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# In this study new and more extended tables of

In this study, new and more extended tables of parameters were estimated for pure fluids and binary mixtures that are relevant to biodiesel systems. Also, calculations for glyceride systems will be shown, which is a topic not investigated before with the CPA model. As before [21], [22], [23], [24], the term “predictive” is used in this context for multicomponent mixture predictions based solely on binary interaction parameters that were estimated using only binary mixture data. This means that no parameter is adjusted or fine-tuned to ternary or multicomponent systems data. For this reason, it was also necessary to develop correlations of the pure OICR-9429 and mixture parameters which can be used whenever experimental data are not available for binary systems.

CPA pure fluid parameters for compounds relevant to the biodiesel production

Binary mixtures

Multicomponent mixtures
In this direction the model was initially applied to describe the LLE of the ethyl laurate (ethyl dodecanoate) – ethanol – glycerol ternary system using the data of Follegatti-Romero et al. [9] at 323.15 K and 353.15 K. The calculations were performed using the experimental feed (overall) compositions. All the used binary parameters are presented in Table 11, while some characteristic calculations are presented in Fig. 27. The percentage average absolute deviation (%AAD = where w stands for weight fractions and n is the number of experimental data points) of model predictions are around 79, 7.5 and 4.4% for ethyl laurate, ethanol and glycerol weight fractions, respectively, in the glycerol rich phase and 10, 26 and 56% for ethyl laurate, ethanol and glycerol weight fractions, respectively, in the ester phase. Such system was modeled before form Follegatti-Romero et al. [9] using the CPA model and the authors present an average deviation around 10 for both phases. The of model predictions from experimental data using the parameters of the present study are 2.0 and 4.7 for the glycerol and ester rich phase, respectively.
Next the model was applied to predict the phase behavior of one commercial biodiesel – glycerol – methanol system using the experimental data of Csernica and Hsu [85]. All the used binary parameters are presented in Table 12, while the results are illustrated in Fig. 28, where it is shown that the model qualitatively predicts the phase behavior of such multicomponent mixture. The percentage average absolute deviation (%AAD) of model predictions are around 5.8, 4.4 and 46% for glycerol, methanol and biodiesel, respectively, weight fractions in the alcohol rich phase and 49 and 10% for the methanol and biodiesel weight fractions in the biodiesel rich phase.
Such preliminary results for ternary or multicomponent mixtures indicate that the accurate prediction of the phase behavior in such systems is feasible, even though many binary parameters, in absence of experimental data for binary mixtures, are predicted using appropriate correlations. In both studied systems, high deviations were observed for the ester composition of the glycerol rich phase and the glycerol composition of the ester rich phase. This finding indicates that the binary parameters for ester-glycerol systems may need more attention. However, such parameters are based on very few experimental data for only seven systems (three methyl- and four ethyl-esters) and, as it was mentioned in Section 3.4, some of the available sets may need to be checked.

Conclusions

Acknowledgements
The authors wish to thank BP International Limited (UK), Statoil (Norway), and Petrobras (Brazil) for supporting this work as part of the CHIGP project (Chemicals in Gas Processing). We wish to thank particularly BP for input and many exciting discussions.

Introduction
Viscosity interprets the internal resistance or friction, in other words it expresses the mobility of the fluid. Viscosity models are important tools to describe the viscosity of the fluid as a function of temperature, pressure and compositions. Lots of scientists suggested viscosity models for engineering calculations. For example, we can refer to Monnery et al. in 1995 [1], Mehrotra et al. in 1996, and Reid et al. in 1987. According to the Monnery et al.\'s proposal in 1995, semi-theoretical methods, which are applicable for liquids and gases, are based on the corresponding states principle, the hard-sphere theory, modified Chapman–Enskog theory or empirical residual concept [2]. Models that are based on the cubic equations of state (EOS) are used in these simulations. Corresponding states principle to a fluid reference in 1987 by Pedersen and Fredenslund [3], principle of states corresponding to the two fluids reference by Aasberg-Petersen et al. in 1991 [4] and viscous models based on the cubic EOS by Guo et al. in 1997 [2] were propounded. Kinetic theory of gases and Chapman–Enskog theory have shaped based on semi-theoretical models. Friction theory (f-theory) was presented by Quiñones-Cisneros et al. in 2000 [5] for viscosity modeling. In the f-theory, an appropriate equation of state can be used for estimating pressure-dependence. In some polar liquids such as alcohols, due to the presence of OH group, a proper equation of state for combining with f-theory is required [6]. CPA-EOS [7] generally is a good choice for modeling the behavior of polar systems phase. The equation of state [7] is created by attaching an association term of SRK-EOS [8] (or the PR-EOS [9]).