• 2018-07
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  • br Thermodynamic modeling br Selection


    Thermodynamic modeling
    Selection of data The solutes were selected based on the set of data needed to evaluate the CPA-EoS for prediction of their solubility in CO2 + cosolvent, as shown in Fig. 1. Critical temperatures, melting temperatures and enthalpies of fusion of the solutes are required, as shown in Equations (1), (3)). Experimental data for vapor pressure and liquid density at different temperatures are used to fit CPA pure component parameters (, , , and ). Phase equilibrium data of the binary systems of the components present in the ternary mixtures are relevant to obtain the binary interaction parameters (). Finally, ternary system data were only used for the comparison between the experimental and predicted data.
    Results Several works have reported solubility data for solutes in mixtures of CO2 plus a cosolvent. However, mainly due to the lack of experimental data for vapor pressure and for the binary equilibrium cosolvent – solute, only 12 solutes, shown in Fig. 2 were selected to be here studied. Different classes of compounds were investigated, including aromatic and aliphatic molecules, alcohols and Atovaquone weight substances. Thus, the solubility of 12 solid solutes in scCO2 in presence of different organic cosolvents was investigated, at pressures between 8 and 40 MPa, temperatures ranging from 308 K to 353 K and Atovaquone weight concentration of cosolvent varying from 0.73 to 10 mol% (Table 1). Polar and non-polar cosolvents were also analyzed, totalizing 19 systems. Among them one is a quaternary system, containing trans-ferulic acid, CO2, ethanol and water. In a first step for the modeling with CPA, pure components were parameterized by fitting vapor pressure and liquid density data. Liquid density data were not easily accessible on the scientific literature and databases for the trans-ferulic acid and paracetamol. On other hand, the values available for cholesterol and for salicylic and benzoic acids were not used because the model was unable to fit these data. The bibliographic references for vapor pressure and liquid phase density data were shown in Table 2. Table A1 of the Supplementary data reports the temperature, pressure and density ranges and the number of data used for each solute. Therefore, pure component parameters for these solutes were estimated only from vapor pressure data. For the parameterization of pure compounds it is important to analyze the nature and number of associating groups, each of these being defined by an association scheme, as proposed by Huang and Radosz [30]. In this work, the two-site (2B) scheme was used for each hydroxyl or carboxyl group contained in the molecule. The approach, called group-contribution scheme, should be applied for the association term, as reported in studies on polifunctional phenolics solubility [31]. Thus and parameters were assumed as having unique values for each solute molecule, i.e. they were not fitted for each type of associative group of the molecule but for each molecule. The properties and approaches used for each pure component are presented in Table 2. In addition, the solvents CO2, hexane and acetone were treated as non-associating components. The section B of Supplementary data exemplifies how the considerations about of number and type of association sites can change the results for prediction of ternary systems. The binary interaction parameters were then estimated for all the binary systems involved in the ternary or quaternary systems. References for experimental data, the values of fitted and the average absolute relative deviation (AARD) are shown in Table 3. Mainly for the cosolvent – solute systems a good description of the experimental data was achieved. Finally, the solubility for each solute in the ternary or quaternary system using CPA-EoS was predicted, and the average logarithmic deviation (ALD) was used to evaluate the accuracy of the prediction, as shown below:where N is the number of experimental points and is the mole fraction solubility of the solute in mixtures of scCO2 and cosolvent.