Mariano Asteasuain

Modeling and optimization of a high-pressure ethylene polymerization reactor using gPROMS

Abstract A gPROMS implementation of a comprehensive steady-state model of the high-pressure polymerization of ethylene in a tubular reactor is presented. Model outputs along the reactor length include the complete molecular weight distribution and branching indexes, as well as monomer conversion, average molecular weights, reactants’ compositions, and reactor temperature and pressure. A detailed calculation of physical and transport properties, such as the reaction mixture density, heat-transfer capacity, viscosity and global heat-transfer coefficient is also included. The reactor model is included in an optimization framework that is used to determine the best operating conditions for producing a polymer with tailor-made molecular structure in terms of the complete molecular weight distribution, branching and polydispersity.

Improved numerical inversion methods for the recovery of bivariate distributions of polymer properties from 2D probability generating function domains

Abstract The 2D probability-generating function technique is a powerful method for modeling bivariate distributions of polymer properties. It is based on the transformation of bivariate population balance equations using 2D probability generating functions (pgf) followed by a recovery of the distributions from the transform domain by numerical inversion. A key step of this method is the inversion of the pgf transforms. Available numerical inversion methods yield excellent results for pgf transforms of distributions with independent dimensions with similar orders of magnitude, for example bivariate molecular weight distributions in copolymerization systems. However, numerical problems are found for 2D distributions in which the independent dimensions have very different ranges of values, such as the molecular weight distribution-branching distribution in branched polymers. In this work, two new 2D pgf inversion methods are developed, which regard the pgf as a complex variable. The superior accuracy of these innovative methods makes them suitable for recovering any type of bivariate distribution. This enhances the capabilities of the 2D pgf modeling technique for simulation and optimization of polymer processes. An application example of the technique in a polymeric system of industrial interest is presented.

OPTIMAL OPERATION OF ETHYLENE POLYMERIZATION REACTORS FOR TAILORED MWD

Abstract A comprehensive steady-state model of the high-pressure ethylene polymerization in a tubular reactor that is able to calculate the complete molecular weight distribution (MWD) as function of the reactor axial distance is presented. MWD is calculated by means of the probability generating function technique. The model is implemented in gPROMS and included in an optimization framework that is used to determine optimal operating conditions for producing a polymer with tailored MWD. Two application examples are presented, the first involves maximization of conversion while maintaining the original MWD, and the second consists in finding the operating conditions needed to produce a polymer with a bimodal MWD.

Deterministic Approaches for Simulation of Nitroxide-Mediated Radical Polymerization

Since its development in the last decades, controlled radical polymerization (CRP) has become a very promising option for the synthesis of polymers with controlled structure. The design and production of tailor-made materials can be significantly improved by developing models capable of predicting the polymer properties from the operating conditions. Nitroxide-mediated polymerization (NMP) was the first of the three main variants of CRP to be discovered. Although it has lost preference over the years against other CRP alternatives, NMP is still an attractive synthesis method because of its simple experimental implementation and environmental friendliness. This review focuses on deterministic methods employed in mathematical models of NMP. It presents an overview of the different techniques that have been reported for modelling NMP processes in homogeneous and heterogeneous media, covering from the prediction of average properties to the latest techniques for modelling univariate and multivariate distributions of polymer properties. Finally, an outlook of model-based design studies of NMP processes is given.

Unscented Kalman Filter. Application of the robust approach to polymerization processes

Abstract The control of polymerization processes has central importance because operational conditions affect the processing and end-use properties of the product. The nonlinear controllers based upon rigorous models make use of the on-line state estimates obtained from the available measurements. For polymerization processes, the Unscented Kalman Filter has shown a rewarding performance for state estimation. Because the presence of outliers distorts the behaviour of the filter, Robust Statistics-based approaches have been proposed to reduce their detrimental effect on variable estimates. Until now, only Huber type M-estimators have been used as loss function of the estimation problem. In this work, the ability of other types of M-estimators to improve estimate robustness without introducing numerical problems is analysed. The performances of the M-estimators are compared for a copolymerization process within the framework of a filtering technique based on the Unscented Transformation, which uses a reformulation of the covariance of measurements errors.