in Wiley InterScience (www.interscience.wiley.com).In this work, optimal operating policies for the ethylene polymerization in solution with a Ziegler-Natta catalyst in a series of tubular and stirred tank reactors are proposed. The polymer is specified through properties such as melt index, stress exponent and density. Usually such properties are predicted by means of a process model once the operating conditions are specified. However, the computation of appropriate operating conditions to match desired resins properties is a much more difficult and not yet industrially established task. This problem can be solved through optimization techniques, an efficient alternative to costly pilot plant or production scale tests. A formulation is proposed, where a stationary model of the flowsheet (DAE system) is cast into a multi-stage model with the spatial flow path coordinate as the independent variable. Discontinuities occur at the stage transitions because of model switches and reactants injection. Several studies, involving different polyethylene resin specifications, are carried out to present the high potential and versatility of the suggested procedure.

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An optimization model is presented to determine optimal operating policies for tailoring high density polyethylene in a continuous polymerization process. Shaping the whole molecular weight distribution (MWD) by adopting an appropriate choice of operating conditions is of great interest when designing new polymers or when improving quality. The continuous tubular and stirred tank reactors are modeled in steady state by a set of differential-algebraic equations with the spatial coordinate as independent variable. A novel formulation of the optimization problem is introduced. It comprises a multi-stage optimization model with differential-algebraic equality constraints along the process path and inequality end-point constraints on product quality. The resulting optimal control problem is solved at high computational efficiency by means of a shooting method. The results show the efficiency of the proposed approach and the benefit of predicting and controlling the complete MWD as well as the interplay between operating conditions and polymer properties.

An efficient parallel algorithm for the computation of parametric sensitivities for differential-algebraic equations (DAEs) with a focus on dynamic optimization problems is presented. A speedup of about 4 can be obtained for process models of more than 13500 DAEs and 75 parameters employing 8 processor cores in parallel using a Windows based system. The algorithm obtains its efficiency by decoupling the sensitivity equations from the state equations of the DAE. Furthermore, the costly Jacobian matrices are computed separately by other processes. The computational effort for a combined state and sensitivity integration can almost be reduced to the computational effort of the pure state integration, which is the theoretical limit of the suggested approach.A. Hartwich · K. Stockmann · W. Marquardt ( ) Aachener A. Hartwich et al.