The binary interaction parameters were then estimated

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. In general, accurate results for the prediction of the solubility in scCO2 + cosolvents using the CPA-EoS were verified. ALD values for each solute (Table 1) varied from 0.04 to 1.5. Few solutes, such as lauric acid, myristic acid, hydroquinone and salicylic acid, presented the highest ALD values. According to Ting et al. [23], higher deviations for carboxylic acids with short chain can be associated to their lower melting temperatures. The melting temperatures for lauric (dodecanoic acid) and myristic (tetradecanoic acid) acids are 316.6 K and 326.5 K, respectively. These values are very close to the temperatures of solubility measurements, indicating that CPA model can not describe these systems at conditions close to the phase transition region. In this way, excluding the myristic rad51 solubility data at 318 K, the ALD value decreased from 1.32 to 0.75 (at T = 308 K), i.e., when the difference between the melting temperature and the solubility temperature measurement, the CPA prediction significantly improves. The ALD value obtained by evaluating all the systems simultaneously was 0.47, and excluding lauric and myristic acids the ALD is decreased to 0.32. Both values are significantly lower than those reported by Ting et al. [23] (ALD = 0.64), when PR + COSMOSAC equation was used for prediction of the solubility of 23 solutes in scCO2 and cosolvents. Excluding trans-ferulic acid, all the solutes here evaluated were also investigated by Ting et al. [23] applying the SAFT model to predict solubility of naphthalene, phenanthrene, anthracene, pyrene and benzoic acid in scCO2 with cosolvents, Yang et al. [22] reported AARD values (between 4.7% and 48.5%) lower than those obtained with a cubic EoS (ranging from 15.0% to 70.8%). This difference was probably due to the fact that these authors have mainly evaluated systems containing non-associating compounds. For instance, to predict the solubility of caffeic acid, which has three association sites, the values estimated using a cubic EoS were more than 100 times lower than the actual experimental data [24]. In addition, the CPA EoS presented good accuracy when predicting the solubility of caffeic acid in scCO2 + ethanol, with ALD = 0.29 [24]. The dispersion between the experimental and calculated data can be visualized in Fig. 3. Fig. 3 divides the compounds in aromatic acids (●), aromatic alcohols (■), aliphatic acids (▲) and aliphatic alcohols ( × ). Underestimated prediction of the solubility data was observed in most cases. The solubility of hydroquinone was the only one significantly overestimated. No systematic deviations, by analyzing the different classes of compounds, was identified, since the highest differences between experimental and calculated data were observed for an aromatic acid (salicylic acid), an aliphatic acid (lauric acid) and an aromatic alcohol (hydroquinone).