Abstract

An industrial semibatch Nylon 6 reactor has been modeled and then optimized. The model developed accounts for most of the important physicochemical phenomena present, like heat transfer, vaporization, polymerization, and so forth. Five parameters are present in the model, which are "tuned" using data from the industrial reactor under one set of operating conditions, producing one grade of the polymer (using initial water concentration, [W]0, of 3.45 wt%). The tuned model is found to predict the behavior of the reactor for two other operating conditions ([W]0 = 2.52% and 4.43%), giving confidence in the model. The optimization involves the minimization of two objective functions, namely the reaction time, tf. and the concentration of the undesirable cyclic dimer in the product, [C2] f , The final monomer conversion, conv f , and the degree of polymerization of the final product, μ nf, are constrained to lie at values currently obtained for the three different cases. The (constant value of the) jacket fluid temperature, Tj , is one of the control variables, whose optimal value is to be ascertained. The pressure history, p(t), in the reactor, which can be manipulated through the vapor release rate, V T (t), is the other optimizing variable. Initially, the shapeof the pressure history is selected to be similar to that used currently, and p(t) is described in terms of four constants, Pmax, t f , S, and tf (tf is decided by the attainment of the desired value of μ nf). Optimal values of Pmax, t f , S, and T f are obtained using the sequential quadratic programming (SQP) method to give the Pareto set (set of equally optimal or noninferior points). An adapted Nondominated Sorting Genetic Algorithm (NSGA) is then used with the optimal results from the SQP study to obtain improved multiobjective Pareto optimal solutions for the three grades of Nylon 6, using the continuous variable, VT (t), and the value Tj as the optimizing variables. The solutions obtained are better than those obtained using the SQP technique with the shape of p(t) fixed a priori. A decision-maker can select the best operating condition from among these equivalent optimal points on the Pareto set, based on considerations which are usually nonquantifiable. The methodology used here can be used for studying other industrial reactors as well. Good mathematical models accounting for all the physicochemical aspects operative in a reactor (and which have been preferably tested on industrial data) are a prerequisite for such optimization studies.