Parameter estimation and thermodynamic model fitting for components in mixtures for bio-diesel production

In the search of clean, sustainable and renewable energy sources, at present the use of bio-diesel from vegetable oils is one of the possibilities being considered. The knowledge of phase equilibrium in mixtures found in the bio-diesel production is essential for the correct design and operation of the process. However, there is still a lack of information about the parameter values for the models used to describe the phase equilibrium, which could lead to incorrect design of the reactors and the separation processes, and to low efficiency caused by low mass transfer due to the presence of heterogeneous mixtures. In this study, two algorithms are described for the model fitting and parameter estimation, which were used to estimate the values of the parameters in the UNIQUAC and NRTL model for a mixture of vegetable oils and bio-diesel. One of the algorithms uses the Simulated Annealing (SA) method, to find good initial estimates, without any previous knowledge of the parameters. Another algorithm uses Successive Quadratic Programming, using the estimates calculated in the SA algorithm to refine these estimates. In both algorithms, the criterion for fitting is the minimization of the square of the difference between calculated and experimental values. In both algorithms, the equilibrium is calculated using the direct global minimization of the Gibbs free energy with respect to the number of moles of each component, at constant T and P, for a given set of model parameters. The results obtained were able to correctly reproduce the experimental values of phase equilibrium composition.