The Journal of Supercritical Fluids

, solubility in supercritical CO 2 was provided for simulation purposes of the extraction process. PCB mixture has predominance of congeners: tetra, penta, hexa, heptachloro biphenyl, tri and tetrachlorobenzene. The calculation procedure was initially applied for a series of aromatic compounds (naphthalene, biphenyl, anthracene and phenanthrene) in order to validate the approach. Experimental solubility data collection has been elaborated from the literature, providing a systematic series of the studied aromatic compounds with CO 2 . The binary parameters for the classical van der Waals quadratic mixing rule (vdW2) were systematically estimated, together with a new set of Clausius–Clapeyron solute vapor pressure in order to describe the temperature dependence and achieve experimental solubility uncertainties. Finally, the estimated parameters were used to simulate solubility values of Askarel oil as function of the operational conditions of extraction by a simultaneous solution of the equilibrium equations for each compound. The thermodynamic modeling demonstrated to be feasible for process analysis and design.


Introduction
Polychlorinated biphenyls (PCB) are chlorinated organic substances which are highly toxic and also considered persistent organic pollutants (PoP). The high thermal and chemical stability of PCB are responsible for their hard degradation, and when these substances are liberated in the environment, their accumulation in ecosystems leads to their incorporation in the food chain, exhibiting biomagnification [1].
PCB structure and the amounts of chlorine atoms are important in determining levels of toxicity, in that the more harmful PCB are those with highest number of chlorine atoms in the molecule. Although the production of these substances had been banned, its presence in the environment is still found. In the 1970s, PCB were produced for specific purpose such as thermal fluid in heat exchangers, lubricant in some equipment, isolating fluid in electrical equipment, resins, pesticides and others. Due to the high risk of this group of chemical substances the manufacture and the commercialization of PCB was forbidden [2][3][4].
The most used process for the treatment of a material containing organic contamination, like PCB, consists on the incineration in plasma ovens with double stage [5]. However, beside the high energy demand, it should be considered the transport of the contaminated material until the place of the incineration and the fact that special conditions are required, increasing the global cost of the process. Techniques using advanced oxidation processes [6,7] have also been investigated and are important for the mineralization of the residue of a process like supercritical fluid extraction (SFE). In this context, the extraction process represents an important way to decrease significantly the mass and also the volume of the material to be transferred for treatment. The SFE is considered to be a green technology due to shorter extraction times and less solvent exposure and disposal [8]. Removal of Askarel oil impregnated in solid materials and soil has been performed by SFE efficiently [9][10][11]. An experimental series of SFE for PCB species with carbon dioxide as solvent has also been determined in the laboratory and demonstrated to be feasible [12], as a pretreatment to the mineralization, either by advanced oxidation or incineration as explained before. Furthermore, an integrated process to treat contaminated material with Askarel could be a supercritical extractor (CO 2 ) followed by catalytic dechlorination of polychlorinated biphenyls under CO 2 and H 2 atmosphere. This route would convert the contaminated species (PCB) to biphenyl [13,14].
In this work, a thermodynamic modeling using cubic equation of state (EoS) and classical mixing rule is presented to describe the solubility of the Askarel in supercritical carbon dioxide as function of the operational conditions of extraction, i.e., temperature, pressure and composition. The correlation part was based on a series of experimental data selected and collected from the literature, not only for PCB species but also aromatic compounds [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. The simulation was also based on experimental analysis of the Askarel oil and a corresponding characterization of the main species to describe the desired solubility curves.

Methods of calculation
Askarel solubility is proposed to be described by the sum of the main species characterized, calculating the concentration of these individual species in the multicomponent mixture that is the application of phase equilibrium thermodynamics from binary mixing rule parameters [35,36].
The Scilab open source tool has been applied to perform the calculations with the aid of numerical methods included in the package, such as Levenberg-Marquadt algorithm for the parameters estimation, non-linear equations solver and diagram plots in the execution of the codes [37].
Askarel oil is a mixture of PCB and chlorobenzenes containing various levels of chlorination. The analysis of Askarel oil demonstrated predominance of the congeners tetra, penta, hexa and heptachlorobiphenyl [14]. Further, Askarel oil presented 25% in mass of tetrachlorobenzene, in which was described by 1,2dichlorobenzene and hexachlorobenzene. This characterization was performed due to the availability of phase equilibrium data for 1,2-dichlorobenzene and hexachlorobenzene with carbon dioxide, and no data were found for tetrachlorobenzene. Solubility data for the congeners tetra, penta, hexa and heptachlorobiphenyl in supercritical carbon dioxide were found in literatures [15,16]. The series reported by Anitescu and Tavlarides [16] has been used as reference in the thermodynamic model parameter estimation.
To determine normal boiling point, critical temperature and critical pressure of the main compounds found in the Askarel, the Joback group contribution method has been applied [38]. The acentric factors (ω) were estimated by the Ambrose-Walton method [39].
A comprehensive series of experimental solubility data of aromatic, chlorinated aromatic and PCB congeners in supercritical CO 2 have been collected from the literature in wide ranges of temperature and pressure. Therefore, the corresponding binary interaction parameters were estimated for the quadratic mixing rules for both attractive and repulsive terms, k ij and l ij , respectively, using Peng-Robinson EoS [40,41]. In order to describe the temperature dependence of the solubility data Clausius-Clapeyron coefficients were also fitted.
The solubility of a solute species in a supercritical fluid (ScF) may be calculated as described by Eq. (3) at moderate and high pressures.
Eq. (3) is the solubility equation and it may be classified as three contributions, i.e., ideal solubility, defined as the ratio of the vapor pressure upon the total pressure, fugacity coefficient that is evaluated by the EoS and taken into account the nonidealities, and finally Poynting factor which express the fugacity correction with respect to the pressure. The last two terms together is also called enhancement factor (E) that express the gain of solubility by operating in supercritical conditions, usually at high pressures. It is noteworthy that Eq. (3) may be solved for the solubility (y i ) by an iterative procedure since the solute mole fraction is also a variable in the fugacity coefficient function.
It is also worthwhile that it was required for the evaluation of the vapor pressure and molar volume of the solute as function of the temperature, which is present in the solubility equation in the ideal solubility term and enhancement factor, respectively. For that Clausius-Clapeyron correlation of the available experimental, or estimated, vapor pressure data were applied for each compound. Vapor pressure data for the studied species were found in literatures [43][44][45]. It is noteworthy that in the correlation of the solubility data for a wide range of temperature, Clausius-Clapeyron coefficients have also been fitted together with the mixing rule interaction parameters. It is demonstrated that this procedure was able to describe the complex temperature dependence of the solubility. Furthermore, the correlations have achieved experimental uncertainties and the set of parameters are able to provide reliable predictions.
Racket equation was used to describe the molar volume of these species [46]. A correction from the liquid phase to the solid phase was applied especially for considering the experimental values of molar volume of a series of aromatic compounds, i.e., naphthalene, biphenyl, phenanthrene and monochlorobenzene. The obtained correction factor was 0.87 ± 0.04 to evaluate the molar volume of the solid phase from the values of the liquid phase by Racket EoS. Table 1 Correlation results of the solubility isotherms of naphthalene in supercritical CO2 as function of pressure, using Peng-Robinson (PR) EoS: estimated parameters and deviations. The experimental values of molar volume of both liquid and solid phases were retrieved from the AIChE DIPPR databank [45].
v sat Previous work has considered the mixture as a pseudo-binary system consisting of Askarel and carbon dioxide [47]. In other words Askarel oil was lumped as a mixture of tetrachlorobenzene, hexachlorobiphenyl and heptachlorobiphenyl. The Askarel properties were obtained as a linear mole fraction mixing rule. In this work, the main components of Askarel oil have been considered (tetra, penta, hexa, heptachlorobiphenyl, 1,2-dichlorobenzene and hexachlorobenzene) and the solubility equation for each solute was simultaneously solved, finding the corresponding equilibrium concentrations (y i ). Then Askarel oil solubility is finally determined as the summation of these main solute six species concentrations considered.
Naphthalene has been chosen as the reference for the thermodynamic model definition with a total of 190 experimental data points. Initially, each available solubility isotherm as function of the pressure was correlated with interaction parameters for the attractive and repulsive terms. Table 1 presents these results and it may be observed that all the deviations approached to the expected experimental uncertainties. The evaluation of the data modeling has been performed according to the absolute average relative deviation (AARD), Eq. (8). A comparison of the root mean square deviation of these correlations have also been calculated and demonstrated that the results usually approach the experimental uncertainties at ca. 10%.
Furthermore, the objective function applied was the relative form with respect to experimental and calculated solubilities. This was due to the low magnitude of the values of solubility and its variation along the pressure of the datasets. The values of k ij are in good agreement with the literature [41]. It may also be observed a temperature dependence of the attractive interaction parameters (k ij ), nevertheless when all isotherms for naphthalene are correlated together the description of the solubility data is not satisfactory. This was also the situation for the other aromatic compounds studied even at only one temperature and in a wider range of temperature. It is also noteworthy that there is a scattering between datasets. However, as explained in the previous section, introducing a reinforcement of the temperature dependence with the Clausius-Clapeyron correlation, Eq. (6), the solubility description is significantly improved, as it may be observed in Table 2 and in Fig. 1 for the naphthalene system. In order to describe the solubility behavior of the Askarel oil in supercritical carbon dioxide, a selection of the predominant PCB compounds was based on the analysis, i.e., tetra, penta, hexa and heptachlorobiphenyl [14]. Table 3 presents the required thermodynamic properties of the Askarel compounds used in the calculation. Joback and Ambrose group contribution methods were applied to determine the properties of the representative species of Askarel [38,39]. As it may be observed for aromatic chlorinated compounds, the melting point increases as the number of chlorine radicals increases. For PCB compounds this is also true as it may be detected in Table 3. As explained in the previous section, there Values of T b of congeners of PCB were found from the literature [42] and the other properties were estimated by group contribution methods [38,39].
is 25% in mass of tetrachlorobenzene in Askarel oil. In this work, tetrachlorobenzene was represented by 1,2-dichlorobenzene and hexachlorobenzene, due to availability of phase equilibrium data with carbon dioxide [31][32][33][34] for the determination of the model parameters.
Using the proposed methodology, solubility data of the series of PCB and hexachlorobenzene were correlated with PR EoS, estimating the corresponding binary interaction parameters and Clausius-Clapeyron constants, as reported in Table 4. Similarly to the aromatic solutes, the solubility behavior could be adequately described, estimating mixing rule parameters (k ij and l ij ) and temperature dependent parameters (A and B) from the vapor pressure expression. Fig. 2 presents the calculated curves in comparison with experimental solubility data for hexachlorobiphenyl in CO 2 .
For 1,2-dicholorobenzene the situation was different due to its state of aggregation at the operational temperature range, i.e., liquid state. Therefore, the determination of interaction mixing rule parameters (k ij and l ij ) was performed by vapor-liquid equilibrium calculation, using experimental values published by Walther and Maurer [34]. The estimated values for k ij and l ij were 0.084 and  0.037, respectively. Vapor pressure constants, Eq. (6), were also estimated from experimental data [43,45] for the solubility calculation (A = 9.86 and B = 2203.72). Solubility calculation method for 1,2-dicholorobenzene by Eq. (3) with these new parameters was also applied for verification purpose and the same type of solute concentration profile was obtained. A simulation test for a two solute system could be performed with the experimental study provided by Liu and Nagahama [48]. The solute concentrations are determined by the resolution of the system of two equations at specific temperature and pressure. Fig. 3 illustrates that this procedure can reproduce satisfactorily the behavior of the phenanthrene solubility in CO 2 and in the presence of naphthalene with the previously estimated binary interaction parameters and solute vapor pressure constants.
Using this mathematical approach, the solubility curves of Askarel oil as function of operational conditions of extraction can be evaluated. Fig. 4 presents the individual species equilibrium concentrations as function of pressure at 313 K. Fig. 5 describes the Askarel solubility profiles at 313 and 323 K. It should be noted that the value of Askarel solubility is actually the summation of the solute mole fractions considered, i.e., tetra, penta, hexa, heptachlorobiphenyl, 1,2-dichlorobenzene and hexachlorobenzene. The order of magnitude and the behavior of the solubility Fig. 4. Solubility profiles of tetra, penta, hexa, heptachlorobiphenyl, 1,2dichlorobenzene and hexachlorobenzene in CO2 at 313 K as function of pressure, simulated by PR EoS with fitted parameters. are in agreement with literature [49] for the commercial Askarel oil Araclor 1254.

Conclusions
It was observed various aspects of difficulty in this calculation approach that have been faced and overcome. Solutes present very low values of solubility and vapor pressure. By the other hand, the values of fugacity coefficients are high and have to change upon independent variables, i.e., concentration, temperature and pressure, especially at the vicinity of the critical point. An analysis and selection of the experimental data collected were fundamentally required. Therefore, this work required a rigorous procedure for the application of experimental information and modeling due to the sensitivity of the calculation. Sublimation pressures of the solutes were evaluated by Clausius-Clapeyron expression and similarly to vapor-liquid equilibrium calculation played an important role in the proposed solubility approach to provide the aid for the temperature dependence.
Main literature source of experimental data [16] shows the application of empirical correlation of the solubility data as function of solvent density [40]. They have showed deviation results in the order of 6%, which is comparable to this work. However, the advantage of the proposed approach with EoS is the applicability in different operational conditions, i.e., pressure, temperature, composition and multicomponent mixtures, allowing also the insertion of other compounds, once it is based on the principle of corresponding states. The fugacity coefficient of a species in a mixture is a partial molar property, or function.
The computational tool developed can be applied for modeling and analysis of solubility data in supercritical fluids with flexibility. The solubility model resulted simple and may also be applied to a desorption approach to describe the supercritical extraction process for operational and design purposes.