Problem definition and goals

Optimization of reactor operation policy is of paramount importance if improvement of product quality and increase of business profits are sought. In very specific terms, optimization of the reactor operation conditions is equivalent to producing the maximum amount of polymer product, presenting the best possible set of end-use properties, with minimum cost under safe and environmentally friendly conditions. This optimum solution is almost always a compromise. Increase of polymer productivity is usually obtained with the increase of the operational costs (increase of reactor volumes, reaction temperatures and reaction times, for instance). Besides, the simultaneous improvement of different end-use properties is often not possible (the improvement of mechanical performance is usually obtained through increase of molecular-weight averages, which causes the simultaneous increase of the melt viscosity and decrease of product processibihty). Therefore, the optimization can only be performed in terms of a relative balance among the many objectives that are pursued. 

In formal mathematical terms, the design of the optimum operation policy requires the definition and minimization of an objective function, in the form  

Based on the previous discussion, the design of the optimum operation policy (computation of u) requires the minimization of an objective function that is subject to equality and inequality constraints. It is important to emphasize that x, y, u, ce, x and may (or may not) depend on time, depending on the particular analyzed problem. It is also important to observe that initial conditions required to solve dynamic problems (as during the analysis of batch reactions) can be included in the set u of manipulated variables. Simulation platforms have been proposed and used to solve these complex optimization problems and they are robust enough to cope with imstable dynamic trajectories and large polymerization reactor models [38, 162-164]. 

The objective function F is usually presented as a weighted sum of deviation values, in the form  

Equation 8.19 can be used for analysis of both steady-state and dynamic optimization problems. In time-varying processes, actual implementation of optimum operation policies requires discretization of the dynamic trajectories [ 165]. In these cases, the vectors of state variables, end-use properties and manipulated variables include the set of discretized values along the whole dynamic trajectory. This means, for example, that NX equals the number of state variables multiplied by the number of discretized intervals (or sampling intervals). Finally, it must be clear that some of the weighting values can be equal to zero, which means that some of the available data may not be relevant for operation of the analyzed polymerization problem. 

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