aC ≠ AC − C). Therefore, in this work the last functional group (aC) was changed to aC − C functional group from the same MG method.
Original functional groups.
An optimization process is used to estimate a hypothetical chemical structure of the undefined petroleum fraction, where its Gibbs free energy is the objective function to be minimized. Since the undefined fraction is treated like a pure component, minimize the liquid fugacity coefficient is equivalent to minimize the Gibbs energy. Thus, the objective function is:(1)where T_{C}, P_{C} and ω are the critical temperature, critical pressure and acentric factor, respectively, with FG being the number of functional groups types. The expression depends on the cubic EOS selected; in this work, the PengRobinson cubic Equation Of State PREOS (Peng and Robinson, 1976) is used to determine the fugacity coefficient as follows:(2)where Z ^{ L } = PV ^{ L }⁄(RT) is the compressibility factor of the liquid phase, A and B are PREOS parameters. The properties of undefined petroleum fractions are usually given at standard conditions; hence, the pressure P and temperature T are set equal to 0.101325 MPa and 288.15 K, respectively; v ^{ L } is the molar liquid volume and R is the gas constant.
This minimization problem is constrained by the molecular weight and density of the corresponding undefined petroleum fraction:(3) (4)
In the above expression, subscripts j and i indicate the functional group j of the undefined fraction i, MW is the molecular weight, υ_{j}, the number (coefficient) of a functional group, Δv_{j} the volume increment, the liquid density. The Δv_{j} is expressed as a function of temperature by means of(5)where A_{1}, A_{2} and A_{3} are the parameters of the GCVOL approach (Ihmels and Gmehling, 2003).
Finally, to solve the minimization problem, Equation (2) requires critical properties (T_{C}, P_{C} and ω). These properties are calculated using Equations from (6) to (8), where, the temperature is in K, pressures in MPa and volume in m^{3}/mol (Marrero and Gani, 2001).(6) (7) (8)
In previous equations t_{Ci}, p_{Ci} and v_{Ci} represent contributions to the critical temperature, the critical pressure, and the critical molar volume because of the presence of a defined functional group i in a molecule.
One of the major contributions of the characterization procedure described above is the assignment of a hypothetical chemical structure to an undefined petroleum fraction. This allows us to handle the undefined fraction as hypothetical pure component and, in principle, to make use of any thermodynamic model exclusively developed for known components and their mixtures. Thus, in addition to PREOS, HuronVidal (Michelsen, 1990) mixing rule together with the UNIversal quasichemical Functional group Activity Coefficients (UNIFAC) approach, as activity coefficient model, are used also in this work for calculating VLE of hydrogen and heavy petroleum fluids, where the groupinteraction parameters Ψ_{nm} in the UNIFAC approach are given by(9)
The parameters α_{nm}, β_{nm} and χ_{nm} are specific parameters for a couple of functional groups n and m, whose values are obtained from literature (Horstmann et al., 2005). Notice that α_{nm} ≠ α_{mn}, β_{nm} ≠ β_{mn}, χ_{nm} ≠ χ_{mn}. It is worth pointing out that hydrogen is handled as a single functional group.
2 Solubility of Hydrogen in Defined Hydrocarbon Components
Before proceeding with the calculation of VLE of systems composed of hydrogen and heavy petroleum fluids, the hydrogen solubility in defined hydrocarbons was estimated in order to evaluate the thermodynamic models and their corresponding binary parameters described above.
Table 2 shows the 13 binary systems involved in this study, which are formed by nine paraffinic and four aromatic compounds. The range of experimental temperatures and pressures are also included and the comparison of calculated with experimental values are given in Table 3.
List of 13 binary mixtures used in this study.
RAD of hydrogen solubility in defined hydrocarbons.
As observed, hydrogen solubility estimation is smaller than the experimental values in all cases. The difference is higher as the carbon number of the component increases; the Relative Average Deviation (RAD) increases from 13% for pentane to 75% for hexatetracontane, whereas, in the case of aromatic compounds increases from 32% to 52% for benzene and pyrene, respectively. Because of these results, groupinteraction parameters Ψ_{nm} were calculated again by fitting calculations to the available VLE experimental data in Table 2. This fitting process requires to identify the functional groups forming the defined components. In case of paraffinic compounds, they can be represented by CH_{3} and CH_{2} functional groups, and aromatic compounds by ACH and AC functional groups. Because CH_{3} and AC belongs to the main group 1 (CH_{2}) and 3 (ACH) respectively, only interaction parameters between CH_{2} and H_{2}, ACH and H_{2}, and ACH and CH_{2} are required.
Table 4 shows the original α_{nm} parameters between main functional groups.
Original groupinteraction parameters (α_{nm}, α_{mn}) between functional groups used in this study (Horstmann et al., 2005).
In the fitting process, for simplicity, parameter α_{nm} is adjusted while β_{nm} and χ_{nm} parameters keep their original values. The fitted groupinteraction parameters are obtained by a minimization process, where the objective function (F_{Obj}) is given by(10)
Here and are the experimental and calculated saturation pressure on the bubble point respectively and N represent the number of data points. The result of this fitting process is a group of new parameters (α_{nm}, α_{mn}) for each binary mixtures (H_{2}hydrocarbon). Figures 1a and 1b show the trend of α_{nm} and α_{mn} parameters for paraffinic and aromatic compounds as function of the carbon number. The correlated parameters take the form of:(11) (12) (13) (14)where, C_{k} is the carbon number of the defined compounds. and are the groupinteraction parameters between CH_{2} and H_{2} functional groups, and are groupinteraction parameters between ACH and H_{2} functional groups. Finally, coefficients a_{n}, b_{n}, c_{n}, d_{n} are shown in Table 5.
Figure 1 Groupinteraction parameters as function of carbon number a) paraffinic compounds, b) aromatic compounds. 
Groupinteraction parameters (α_{nm}) between functional groups used in this study.
Similar results have been obtained by Florusse et al. (2003); they used a Statistical Associating Fluid Theory (SAFT) model to predict hydrogen solubility in heavy alkanes, where the corresponding crossbinary interaction parameters were obtained as a function of the carbon number as well.
Figures 2a and 2b show experimental (♦) and calculated hydrogen solubility data for pyrene and hexatetracontane, respectively. The original groupinteraction parameters underestimate hydrogen solubility () whereas the predicted values are in better agreement with experimental data (—).
Figure 2 Solubility of hydrogen a) pyrene at 433.2 K, b) hexatetracontane at 402.4 K. 
Table 3 summarizes the RAD of all defined components with the original groupinteraction parameters and with those given by Equations from (11) to (14).
3 Solubility of Hydrogen in Undefined Petroleum Fractions
As first step, critical properties and molecular pseudostructures of the seven undefined petroleum fractions studied in this work were determined using the characterization procedure described in Section 1. Table 6 shows density, molecular weight and hydrogencarbon ratio of the seven undefined fractions used in this work. As will be discussed later, the last two properties play an important role in modeling such systems with hydrogen. In all cases, the experimental error reported in the literature for hydrogen solubility was ±5% (Cai et al., 2001; Ji et al., 2013), except for AB system where such experimental error was not reported (Lal et al., 1999).
Relevant physical properties of the undefined petroleum fractions used in this work.
Once the molecular pseudostructure is formed with the functional groups from Table 1, it is possible to make a distinction between paraffinic, naphthenic and aromatic contributions through to the nointeger coefficients (υ_{j}) resulting from the minimization process. Notice that although nine functional groups are used in the characterization procedure (see Tab. 1), there are only two main functional groupS according to the UNIFAC method: first six functional belong to the main CH_{2} functional group, whereas the rest of them belong to the main ACH functional group. Accordingly, the calculated coefficients υ_{j} can be added in order to obtain the carbon number according to these two main functional groups. Therefore, Equations from (11) to (14) can be used to estimate groupinteraction parameters between the H_{2} and the functional groups calculated by the characterization procedure.
As illustration, Figure 3 shows the experimental and predicted hydrogen solubility in CHVGO (at 603.15 K) which has a molecular weight of 350 g/mol. The black diamonds (♦) represent the experimental values and the crossed bars represent the experimental reported error of ±5%. Calculations using the original groupinteraction parameters (— —) underestimates the hydrogen solubility, as it is also observed for the defined hydrocarbons from Table 2; in this case the RAD is 51%. When our proposed correlations, Equations from (11) to (14), are used to estimate groupinteraction parameters, the predicted values (⋅⋅⋅⋅) remains below experimental data, but the RAD is reduced up to 25%. To improve the accuracy of hydrogen solubility prediction, a modification of the original minimization process of characterization is suggested. This modification consists of including another constraint, in addition to Equations (3) and (4). We believed that this constraint should somehow account for the chemical nature of the undefined fractional. Hence, the HydrogenCarbon ratio (H/C) is proposed as a third constraint. According to experimental observations made by Ji et al. (2013), this parameter may be related to the aromaticity of undefined fraction.
Figure 3 Solubility of hydrogen in CHVGO petroleum fraction at 603.15 K as a function of groupinteraction parameters. 
Figure 4 shows the coefficients (υ_{j}) obtained from the original characterization procedure and the modified one with the hydrogencarbon ratio as constraint. The latter gives smaller values for the aromatic functional groups and larger values for all other functional groups. According to Park et al. (1996) hydrogen solubility decreases as the number of aromatic rings increases. Hence, we believe that the inclusion of the H/C ratio may help to construct a pseudostructure in better agreement with its aromatic nature. Figure 3 shows the predicted hydrogen solubility (—) using the modified characterization procedure. As seen, predicted hydrogen solubilities are in better agreement with experimental data (RAD = 5%).
Figure 4 Coefficients calculated by characterization process. 
The modified characterization procedure is summarized in Figure 5, where the stages are described in a flowchart. Here (H⁄C)_{j} is the hydrogencarbon ratio of a functional group j and (H⁄C)_{Exp} is the experimental hydrogencarbon ratio of a i undefined petroleum fraction.
Figure 5 Flow chart of the modified characterization process. 
As observed in Table 6, three undefined fractions have molecular weights below 360 g/mol, whereas the rest of them have values above 500 g/mol. Although good results were achieved in the former, hydrogen solubility was overestimated in the latter. When the calculated pseudostructures are reviewed, it is found that they are formed mainly by paraffinic and cyclic functional groups and by a small portion of aromatic ones. This seems to be the reason why the hydrogen solubility is overestimated. Hence, a sensitivity analysis was made to know the effect of the H/C ratio in the characterization process from Figure 5.
In Figure 6a, three different pseudostructures of AB depending on the H/C ratio are shown. When H/C parameter is set equal to the experimental value, the pseudostructure is mainly formed by paraffinic and naphthenic functional groups and hydrogen solubility is overestimated (RAD > 50%). In contrast, hydrogen solubility is underestimated (RAD > 20%) when H/C parameter is set equal to 30% below the experimental value. In latter case, aromatic functional groups predominate over paraffinic and naphthenic ones. Figure 6b shows the trend of the RAD as function of the used H/C ratio. It can be seen that there is minimum value when H/C parameter is set around 80% of the experimental value; its corresponding pseudostructure is shown in Figure 6a. At this point, it is important to emphasize that the characterization procedure do not intend to make a characterization at molecular level, but look for an average structure that allow to reproduce bulk properties (CarreónCalderón et al., 2012, 2014; UribeVargas et al., 2016).
Figure 6 Sensitivity analysis of H/C parameter used in the characterization process for AB. a) Pseudostructure arrangements of AB depending on percent of the H/C ratio, b) RAD vs. percent of H/C ratio used in the minimization process. 
As with the A/B undefined petroleum fraction, the same sensitivity analysis was made for the VNAR, KRAR, and LAHR fractions. Figure 7 illustrates that minimum values of the RAD are achieved when H/C parameter lies between 80 and 85% of the experimental value. Therefore, we suggested to set the H/C ratio in this interval in order to obtained better results for heavy undefined petroleum fraction with molecular weights above 500 g/mol.
Figure 7 Sensitivity analysis of RAD as a function of H/C parameter in the characterization process for different cuts. 
The results of hydrogen solubility prediction in Athabasca Bitumen (AB) at different temperatures and pressures are illustrated in Figures 8a and 8b. Here, the experimental value of the H/C ratio is 1.51, but, according to that previously discussed, it was set equal to 1.208, obtaining an overall RAD of 6.8%. In Table 7 all results are summarized, the overall RAD being equal to 14.12%.
Figure 8 Prediction of hydrogen solubility in Athabasca Bitumen a) at 373.15 K, 473.15 K and 573.15 K, b) at 323.15 K, 423.5 K and 523.15 K. 
RAD on prediction of H_{2} solubility in undefined hydrocarbon fractions.
Conclusions
The characterization procedure presented by CarreónCalderón et al. (2012, 2014) was extended to predict hydrogen solubility in heavy undefined petroleum fractions including H_{2} as another functional group, and the hydrogencarbon ratio as third constraint in the characterization process. Groupinteraction parameters between hydrogen and the main functional groups of the UNIFAC approach were calculated through a set of correlations based on experimental vaporliquid equilibria data of binary mixtures of hydrogen and defined hydrocarbons. These modifications were enough for prediction purposes with molecular weights below 500 g/mol. For undefined petroleum fraction with molecular weights above 500 g/mol, the hydrogencarbon ratio was modified to 80% of its experimental value. The inclusion of the hydrogencarbon ratio was revealed as important property in order to construct the hypothetical structures in better accordance with its molecular nature.
Acknowledgments
The authors express their gratitude to the Mexican Institute of Petroleum and SENERCONACyT for financial support through the Y.61006 research project.
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Cite this article as: H. AguilarCisneros, V. UribeVargas, B. CarreónCalderón, J.M. DomínguezEsquivel and M. RamirezdeSantiago (2017). Hydrogen Solubility in Heavy Undefined Petroleum Fractions Using Group Contributions Methods. Oil Gas Sci. Technol 72, 2.
All Tables
Original groupinteraction parameters (α_{nm}, α_{mn}) between functional groups used in this study (Horstmann et al., 2005).
Groupinteraction parameters (α_{nm}) between functional groups used in this study.
Relevant physical properties of the undefined petroleum fractions used in this work.
All Figures
Figure 1 Groupinteraction parameters as function of carbon number a) paraffinic compounds, b) aromatic compounds. 

In the text 
Figure 2 Solubility of hydrogen a) pyrene at 433.2 K, b) hexatetracontane at 402.4 K. 

In the text 
Figure 3 Solubility of hydrogen in CHVGO petroleum fraction at 603.15 K as a function of groupinteraction parameters. 

In the text 
Figure 4 Coefficients calculated by characterization process. 

In the text 
Figure 5 Flow chart of the modified characterization process. 

In the text 
Figure 6 Sensitivity analysis of H/C parameter used in the characterization process for AB. a) Pseudostructure arrangements of AB depending on percent of the H/C ratio, b) RAD vs. percent of H/C ratio used in the minimization process. 

In the text 
Figure 7 Sensitivity analysis of RAD as a function of H/C parameter in the characterization process for different cuts. 

In the text 
Figure 8 Prediction of hydrogen solubility in Athabasca Bitumen a) at 373.15 K, 473.15 K and 573.15 K, b) at 323.15 K, 423.5 K and 523.15 K. 

In the text 