Optimization of nonvaporizing nylon 6 reactors with stopping conditions

Abstract

In this study, optimal temperature profiles or histories T(t) are obtained for nonvaporizing plug-flow or batch Nylon 6 reactors using the minimum principle. Two objective functions are studied, one in which the monomer conversion is maximized, and the other in which the undesirable cyclic dimer concentration in the product stream is minimized. The control variable, temperature, is constrained to lie between 220 and 270°C in order to ensure single-phase polymerization. The most significant difference between this study and earlier ones is that the residence or reaction time t_f is not specified a priori, but is determined optimally by the use of a "stopping" condition such that the polymer product has a number-average chain length μ, equal to some desired value μ_n,d. This makes the algorithm considerably more complex, but the results are more meaningful. Qualitatively different optimal temperature profiles are obtained for the two objective functions studied, representing the complex interplay of several opposing factors in determining optimal conditions. This study also lays the foundation for even more complex, but relevant, optimization studies.