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    • This work is inspired by the

    2019-10-22

    This work is inspired by the systematic work of Coutinho and co-workers, who obtained several very useful experimental data, which will be also used in our work, and applied the CPA equation of state for the modeling of systems relevant to the production of biodiesel [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19]. Consequently, many CPA pure fluid and binary parameters for systems containing, fatty Schaftoside esters, glycerol, alcohols and water already exist. In one of their recent studies, Oliveira et al. modeled binary and ternary mixtures containing fatty acid esters, alcohols, glycerol and/or water using various models, such as UNIFAC, SRK, PSRK, PR-MHV2, SRK-MHV2 and CPA [18]. It was concluded that the CPA model presents the best correlations for such systems [18]. Furthermore, good results were obtained by Oliveira et al. for the water solubility in esters and some biodiesel samples against their own measurements [11]. Coutinho and co-workers have also established in many cases e.g. for ester-water, acid-water, methanol-ester and ethanol-ester mixtures that the CPA interaction parameters depend linearly on the molecular weight [11], [13], [15]. In principle, these are promising results, however, as it will become clear next, there are some issues that need investigation. Oliveira et al. obtained useful experimental data on the vapor-liquid equilibrium (VLE) of glycerol – alcohol binary systems, while they applied the CPA equation of state to describe such data [12]. Also, the CPA model was applied to describe the VLE of water – glycerol binary and the liquid-liquid equilibrium (LLE) of the methanol – methyl oleate – glycerol ternary system. CPA pure fluid parameters for glycerol were estimated using data from DIPPR database in the 0.45 < T < 0.85 temperature range. For glycerol, two different association schemes were tried, the 4C (two positive and two negative sites on every molecule) and the 3 × 2B (three positive and three negative sites on every molecule) schemes, respectively (see Table 1), while two different parameter sets were estimated using the 3 × 2B association scheme. It was proved that the 3 × 2B parameter set 2 gives the best results for the binary mixtures of glycerol with water and alcohols. However, this parameter set fails to describe the vapor pressure of the pure compound as is shown in Fig. 1. The error in vapor pressure is significant (>100%). These problems are not discussed in the original publication which calls for a re-estimation of the glycerol parameters for CPA. As will be discussed in the next section, glycerol exhibits complex phase behavior with LLE with diverse compounds (esters, hexane, etc.), thus very accurate glycerol parameters are required for reliable modeling. Similar problems for other compounds, such as methyl oleate and methyl octadecanoate, are noticed, which may be explained by the fact that DIPPR correlations could have been revised in recent versions. In more detail, the parameters of references [11], [12], [14] result in vapor pressure calculations with average deviations from the DIIPR database (version 5.0.1, [20]) around 21% for methyl oleate (in the 340–687 K temperature range) and 7% for methyl octadecanoate (in the 310–620 K temperature range, see Figs. S1 and S2 of the supplementary material). Thus, implantation was concluded that the CPA parameters for compounds of relevance to biodiesel-applications should be revised and estimated using more recent DIPPR versions and experimental data available in literature. In this direction, new and more extended parameter tables are provided in this study for systems relevant to biodiesel production. Furthermore, in many cases in the aforementioned literature studies, the evaluation of the results for the predicting ability of the model is not straightforward, although the correlations of the data may be valuable. In more detail, sometimes ternary or multicomponent mixtures were modeled using the binary parameters obtained from the binary sub-systems, while, in a second approach, calculations were performed using binary parameters adjusted to the multicomponent mixtures data [14], [17]. However, in this way very different binary interaction parameters (k) and cross association volumes (β) were estimated. In some cases (for example glycerol-methanol or glycerol-ethanol [14], [17]) positive k values were estimated using the first approach (binary data) and negative using the second one (multicomponent data). Such differences may lead to very different modeling results for the binary systems, which indicates that a more careful investigation of the predicting ability of the model is needed. Moreover, in some cases, the binary parameters, in lack of appropriate experimental data for binary mixtures, were adjusted to ternary mixture data [8]. Such approach could result in satisfactory correlations, which can be also valuable, but does not offer the ability of judging on the predictive ability of the model and more importantly indicate the need of successful predicting methods-correlations of the binary model parameters.