Kinetic Analysis and Optimization of Long Chain Branched Propylene Polymerization System

A kinetic model has been proposed for a binary catalyst system with the available experimental data from the open literature, in which one catalyst produces polypropylene macromonomer, while the other catalyst attacks the macromonomers as side chains to the isotactic polypropylene backbone. After validating the model with the experimental data, it has been extended to find the optimal process conditions for the desired combination of conflicting objectives that leads to manufacturing of polymer with controlled branching suitable for varied kind of applications. A well-established multi-objective optimization technique, NSGA II, has been utilized for this purpose. Some of the Pareto optimal points are found to be better than the experimental data and show improvement in process performance

Modeling and Optimization of propylene polymerization with branching

A kinetic model has been proposed to fit the experimental data (2003) available from the open literature for branched propylene polymerization system. The present system considered is a binary catalyst system, in which the first catalyst produces the atactic polypropylene macromonomer whereas the second one grafts the atactic polypropylene macromonomers to isotactic polypropylene backbone leading to branching. The proposed kinetic model, first of its kind that has been validated with experimental data, is extended to find the optimal process conditions for the desired combination of conflicting objectives. For this purpose, multi-objective optimization technique nondominating sorting genetic algorithm II (NSGA II) has been utilized. A wide variety of process choices have been obtained for the optimization set up which shows improvement in process performance as compared to similar process performances reported in the open literature

Controlled Branching of Industrially Important Polymers: Modeling and Multi-objective Optimization

Long chain branching (LCB) in any polymerization is of profound importance. It helps in improving certain properties such as melt strength and strain hardening. Branched polymers are, therefore, having different characteristics than linear polymers. In addition to having good end use properties, they are well suited for various processing applications such as blow molding, thermoforming, extrusion coating etc. As real world applications demand different extents of branching of polymers for different applications, this study aims to perform an investigation for a controlled way of long chain branching of polymers with enhanced properties. The main goal of this research is, therefore, three fold; viz. i) Finding the optimal process conditions for the desired combination of conflicting objectives, ii) Development of a kinetic model for long chain branched polypropylene system based on the available experimental data from open literature and simultaneously performing the multi objective optimization for the desired combination of conflicting performance objectives within experimental limits, and iii) Development of Kriging based surrogate model to replace the first principles based computationally expensive model to save execution time, while performing the multi objective optimization task for a highly non-linear, multi-modal search space. First, a batch optimization study for the bulk polymerization of vinyl acetate has been considered to find optimal process conditions for imparting LCB in polymer architecture. A theoretical study has been conducted with a validated model to observe the effect of live radical concentration on long chain branching as this is an important factor for branching in polymer molecule via ‘chain transfer to polymer’ route

Towards Better Integration of Surrogate Models and Optimizers

Surrogate-Assisted Evolutionary Algorithms (SAEAs) have been proven to be very effective in solving (synthetic and real-world) computationally expensive optimization problems with a limited number of function evaluations. The two main components of SAEAs are: the surrogate model and the evolutionary optimizer, both of which use parameters to control their respective behavior. These parameters are likely to interact closely, and hence the exploitation of any such relationships may lead to the design of an enhanced SAEA. In this chapter, as a first step, we focus on Kriging and the Efficient Global Optimization (EGO) framework. We discuss potentially profitable ways of a better integration of model and optimizer. Furthermore, we investigate in depth how different parameters of the model and the optimizer impact optimization results. In particular, we determine whether there are any interactions between these parameters, and how the problem characteristics impact optimization results. In the experimental study, we use the popular Black-Box Optimization Benchmarking (BBOB) testbed. Interestingly, the analysis finds no evidence for significant interactions between model and optimizer parameters, but independently their performance has a significant interaction with the objective function. Based on our results, we make recommendations on how best to configure EGO

Multiobjective optimization of long-chain branched propylene polymerization

A model has been developed based on the available experimental data for propylene polymerization with long-chain branching. The system considered is a bicatalyst system, where the first catalyst produces the atactic polypropylene macromonomer and second one grafts the atactic polypropylene macromonomers to isotactic polypropylene backbone. Pareto optimal solutions for long-chain branched polypropylene with the binary catalyst system are obtained by adapting nondominated sorting genetic algorithm for a particular multiobjective setup. Optimization objective is to produce polymer of maximum weight average molecular weight and maximum grafting density (expressed as number of macromonomers per 1000 backbone monomer units) in minimum polymerization time. Two catalysts and one cocatalyst concentration, second catalyst addition time are taken as decision variables with relevant process constraints that take care of model validity over prescribed operating range. A wide variety of process choices have been obtained for the optimization setup which shows betterment in process performance (e.g., ∼17% improvement in grafting density and 1% improvement in weight average molecular weight with the same polymerization time attained as compared to the processes reported in the literature Ye and Zhu, 2013)

Modeling of propylene polymerization with long chain branching

A kinetic model has been proposed to describe the propylene polymerization process with long chain branching for a twin catalyst system to fit the experimental evolution of molecular weights, polydispersity index of atactic polypropylene, isotactic polypropylene and the grafting density at different catalyst and cocatalyst concentrations. Kinetic parameters are estimated by real coded genetic algorithm (an evolutionary optimization technique) from experimental data available in open literature. The validated model has the capability of predicting the branching density as a function of catalyst addition pattern, catalyst ratios and copolymerization time. Further, the validated model has been used to calculate the 'molecular weight long chain branching distribution'. Parametric sensitivity study has been conducted to analyze the effect of kinetic parameters on the long chain branching formation and other molecular properties of the polyme

Kriging Surrogate Based Multi-objective Optimization of Bulk Vinyl Acetate Polymerization with Branching

Despite the established superiority in finding the global as well as well-spread Pareto optimal (PO) points, the need of more numbers of function evaluations for population based evolutionary optimization techniques leads to a computationally demanding proposal. The case becomes more miserable if the function evaluations are carried out using a first principle based computationally expensive model, making the proposal not fit for online usage of the application. In this work, a Kriging based surrogate model has been proposed to replace a computationally expensive model to save execution time while performing an optimization task. A multi-objective optimization study has been carried out for the bulk vinyl acetate polymerization with long-chain branching using these surrogate as well as expensive models and Kriging PO solutions similar to those found by the first principle models are obtained with a close to 85% savings in function evaluations

Multi-objective optimization of bulk vinyl acetate polymerization with branching

Inclusion of long chain branching (LCB) in polymers is a challenging and important task in any free radical polymerization as LCB influences polymer product quality. In the present case, batch optimization study for the bulk polymerization of vinyl acetate has been considered to find optimal process conditions for imparting LCB in polymer architecture. A theoretical study has been conducted with a validated model to observe the effect of live radical concentration on LCB as this is an important factor for branching in polymer via chain transfer to polymer route. In order to obtain better polymer product in less time at various temperatures, a need was observed to perform a multi-objective optimization study as the selected objectives were conflicting in nature. Owing to the complex nature of moment-based species balance equations and molecular weight distribution function, elitist non-dominated sorting genetic algorithm II (NSGA II), a well-established multi-objective evolutionary algorithm, has been employed as an evolutionary computation method to find out the Pareto optimal solutions. Minimization of polymerization time, maximization of molecular weight and maximization of number average degree of branching (Bn) can be simultaneously achieved, while the solutions were obtained within the experimental range of polydispersity index and weight average molecular weight (Mw) given in the open literature. Results show a wide range of process choices satisfying process objectives and constraints, both in low as well as high temperature region