Simulation of Organic Liquid Products Deoxygenation by Multistage Countercurrent Absorber/Stripping Using CO2 as Solvent with Aspen-HYSYS: Thermodynamic Data Basis and EOS Modeling

In this work, the thermodynamic data basis and equation of state (EOS) modeling necessary to simulate the fractionation of organic liquid products (OLP), a liquid reaction product obtained by thermal catalytic cracking of palm oil at 450 °C, 1.0 atmosphere, with 10% (wt.) Na2CO3 as catalyst, in multistage countercurrent absorber/stripping columns using supercritical carbon dioxide (SC-CO2) as solvent, with Aspen-HYSYS was systematically investigated. The chemical composition of OLP was used to predict the density (ρ), boiling temperature (Tb), critical temperature (Tc), critical pressure (Pc), critical volume (Vc), and acentric factor (ω) of all the compounds present in OLP by applying the group contribution methods of Marrero-Gani, Han-Peng, Marrero-Pardillo, Constantinou-Gani, Joback and Reid, and Vetere. The RK-Aspen EOS used as thermodynamic fluid package, applied to correlate the experimental phase equilibrium data of binary systems OLP-i/CO2 available in the literature. The group contribution methods selected based on the lowest relative average deviation by computing Tb, Tc, Pc, Vc, and ω. For n-alkanes, the method of Marrero-Gani selected for the prediction of Tc, Pc and Vc, and that of Han-Peng for ω. For alkenes, the method of Marrero-Gani selected for the prediction of Tb and Tc, Marrero-Pardillo for Pc and Vc, and Han-Peng for ω. For unsubstituted cyclic hydrocarbons, the method of Constantinou-Gani selected for the prediction of Tb, Marrero-Gani for Tc, Joback for Pc and Vc, and the undirected method of Vetere for ω. For substituted cyclic hydrocarbons, the method of Constantinou-Gani selected for the prediction of Tb and Pc, Marrero-Gani for Tc and Vc, and the undirected method of Vetere for ω. For aromatic hydrocarbon, the method of Joback selected for the prediction of Tb, Constantinou-Gani for Tc and Vc, Marrero-Gani for Pc, and the undirected method of Vetere for ω. The regressions show that RK-Aspen EOS was able to describe the experimental phase equilibrium data for all the binary pairs undecane-CO2, tetradecane-CO2, pentadecane-CO2, hexadecane-CO2, octadecane-CO2, palmitic acid-CO2, and oleic acid-CO2, showing average absolute deviation for the liquid phase (AADx) between 0.8% and 1.25% and average absolute deviation for the gaseous phase (AADy) between 0.01% to 0.66%.

critical properties (T b , T c , P c , V c ), and acentric factor (ω) of all the compounds present in OLP predicted by the group contribution methods of Marrero-Gani, Han-Peng, Marrero-Pardillo, Constantinou-Gani, Joback and Reid, and Vetere. The RK-Aspen applied to correlate the experimental phase equilibrium data of binary systems organic liquid products compounds (OLP)i -CO 2 available in the literature. The regressions show that RK-Aspen EOS was able to describe the experimental phase equilibrium data for all the binary pairs (multi-component mixture compounds)i -CO 2 under investigation. Predictive methods selected by considering their applicability to describe the chemical structure of molecules, including the effects of carboxylic acids and hydrocarbons chain length and molecular weight, and simplicity of use.
Based on the chemical composition of OLP described in Table S1, experimental data for critical properties available in the literature selected to the following class of hydrocarbons including alkanes from C 2 -C 20 , cyclic from C 3 -C 17 , alkenes with only one double bound from C 4 -C 20 , and aromatics from C 6 -C 15 , carboxylic acids of linear chain length from C 1 -C 10 , as well as C 16 , C 18 , C 20 , and C 22 , carboxylic acids with one or two double bounds including C 16:1 , C 16:2 , C 18:1 , C 18:2 , C 20:1 , C 20:2 , C 22:1 , C 22:2 , alcohols of linear chain length from C 2 -C 10 .
Methods to Predict Thermo-Physical (T b ) and Critical Properties (T c , P c , V c ) The predictive methods by Joback and Reid [63], Constantinou-Gani [64], Marrero-Marejón and Pardillo-Fontdevila [65], and Marrero-Gani [66] applied to estimate the normal boiling temperature (T b ) and critical properties (T c , P c , V c ) of all the compounds present in OLP. Table 1 presents the equations of all the predictive methods applied to compute T b , T c , P c , and V c [63][64][65][66]. Table 1. The equations used to predict/estimate the thermo-physical (T b ) and critical properties (T c , P c , V c ) of all the compounds present in OLP, by the methods of Joback and Reid [63], Constantinou and Gani [64], Marrero-Marejón and Pardillo-Fontdevila [65] and Marrero and Gani [66].

Constantinou-Gani [64]
Marrero-Gani [66] Joback & Reid [63] Marrero-Pardillo [65] T b = 198.2 + ∑ n i T bi T b = 204.66 + ∑ T c = T b 0.584 + 0.965 (∑ n i T ci ) − ∑ n j T cj The method by Constantinou-Gani [64], is based only on the molecular structure of molecules, being applied in two levels: the first level treats simple functional groups, also called first order groups, and the second level treats the second order groups, formed by blocks of first order groups. In the equations described in Table 1, T b1i , T c1i , P c1i and V c1i , represent the group contribution of first order level for the corresponding properties, and N i how many times the group i occurs in the molecule. In a similar way, T b2j , T c2j , P c2j and V c2j represents the group contributions of second order level, and M j how many times the group j occurs in the molecule.
Marrero-Gani [66], proposed a method analogous to that of Constantinou-Gani [64], in which a group contribution of third order is added, whereas T b3k , T c3k , P c3k and V c3k represent these contributions, and O k how many times the group k occurs in the molecule.
Joback and Reid [63], proposed a method to estimate the normal boiling temperature (T b ) and critical properties (T c , P c , V c ) using group contribution, where Σ symbolizes the sum of all the contributions of each group corresponding to the parts of a molecule. To compute the critical temperature (T c ), Joback and Reid [63] proposed a method dependent on the normal boiling temperature (T b ).
By the method of Joback and Reid [63], n i is the number of contributions, while T bi and T ci are the normal boiling temperature and critical temperature associated to the i-th group contribution. To compute the critical pressure (P c ), the method by Joback and Reid [63], considers the number of atoms within the molecule, where n A specifies the number of atoms in the molecule, and P ci the critical pressure associated to the i-th group contribution.
Marrero-Pardillo [65], proposed a method to predict the normal boiling temperature (T b ) and critical properties (T c , P c , V c ) of pure organic molecules that uses a novel structural approach. This methodology uses the interactions between the groups of charges within the molecule, instead of the simple group contribution. To estimate the critical pressure (P c ), and likewise the method by Joback and Reid [63], this method also considers the number of atoms in the molecule.

Methods Selected to Predict the Acentric Factor (ω)
The prediction of acentric factor performed by using direct group contribution methods as described by Costantinou et al. [67] and Han and Peng [68], as well as an indirect method using its definition from vapor pressure data, based on the proposal of Araújo and Meireles [69]. In this case, the correlation by Vetere [70] was used, making it possible to estimate the vapor pressure from molecular structure. Experimental values for acentric factors obtained as the follows: Predicted by using experimental data of critical properties, and experimental data of vapor pressure at T r = 0.7 [71]; II. Predicted by using experimental values of critical properties and vapor pressure data at T r = 0.7, computed with Wagner's equation [72], and the parameters obtained from experimental data fitting.

Statistical Analysis of Predicted
Thermo-Physical Property (T b ), Critical Properties (T c , P c , V c ), and Acentric Factor (ω) of OLP Compounds The same criteria used by Melo et al. [73] and Araújo and Meireles [69] were used to select the best methods to predict the thermo-physical property, critical properties, and acentric factor of OLP compounds. The criteria based on statistical analysis (measurements of central tendency and dispersion).
The decisive criteria to select the best prediction methods for the thermo-physical properties, critical properties, and acentric factor are the measurement of central tendency, represented by the average relative deviation (ARD), the dispersion of deviations (R), and the standard deviation (S), using the procedures as follows: 1.
The lower values for the average relative deviation (ARD) and standard deviation (S) define the best methods;

2.
In cases where the lower average deviation corresponds to the higher standard deviation, or vice versa, the method is selected by the lower range of deviation (R).
The predicted data for the thermo-physical property, critical properties, and acentric factor computed by the methods and procedures described in Methods to Predict Thermo-Physical (T b ) and Critical Properties (T c , P c , V c ) and Methods Selected to Predict the Acentric Factor (ω), analyzed on basis its consistency related the physicochemical behavior expected for homologous series.
This test applied to hydrocarbons [61], by relating the thermo-physical property, critical properties, and the acentric factor with the number of carbons in carbon chain length or molecular weight of hydrocarbons.

Correlation of Phase Equilibrium Data for the Binary System OLP Compoundsi -CO 2 EOS Modeling
The thermodynamic modeling applied to describe the OLP fractionation in a multistage countercurrent absorber/stripping column using SC-CO 2 as solvent, performed by the Redlich-Kwong Aspen EOS.
The RK-Aspen EOS equation of state applied to correlate the binary systems organic liquid products compoundsi -CO 2 available in the literature, as described in Table 2. The RK-Aspen EOS with the van der Waals mixing rules and RK-Aspen combining rules for two temperature-independent binary interaction parameters, described in details by Table 2. Table 2. The RK-Aspen EOS with the van der Waals mixing rules and RK-Aspen combining rules for two temperatureindependent binary interaction parameters k aij = k 0 aij and k bij = k 0 bij .

RK-Aspen
Mixing Rules a = ∑ ∑ x i x j a ij van der Waals (RK-Aspen) b = ∑ ∑ x i x j b ij a ij = a ii a jj Where k aij = k 0 aij and k bij = k 0 bij are the binary interaction parameters, considered as temperature-independent. The RK-Aspen binary interaction parameters obtained using the Aspen Properties computational package from Aspen Plus. The program uses the Britt-Lueck algorithm, with the Deming parameters initialization method, to perform a maximum like-hood estimation of the following objective function, described by Equation (1).
where, x e i and y e i are the experimental compositions of i-th compound in the coexisting liquid and gaseous phases, respectively, and σ the standard deviations, applied to the state conditions (T, P) and x c i and y c i compositions of i-th compound predicted with EOS. The average absolute deviation (AAD) computed to evaluate the agreement between measured experimental data and the calculated/predicted results for all the binary systems investigated.
High-Pressure Equilibrium Data for the Binary Systems OLP Compoundi -CO 2 Table 3 shows the experimental high-pressure gaseous-liquid equilibrium data for the binary systems OLP compoundi -CO 2 used to compute the binary interaction parameters. For the binary pairs OLP compoundsi -CO 2 not available in the literature, k aij = k 0 aij and k bij = k 0 bij were set equal to zero in the matrix of binary interaction parameters. Because high-pressure phase equilibrium data for the complex system OLP-CO 2 is not available in the literature, the proposed methodology was tested to simulate the thermodynamic modeling by de-acidification of olive oil, represented by a quaternary model mixture oleic acid-squalene-triolein-CO 2 . Table 4 summarizes the experimental high-pressure gaseous-liquid equilibrium data for the binary systems olive oil key (oleic acid, squalene, triolein) compoundsi -CO 2 used to compute the binary interaction parameters. Table 4. Experimental gaseous-liquid equilibrium data for the binary systems oleic acid-CO 2 , squalene-CO 2 , and triolein-CO 2 used to compute the binary interaction parameters of RK-Aspen EOS [81][82][83][84][85].

Schematic Diagram of Phase Equilibria Data Correlation
The Aspen Properties ® package program used for the regression of experimental phase equilibrium data described in Tables 3 and 4. Figure 1 illustrates the simplified schematic diagram of the main correlation steps of phase equilibria data for the binary system OLP compoundsi -CO 2 , and the binary system olive oil key (oleic acid, squalene, triolein) compoundsi -CO 2 , performed by using the Aspen Properties ® .
The program provides several options showing how to perform regression, including several different types of objective functions. The default objective function is the Maximum likelihood objective function, given by Equation (1). To obtain the binary interaction parameters in Aspen Properties ® , the following procedure was applied, regardless the type of system and model to which data will be correlated.
Specification of the method (where the model applied for the regression of the experimental data is chosen); 3.
Introduction or choice of experimental data (T-xy, P-xy, TP-x, T-x, TP-xy, T-xx, P-xx, TP-xx, TP-xxy, etc.) depending on the type and information of the system; at this stage it is possible to either search for the compounds from the Aspen Properties ® data base or enter experimental data manually; 1. Choice of components; 2. Specification of the method (where the model applied for the regression of the experimental data is chosen); 3. Introduction or choice of experimental data (T-xy, P-xy, TP-x, T-x, TP-xy, T-xx, P-xx, TP-xx, TP-xxy, etc.) depending on the type and information of the system; at this stage it is possible to either search for the compounds from the Aspen Properties ® data base or enter experimental data manually; 4. Regression of data: In this step the type of parameter, the parameters (according to the coding of the program) to be adjusted/correlated, the initial estimate and the limits for the regression chosen.

Figure 1.
Simplified schematic diagram of the main correlation steps of phase equilibrium data for the binary system organic liquid products compounds-i-CO2, and the binary system olive oil key (oleic acid, squalene, triolein) compoundsi-CO2, performed by using the Aspen Properties ® .

Normal Boiling Temperature (Tb) of OLP Compounds
The most indicated methods, consistent with the selection criteria described in Section 2.1.2, adopted to estimate the normal boiling temperature (Tb) of hydrocarbons classes present in OLP, illustrated in Table 5. For the n-alkanes and alkenes, the method by Marrero-Gani [66], provided the best correlation/regression to experimental data, while the method by Constantinou-Gani [64], shows the best correlation/regression for unsubstituted and substituted cyclics, and that by Joback and Reid [63], was the best for aromatics. Kontogeorgis and Tassios [86], reported that Joback and Reid [63] method was not suitable to estimate critical properties of alkanes of high molecular weight and selected Constantinou-Gani [64], as the best method. Table 5. Selected methods to predict the normal boiling temperature (Tb) of hydrocarbons classes (n-alkanes, alkenes, unsubstituted cyclics, substituted cyclics, and aromatics), of all the compounds present in OLP, obtained by thermal catalytic cracking of palm oil at 450 °C , 1.0 atmosphere, with 10% (wt.) Na2CO3 [17].  Simplified schematic diagram of the main correlation steps of phase equilibrium data for the binary system organic liquid products compoundsi -CO 2 , and the binary system olive oil key (oleic acid, squalene, triolein) compoundsi -CO 2 , performed by using the Aspen Properties ® .

Prediction of Thermo-Physical Properties and the Acentric Factor of OLP Compounds
The most indicated methods, consistent with the selection criteria described in Section 2.1.2, adopted to estimate the normal boiling temperature (T b ) of hydrocarbons classes present in OLP, illustrated in Table 5. For the n-alkanes and alkenes, the method by Marrero-Gani [66], provided the best correlation/regression to experimental data, while the method by Constantinou-Gani [64], shows the best correlation/regression for unsubstituted and substituted cyclics, and that by Joback and Reid [63], was the best for aromatics. Kontogeorgis and Tassios [86], reported that Joback and Reid [63] method was not suitable to estimate critical properties of alkanes of high molecular weight and selected Constantinou-Gani [64], as the best method. Table 5. Selected methods to predict the normal boiling temperature (T b ) of hydrocarbons classes (n-alkanes, alkenes, unsubstituted cyclics, substituted cyclics, and aromatics), of all the compounds present in OLP, obtained by thermal catalytic cracking of palm oil at 450 • C, 1.0 atmosphere, with 10% (wt.) Na 2 CO 3 [17].  Table 6 shows the selected methods to predict the critical temperature (T c ) of hydrocarbons classes (n-alkanes, alkenes, unsubstituted cyclics, substituted cyclics, and aromatics), present in OLP. The method by Marrero-Gani [66], is the most suitable for n-alkanes, alkenes, unsubstituted and unsubstituted cyclic hydrocarbons, as it showed the best correlation/regression to experimental data, while that by Constantinou-Gani [64], provided the best correlation/regression to experimental data for aromatics. Owczarek and Blazej [87] applied the methods by Joback and Reid [63] and Constantinou-Gani [64], to predict the critical temperature (T c ) of substituted and unsubstituted cyclic hydrocarbons, reporting deviations of 0.93% and 0.82%, respectively, when using the method by Joback and Reid [63], as well as deviations of 1.77% and 2.00%, respectively, with the method by Constantinou-Gani [64]. The results showed that computed deviations of substituted and unsubstituted cyclic hydrocarbons were 1.41% and 1.69%, respectively, when using the method by Joback and Reid [63], as well as 0.79% and 3.08%, with the method by Constantinou-Gani [64], higher than that described in Table 6, when using the method by Marrero-Gani [66]. The method by Constantinou-Gani [64] is the most suitable for aromatics. As by the estimation of normal boiling temperature (T b ), prediction of critical temperature (T c ) of aromatic hydrocarbons included also n-alkyl-benzenes, alkyl-benzenes, poly-phenyls, as well as condensed polycyclic aromatics. Table 6. Selected methods to predict the critical temperature (T c ) of hydrocarbons classes (n-alkanes, alkenes, unsubstituted cyclics, substituted cyclics, and aromatics), of all the compounds present in OLP, obtained by thermal catalytic cracking of palm oil at 450 • C, 1.0 atmosphere, with 10% (wt.) Na 2 CO 3 [17]. The most indicated methods to estimate the critical pressure (P c ) of hydrocarbons functions present in OLP are illustrated in Table 7. For n-alkanes, the method by Marrero-Padillo [65], provided the best results, while that by Marrero-Gani [66], selected for alkenes. For unsubstituted cyclic, the method by Joback and Reid [63], was selected. For substituted cyclic, the method by Constantinou-Gani [64], was selected. By predicting the critical pressure (P c ) of aromatics, only the alkyl-benzenes were considered, being the method by Marrero-Gani [66], the best one. This is due to the high average relative deviation obtained for polycyclic condensates and poly-phenyls using all the methods described in Table 1, with ADR higher than 15%, reaching for some cases (m-terphenyl-Cas 92-06-8) 45%. In this sense, none of the methods evaluated showed good precision to estimate the critical pressure (P c ) of polycyclic condensates and poly-phenyls aromatic. Table 7. Selected methods to predict the critical pressure (P c ) of hydrocarbons classes (n-alkanes, alkenes, unsubstituted cyclics, substituted cyclics, and aromatics), of all the compounds present in OLP, obtained by thermal catalytic cracking of palm oil at 450 • C, 1.0 atmosphere, with 10% (wt.) Na 2 CO 3 [17].  Table 8 shows the selected methods to predict the critical volume (V c ) of hydrocarbons classes (n-alkanes, alkenes, unsubstituted cyclics, substituted cyclics, and aromatics), present in OLP. The method by Marrero-Gani [66], is the most suitable for n-alkanes and substituted cyclic hydrocarbons, as it showed the best correlation/regression to experimental data, while that Joback and Reid [63], selected for unsubstituted cyclic hydrocarbons. The method by Marrero-Pardillo [65], selected for alkenes, while that by Constantinou-Gani [64], provided the best correlation/regression to experimental data for aromatics. Table 8. Selected methods to predict the critical volume (V c ) of hydrocarbons classes (n-alkanes, alkenes, unsubstituted cyclics, substituted cyclics, and aromatics), of all the compounds present in OLP, obtained by thermal catalytic cracking of palm oil at 450 • C, 1.0 atmosphere, with 10% (wt.) Na 2 CO 3 [17]. The selected methods to estimate the acentric factor (ω) of hydrocarbons classes present in OLP illustrated in Table 9. For n-alkanes and alkenes, the method by Han-Peng [68], provided the best results, while the indirect method by Vetere [70], was selected for unsubstituted cyclic, unsubstituted cyclic and aromatics. Table 9. Selected methods to predict the acentric factor (ω) of hydrocarbons classes (n-alkanes, alkenes, unsubstituted cyclics, substituted cyclics, and aromatics), of all the compounds present in OLP, obtained by thermal catalytic cracking of palm oil at 450 • C, 1.0 atmosphere, with 10% (wt.) Na 2 CO 3 [17].  ), critical properties (T c , P c , V c ), and acentric factor (ω) of OLP compounds, recommended for the main chemical compounds present in the OLP obtained by thermal-catalytic cracking of palm oil, as described by Mâncio et al. [17]. The prediction of the normal boiling temperature and critical properties of carboxylic acids and esters of carboxylic acids followed the recommendations of Araújo and Meireles [69], and for estimation of acentric factor (ω), the indirect method proposed by Ceriani et al. [88]. This method makes use of group contributions with high similarities to the molecular structure of carboxylic acids and esters of carboxylic acids. In addition, the method proposed by Ceriani et al. [88], also applied for estimation of critical properties of ketones, while the method of Nikitin et al. [89], applied for alcohols. The estimated values of thermo-physical (T b ), critical properties (T c , P c , V c ), and acentric factor (ω) of olive oil key (oleic acid, squalene, triolein) compounds summarized in Table 10. The values for the thermo-physical (T b ), critical properties (T c , P c , V c ), and acentric factor (ω) of olive oil model mixture compounds (oleic acid, squalene, triolein) are those predicted by the authors described in Table 4. Table 10. Estimated/Predicted values of thermo-physical (T b ), critical properties (T c , P c , V c ), and acentric factor (ω) of olive oil key (oleic acid, squalene, triolein) compounds [81][82][83][84][85].  Table 11 presents the RK-Aspen EOS temperature-independent binary interaction parameters adjusted with experimental phase equilibrium data for the binary systems hydrocarbonsi -CO 2 and carboxylic acidsi -CO 2 , as well as the absolute mean deviation (AAD) between experimental and predicted compositions for both coexisting liquid and gaseous phases. The regressions show that RK-Aspen EOS was able to describe the highpressure gaseous-liquid phase equilibrium data for all the systems investigated. Table 11. RK-Aspen EOS temperature-independent binary interaction parameters adjusted with experimental phase equilibrium data for the binary systems hydrocarbonsi -CO 2 and carboxylic acidsi -CO 2 .  Table 12 summarizes the RK-Aspen EOS temperature independent binary interaction parameters adjusted to experimental high-pressure phase equilibria of olive oil key (oleic acid, squalene, triolein) compoundsi -CO 2 , used as test system to simulate the thermodynamic modeling by de-acidification of olive oil, represented by a quaternary model mixture oleic acid-squalene-triolein-CO 2 .

Equation of State (EOS) Modeling for the Binary Systems Olive Oil Key (Oleic Acid, Squalene, Triolein) Compoundsi -CO 2
The thermodynamic modeling for the binary systems olive oil key (oleic acid, squalene, triolein) compoundsi -CO 2 performed with RK-Aspen EOS with the van der Waals mixing rules and RK-Aspen combining rules for two temperature-independent binary interaction parameters. The EOS modeling described in form P-x CO2 ,y CO2 diagram showing a comparison between predicted and experimental high-pressure equilibrium data for the binary systems oleic acid-CO 2 (Bharath et al., 1992), squalene-CO 2 (Brunner et al., 2009), and triolein-CO 2 (Weber et al., 1999), as shown in Figures 2-4, respectively. The regressions show that RK-Aspen EOS was able to describe the high pressure equilibrium data for the binary systems olive oil key (oleic acid, squalene, triolein) compoundsi -CO 2 . Table 12. RK-Aspen EOS k aij = k 0 aij and k bj = k 0 bij adjusted with experimental phase equilibrium data for the binary systems of olive oil key compoundsi -CO 2 .     The thermodynamic modeling for the binary systems olive oil key (oleic acid, squalene, triolein) compounds-i-CO2 performed with RK-Aspen EOS with the van der Waals mixing rules and RK-Aspen combining rules for two temperature-independent binary interaction parameters. The EOS modeling described in form P-xCO2,yCO2 diagram showing a comparison between predicted and experimental high-pressure equilibrium data for the binary systems oleic acid-CO2 (Bharath et al., 1992), squalene-CO2 (Brunner et al., 2009), and triolein-CO2 (Weber et al., 1999), as shown in Figures 2-4, respectively. The regressions show that RK-Aspen EOS was able to describe the high pressure equilibrium data for the binary systems olive oil key (oleic acid, squalene, triolein) compounds-i-CO2.
x CO2 [Bharath et. al, 1992] y CO2 [Bharath et. al, 1992] x CO2 [        Simulation Modeling for the Model System Olive Oil Key (Oleic Acid-Squalene-triolen-CO2 Because high-pressure phase equilibrium data for the complex system OLP-CO2 is not available in the literature, the proposed methodology tested to simulate the thermodynamic modeling by de-acidification of olive oil, represented by a quaternary model mixture oleic acid-squalene-triolein-CO2. Table 13 presents the RK-Aspen EOS temperature independent binary interaction parameters adjusted to the experimental high-pressure equilibrium data for the multicomponent olive oil-CO2, described in Table 14 [90], and represented in this work as a multicomponent model mixture oleic acid-squalene-triolein-CO2. In addition, Table 13 presents the root-mean-square deviation (RMSD) between the multicomponent experimental high-pressure equilibrium data and the computed results for the coexisting gaseous-liquid phases. Table 13. RK-Aspen EOS temperature-independent binary interaction parameters adjusted with experimental highpressure phase equilibrium data for the model systems oleic acid(1)-squalene(3)-triolein(2)-CO2(4).  Because high-pressure phase equilibrium data for the complex system OLP-CO 2 is not available in the literature, the proposed methodology tested to simulate the thermodynamic modeling by de-acidification of olive oil, represented by a quaternary model mixture oleic acid-squalene-triolein-CO 2 . Table 13 presents the RK-Aspen EOS temperature independent binary interaction parameters adjusted to the experimental high-pressure equilibrium data for the multicomponent olive oil-CO 2 , described in Table 14 [90], and represented in this work as a multicomponent model mixture oleic acid-squalene-triolein-CO 2 . In addition, Table 13 presents the rootmean-square deviation (RMSD) between the multicomponent experimental high-pressure equilibrium data and the computed results for the coexisting gaseous-liquid phases.

1-2 1-3 1-4 2-3 2-4 3-4 RMSDx
The State conditions (T, P) by the experimental high-pressure equilibrium data for the multicomponent olive oil-CO 2 , described in Table 14. Table 15 presents the average absolute deviation (AAD) between the predicted and experimental high-pressure phase equilibrium data for the model systems oleic acid(1)squalene(3)-triolein(2)-CO 2 (4). Table 13. RK-Aspen EOS temperature-independent binary interaction parameters adjusted with experimental high-pressure phase equilibrium data for the model systems oleic acid(1)-squalene(3)-triolein(2)-CO 2 (4).   Table 16 presents the RK-Aspen EOS temperature independent binary interaction parameters adjusted in this work to experimental high-pressure equilibrium for the system olive oil-CO 2 at 313 K with 2.9 and 7.6 [wt.%] FFA. The RK-Aspen EOS was able to describe the high-pressure phase equilibria of multicomponent system olive oil-CO 2 [90], showing RMSD between 3E-07 to 0.0138 for the liquid phase and between 0.0009 to 2E-04 for the gaseous phase, by considering the system was represented by the multicomponent model mixture triolein-squalene-oleic acid-CO 2 . Table 16. Estimated RK-Aspen-EOS binary interaction parameters for multicomponent system FFA (oleic acid)(l)-Triglyceride (triolein)(2)-Squalene(3)-CO 2 (4). The distribution coefficients-Ki of key compounds by the experimental high-pressure phase equilibria for the multicomponent system olive oil-CO 2 , described on solvent free basis, as shown in Table 17. Table 17 presents the experimental distribution coefficients of FFA (l), triglyceride (2), and squalene (3) and the estimated distribution coefficients computed using the binary interaction parameter presented in Table 13. The results show the precision of RK-Aspen EOS to describe the multicomponent system for the state conditions (T, P), and free fatty acid (FFA) content in feed. The distribution coefficients described on a solvent free basis provide information about the phase in which the compounds are preferably enriched in the extract (Ki > 1) or in the bottoms (Ki < 1). Figures 5-7 show the distribution coefficients for the key compounds of olive oil computed on CO 2 free basis. The results show that FFA and squalene are preferably enriched in the extract (Ki > 1), while the triolein is enriched in the bottoms (Ki < 1) by de-acidification of olive oil using SC-CO 2 in countercurrent packed columns.  The proposed methodology proved to simulate with high accuracy the thermodynamic modeling by de-acidification of olive oil, represented by a quaternary model mixture oleic acid-squalene-triolein-CO2, and hence can be applied to simulate the fractionation of OLP in multistage countercurrent absorber/stripping columns using SC-CO2 as solvent, with Aspen-HYSYS.
The RK-Aspen EOS was able to describe the high-pressure phase equilibria of multicomponent system olive oil-CO2 [90], showing RMSD between 3 × 10 −7 to 0.0138 for the liquid phase and between 0.0009 to 2 × 10 −4 for the gaseous phase, by considering the system was represented by the multicomponent model mixture triolein-squalene-oleic acid-CO2.
The proposed methodology proved to simulate with high accuracy the thermodynamic modeling by de-acidification of olive oil, represented by a quaternary model mixture oleic acid-squalene-triolein-CO2, and hence can be applied to simulate the fractionation of OLP in multistage countercurrent absorber/stripping columns using SC-CO2 as solvent, with Aspen-HYSYS.
Supplementary Materials: The following are available online. Table S1. Chemical composition of OLP. Table S2. Estimated/Predicted values of thermo-physical (Tb), critical properties (Tc, Pc, Vc), and acentric factor (ω) of chemical compounds present in OLP.

Conclusions
The EOS modeling described in form P-x CO2 ,y CO2 diagram for the binary systems oleic acid-CO 2 (Bharath et al., 1992), squalene-CO 2 (Brunner et al., 2009), and triolein-CO 2 (Weber et al., 1999), shows that RK-Aspen EOS was able to describe the high pressure equilibrium data for the binary systems olive oil key (oleic acid, squalene, triolein) compoundsi -CO 2 .
The RK-Aspen EOS was able to describe the high-pressure phase equilibria of multicomponent system olive oil-CO 2 [90], showing RMSD between 3 × 10 −7 to 0.0138 for the liquid phase and between 0.0009 to 2 × 10 −4 for the gaseous phase, by considering the system was represented by the multicomponent model mixture triolein-squalene-oleic acid-CO 2 .
The proposed methodology proved to simulate with high accuracy the thermodynamic modeling by de-acidification of olive oil, represented by a quaternary model mixture oleic acid-squalene-triolein-CO 2 , and hence can be applied to simulate the fractionation of OLP in multistage countercurrent absorber/stripping columns using SC-CO 2 as solvent, with Aspen-HYSYS.
Supplementary Materials: The following are available online. Table S1: Chemical composition of OLP. Table S2: Estimated/Predicted values of thermo-physical (T b ), critical properties (T c , P c , V c ), and acentric factor (ω) of chemical compounds present in OLP.