Dynamic prediction of the bivariate molecular weight–copolymer composition distribution using sectional-grid and stochastic numerical methods

From Molecular to Plant‐Scale Modeling of Polymerization Processes: A Digital High‐Pressure Low‐Density Polyethylene Production Paradigm

“…(17)- (19)) is in general a notably difficult numerical problem [18]. To deal with the above high-dimensionality problem, several numerical methods have been proposed in the literature to reduce the infinite system of differential equations into a loworder system.…”

“…To deal with the above high-dimensionality problem, several numerical methods have been proposed in the literature to reduce the infinite system of differential equations into a loworder system. These can be broadly classified into kinetic lumping methods [19,20], global orthogonal collocation [21,22], method of moments [23][24][25][26][27][28], numerical fractionation methods [29][30][31], discrete weighted Galerkin [32][33][34], orthogonal collocation on finite elements [35,36], and sectional grid methods [15,18,37,38]. The above numerical methods are computationally complex and require special mathematical skills.…”

“…Based on the original work of Kumar and Ramkrishna [37], the fixed pivot technique (FPT) was applied to linear and nonlinear polymerization systems to predict the MWD [36,38] and joint MW-LCB [15] and MW-CC [18] distributions in batch and continuous reactors. According to the FPT, the different polymer chain populations are assigned to selected discrete points that are called grid points.…”

Prediction of the molecular and polymer solution properties of LDPE in a high-pressure tubular reactor using a novel Monte Carlo approach

“…In a series of publications Krallis et al, 2008), the development and application of a computationally efficient kinetic Monte Carlo (MC) algorithm to various time-varying free-radical polymerization systems was demonstrated. In particular, the kinetic MC algorithm can be successfully employed to predict the average and distributed molecular properties of polymer chains produced in a dynamic polymerization system.…”

“…Based on the general framework of molecular species population balances in a polymerization system, a number of deterministic and probabilistic models have been developed dealing with the prediction of molecular properties of linear and branched polymers. The various modeling approaches have been presented and reviewed in a series of recent publications by Kiparissides and his co-workers (Kiparissides, 2006;Meimaroglou et al, 2007Meimaroglou et al, , 2008Saliakas et al, 2007;Krallis et al, 2008).…”