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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A comprehensive mathematical model for the ethylene/1-butene polymerization in solution with Ziegler-Natta catalyst is developed. The process comprises a series of continuously stirred and tubular reactors in which polyethylene resins with different properties may be produced. The mechanistic model considers the moments of the bivariant molecular weight distribution in order to ascertain the average molecular weight and polydispersity. The polymer quality is verified through the melt index, density and stress exponent, which is a measure of the polydispersity. The model developed investigates the stationary and dynamic behavior of the process following step changes in feed conditions. It allows for the prediction of non-linear and inverse responses, encouraging the use of the model for optimization and control purposes. copolymerization of ethylene and 1-butene with a soluble Ziegler-Natta catalyst. Both contributions use pilot-plant data in order to estimate the process parameters and then validate the model predictions. Embiruçu et al. (2000Embiruçu et al. ( , 2008a study the ethylene polymerization with a soluble Ziegler-Natta catalyst, in a series of continuous stirred tank and plug flow reactors. The kinetic and physical parameters are estimated using dynamic plant data. The dynamic mathematical model developed allows for the prediction of both the final polymer properties and process performance. Hinchliffe et al. (2003) developed a hybrid model for the ethylene coordination polymerization in solution. A mechanistic description is used for process understanding, while an empirical model, based on neural networks, is used to decrease the mismatch between the industrial process and the model which arises when predicting the instantaneous molecular weight distribution.Within this context, the main objective of this study is to develop a mathematical model for the ethylene/1-butene copolymerization with a soluble Ziegler-Natta catalyst. The process takes place in a series of continuous stirred tank and plug flow reactors, which, due to their operational versatility, enable several simulation studies to be carried out. The characteristics of both reactors can be combined in order to produce different polyethylene grades. The steadystate and the dynamic behavior of the reactor performance, as well as the polymer properties, are evaluated following changes in feed conditions.First the copolymerization process is described and subsequently the kinetic mechanism and its particularities are illustrated. Then the mathematical model as well as the correlations for the polymer properties are described.Simulation studies then illustrate model predictions following step changes in certain input variables and finally the conclusion is presented. Process DescriptionThe process comprises an industrial plant of ethylene/1-butene copolymerization with a soluble Ziegler-Natta catalyst in a series of continuous stirred tank reactors (CSTR) and plug flow reactors (PFR), as depicted in Figure 1. The catalyst feed is a mixture of v...

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.

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This paper addresses real-time optimization strategies which can be readily implemented in industrial polymerization processes, even in case they show very fast dynamics. At the upper layer dynamic and steady-state real-time optimizations (D-RTO and RTO) are suggested and compared. A novel multistage formulation for the real-time dynamic optimization problem is introduced. It relies on a purely economic objective without additional stabilizing terms and facilitates an integrated treatment of a sequence of alternating dynamic and stationary operational stages. A case study shows that closed-loop D-RTO allows reducing off-spec material as well as exploiting or rejecting disturbances to maximize overall profit. The computational delay not only determines closed-loop performance but also significantly impacts the profit margin. The results indicate that even the simplest variant of the investigated strategies can significantly improve economic performance, since the transitions can be completed much faster than in current industrial practice.