Optimal Grade Transition in Polymerization Reactors: A Comparative Case Study†

A detailed study of grade transitions, as encountered in polymerization reactors, is presented. We explore various issues such as the nonconvexity of the associated dynamic optimization problem and study its impact on the optimal policies when the widely used sequential quadratic programming (SQP) solvers are applied. The results underscore the need for global optimization algorithms to fully realize the benefits of grade transition that are typically nonconvex, because of the nonlinear dynamics of the process. A study of the structure of the objective function used in optimization of grade transitions indicates that opportunities exist for varying the degree of nonconvexity using a priori knowledge of the new grade and appropriate choice of weight matrices in the objective function. For comparison with the SQP solution, we use a nongradient, parallel search stochastic method, namely differential evolution (DE). Our simulations indicate that, although the DE solution is highly dependent on the algorithm parameters and mutation strategy, the SQP solution is dependent on the initial guess value and consistently provides faster convergence. However, if the objective function is modified using the a priori knowledge of the new grade and appropriate choice of the weight matrices, transition policies based on SQP become less dependent on the initial guess value and identical to the best DE solution while retaining its benefits of faster convergence. Finally, we also explore the issue of explicit minimization of the grade changeover time. We also present a study exhibiting sensitivity of the DE algorithm to its parameters. All of the aforementioned issues have been demonstrated for the grade transition of polymethyl methacrylate (PMMA) in a nonisothermal continuous stirred tank reactor (CSTR).