Parameter Estimation and Thermodynamic Model Fitting for Components in Mixtures for Bio-diesel Production

There is a growing interest in the search of clean, sustainable and renewable energy sources. Among them, the use of bio-diesel from vegetable oils is being considered. The knowledge of the 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. Therefore, for the correct calculation of phase equilibrium it is necessary to have reliable estimates of the thermodynamic model parameters. In this work, two algorithms are described for the model fitting and parameter estimation, which were used to estimate the values of the parameters in the UNIQUAC model for a mixture of vegetable oils and bio-diesel. One of the algorithms uses the Simulated Annealing method, in order to find 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. Also, 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, due to the non-linearity and non-convexity of the model. The minimization of the Gibbs free energy model was done using the software GAMS/CONOPT2. The results obtained were able to correctly reproduce the experimental values of phase equilibrium composition.