Optimization of nonvaporizing nylon 6 reactors with stopping conditions and end-point constraints

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, conv_tf, is maximized, and the other in which the undesirable side product (cyclic dimer) concentration in the output stream, [C₂]_tf, is minimized. The control variable, temperature, is constrained to lie between 220°C 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_n, equal to some desired value μ_n.d. Simultaneously, an end-point constraint is used, which, depending on the objective function used, forces either the cyclic dimer concentration or the monomer conversion at the end of the reactor to lie at a specified value, [C₂]_d or conv_d. Thus, this algorithm incorporates stopping conditions as well as end-point constraints and so is more complex than earlier ones, but the results are more meaningful. Different nonisothermal optimal temperature profiles are obtained for the two objective functions studied, depending on the values of μ_n.d, conv_d, [C₂]_d, and the feed water concentration, representing the complex interplay of several opposing factors.