OPTIMIZATION FOR THE MINIMUM REACTION-TIME OF PET ESTERIFICATION

We have investigated the direct esterification reaction between tereph thalic acid (TPA) and ethylene glycol (EG) in semi-batch reactors, the first stage process for making polyethylene terephthalate (PET), to g et optimum conditions for the minimum reaction time. An independent-va riable-minimization problem, i.e., a free-end-time/fixed-endpoint prob lem, has been formulated for the system, and then converted to a depen dent-variable-minimization (fixed-end-time/free-end-point) problem by a coordinate transformation, for the latter problem readily yields to established solution methods. We have solved this reformulated problem to obtain the optimal temperature profiles in the reactor required fo r the minimum reaction time, by iteratively improving the temperature (manipulating variable) profile using the Pontryagin's minimum princip le. The results prove that the method employed here successfully finds an optimal solution for the PET esterification process. The reduction of the reaction time realized following this optimal temperature prof ile in the reactor was, however, found to be smaller than expected, du e to the approximating assumptions of neglecting the solubility equati on of TPA in the model. The results obtained using a more improved mod el of the system will be reported in the future.