Dynamic optimization of multicomponent batch distillation processes using continuous and discontinuous collocation polynomial policies

Optimization of batch distillation has been studied extensively over the last 30 years. Previously, the solution methods were basically derived or computed using short-cut models due to the lack of suitable computation techniques. In this study, a modified approach based on the work of Biegler and coworkers (L. T. Biegler, Comput.Chem.Eng., 8 (1984) 243; J. E. Cuthrell and L. T. Biegler, AIChE J., 8 (1987) 1257) was implemented to determine optimal constrained solutions for a ternary system with various objective functions, such as maximum product, minimum energy required and mininum end time, using a rigorous model. Unlike previous investigations, the optimal control solutions derived in this study were independent of the process model implemented. Therefore, no limitation on the distillation models exists, i.e. any rigorous model can be used to find solutions.

The optimal control problem for the batch distillation of mixtures of benzene, toluene and o-xylene was solved. The solutions were assumed to be continuous or discontinuous polynomials. It was found that a discontinuous solution is superior to continuous results because of the discontinuous nature of the system itself.