Optimization of the polycondensation step of polyethylene terephthalate formation in semibatch reactors

The polycondensation stage of polyethylene terephthalate (PET) formation is assumed to include side reactions leading to the formation of diethylene glycol, vinyl end groups, and acid end groups, in addition to the usual polymerization of bis (2‐hydroxyethyl) terephthalate (BHET) in semi‐batch reactors. A, flexible objective function has been proposed with temperature and pressure as control variables. Computations from the first variation technique show that the pressure should be reduced to the lowest limit under all possible conditions. Consequently, optimal temperature profiles in batch reactors are obtained for various lower limits of reactor pressures using the combination of first and second variation techniques. For the first variation technique, the vector iteration method of computation was used, and the near optimal profile so obtained was used as the initial guess for the second variation technique. The result of optimization shows that the lower limit of pressure and weighting parameters appearing in the objective function have profound effects on the optimum profiles. For higher pressures, it is shown that a high temperature must be used initially; but must be lowered later to minimize the formation of side products. However, for lower pressures, the temperature must be increased from a low value initially; but for large polymerization times, the temperature must be further reduced to minimize the formation of side products. It is thus seen that the optimum temperature profile for low pressures exhibits a broad maximum.