(266a) Monte-Carlo-Simulation-Based Optimization Methods for Copolymerization Process

Molecular weight distribution (MWD) and chemical composition distribution (CCD) are two most important microstructural indices for many copolymers [1]. They can provide detailed information about the end-use properties of the polymer. One method to obtain the microstructural information of polymer molecules, which is difficult to determine via traditional equation-based methods, is through Monte Carlo (MC) simulation [1]. This method is essentially â??math-freeâ? and do not need to solve complex differential-algebraic equations. However, the MC method could be very slow due to the fact that a large number of chains must be simulated to generate accurate results. On the other hand, when it is applied to optimization, the MC method results in the challenge that accurate derivatives are not available due to the stochastic nature of the MC simulation.

Therefore, an efficient derivative-free optimization method using trust region concepts is developed in this project. Along with the trust region method, a series of local surrogate models are systematically constructed to approximate the original system described by the embedded MC simulation [2]. Moreover, during the implementation of this trust region method, the balance between the computational time cost and the accuracy of the MC simulation should be well dealt with, as a larger molecular chain number can improve the simulation accuracy, but at the same time slow down the process. Under the framework of parallel MC method [3], this study also proposes a strategy with adaptive molecular chain numbers for MC simulations to reduce the computational time cost. On the basis of the stochastic feature in MC simulation, the violations of the microstructural quality constraints and the simulation errors of specific simulated chains are taken into account to determine the appropriate number of simulated chains at each iteration. Finally, an example of a ternary polymerization process is presented to illustrate the efficiency and convergence of the proposed methods.

Keywords: Monte Carlo simulation, Chemical composition distribution, Optimization

Reference:

[1] Soares, J. B. P., McKenna, T. F. L. (2012). Polyolefin Reaction Engineering. Weinheim: Wiley-vch Verlag GmbH & Co. KGaA

[2] Eason, J. P., Biegler, L. T. (2015). Reduced model trust region methods for embedding complex simulations in optimization problems. Computer Aided Chemical Engineering, 37, 773-778.

[3] Weng, J., Chen, X., Yao, Z., Biegler, L. T. (2015). Parallel Monte Carlo Simulation of Molecular Weight Distribution and Chemical Composition Distribution for Copolymerization on a Graphics Processing Unit Platform. Macromolecular Theory & Simulations, 24(5), 521â??536.