Optimization of a batch reactor to produce the elastomeric copolyester prepolymer copoly(ethylene‐polyoxyethylene terephthalate)(CEPT)

Abstract

A mathematical algorithm that optimizes the reactor to produce the elastomeric copolyester copoly(ethylene‐polyoxyethylene terephthalate), CEPT, is shown in this work. The optimization was carried out this way: First, an initial isothermal guess of temperature profile is made and the differential equtions system, which describes the CEPT production process, is solved, Second, the reaction time is fixed and the objective function is calculated. Third, the adjoint variable equations system is solved and the Hamiltonian's function is calculated. Fourth, a new temperature profile is found by using the control vector iteraction procedure. Finally, steps one to three are repeated until the objective function reaches a minimum value. The results of the optimization establish that the copolytransesterification reactor should be operated initially to high temperature (about 285°C), which should be reduced quickly to near 250°C to purposely diminish the production of by‐products.

Multi‐Objective Optimization of a Batch Copoly(ethylene‐polyoxyethylene terephthalate) Reactor Using Different Adaptations of Nondominated Sorting Genetic Algorithm

“…The details of the side products formation are given in Table 1. As final properties of the polymer are heavily influenced by the presence of various end groups, therefore, control of functional groups in polymer melt is very essential during CEPT formation 10–15. For example, small amount of DEG in the CEPT causes a decrease in crystalline character that reduces the strength and lowers the melting point of the resulting polymer 11–13.…”

“…A small amount of acetaldehyde gives unusual flavor and color to the film and fiber 10,13. Due to increased commercial importance of CEPT copolyetheresters,1,2,15 rigorous optimal operation of CEPT formation is needed to improve the productivity as well as the quality of the final polymer.…”

“…Attempts have been made to obtain optimal operation of a batch CEPT reactor15 using Pontryagin's minimum principle,16,17 which considers only minimization of final polymerization time. However, optimal operation of the CEPT reactor is associated with several important conflicting and noncommensurate objectives that needed to be optimized simultaneously in the presence of suitable constraints.…”

“…It is always desirable to obtain the best quality product (i.e., product having the least impurities) with a minimum production time (maximum throughput). Usually, a copolytransesterification reaction is favored at higher polymerization temperature1–3,15 and helps to reduce batch time, but it increases the undesirable side products. Similarly, lower polymerization temperature always helps to reduce the undesirable side products,1–3,15 but it requires long polymerization time to get the final desired product.…”

“…Usually, a copolytransesterification reaction is favored at higher polymerization temperature1–3,15 and helps to reduce batch time, but it increases the undesirable side products. Similarly, lower polymerization temperature always helps to reduce the undesirable side products,1–3,15 but it requires long polymerization time to get the final desired product. Thus, for a given catalyst loading, reaction temperature of batch copolymerization reactor is the ideal control variable (decision variable) for CEPT formation.…”