(693e) Dynamic Modeling and Optimization of the Bivariate Molecular Weight - Long Chain Branching Distributions in Highly Branched Polymerization Systems Using Monte Carlo and Sectional Grid Methods

Simulation of nonlinear, free radical polymerization systems has been a major field of studies for the last twenty years, since the molecular properties of polymers (e.g., molecular weight distribution, MWD, copolymer composition distribution, CCD, long chain branching distribution, LCBD, etc.) are directly related to their end-use properties (e.g., physical, chemical, mechanical, rheological, etc.). Hence, the ability to control accurately the molecular architecture of polymer chains in a polymerization reactor is of profound interest to the polymer industry. In the present study, a population balance approach is described to follow the time evolution of bivariate molecular weight ? long chain branching (MW-LCB) distributions in free-radical polymerization systems. A sectional grid method, the so-called fixed pivot technique (FPT) of Kumar and Ramkrishna (1996), was properly revised for solving the bivariate population balance equations for the ?live? and ?dead? polymer chains. According to this method, the ?live' and ?dead' polymer chain populations were assigned to a finite number of discrete points. Then, dynamic molar species equations for ?live' and ?dead' polymer chains were derived for the selected discrete points. An alternative approach, which takes into account the discrete and stochastic character of the process, is the use of probabilistic tools (i.e., Monte Carlo simulations). A powerful Monte Carlo (MC) algorithm, based on the developments of Gillespie (1977), was implemented in the present work for the simulation of highly-branched polymerization processes. This algorithm provides a simple and effective way for the prediction of the dynamic evolution of the bivariate molecular weight-long chain branching distributions by tracking the changes of a sampled molar population. This population consists of monomer and initiator molecules, ?live' and ?dead' polymer chains, all interacting through specific chemical reaction steps in accordance to the general polymerization kinetic scheme. In the present work, a comparative study is carried out in order to evaluate the proposed numerical methods, used for the simulation of batch free radical polymerization processes, in terms of accuracy, stability and computational requirements. Furthermore, the predictive capabilities of both methods are demonstrated by a direct comparison of model predictions with experimental measurements on the bivariate MW-LCB distribution of highly branched polymers, including polyvinyl acetate (PVAc) and low density polyethylene (LDPE). The developed methods are general and can be used for the prediction of the structural molecular properties (e.g., MWD, CCD, LCD, etc.) of linear and branched polymers as well as to the dynamic optimization of polymerization reactors. Literature Kumar S. and Ramkrishna D., (1996). ?On the solution of population balance equations by discretization ? I. A fixed pivot technique.'. Chemical Engineering Science, 51, 1311. Gillespie, D.T., (1970). ?Exact stochastic simulation of coupled chemical reactions.' The Journal of Physical Chemistry, 81(25), 2340.