Part V: Dynamic evolution of the multivariate particle size distribution undergoing combined particle growth and aggregation

Convergence analysis of finite volume scheme for nonlinear aggregation population balance equation

“…Because of complex nature of Equation , the analytical solutions are only derived for very simple kernels such as constant, sum, and product kernels by Scott and Aldous . Several numerical schemes were presented by many researchers to solve a pure aggregation PBE (Equation ): finite difference method, finite element method, Monte Carlo method, Galerkin's method, method of moments, finite volume schemes (FVS), fixed pivot technique, and cell average technique …”

Discussion on DQMOM to solve a bivariate population balance equation applied to a grinding process

“…The solid phase characteristics are described by the particle size or volume. More rarely, two or more properties for the discontinuous phase are considered (such as surface/volume, size/composition, or volume/size [5][6][7]. Bivariate or multidimensional population balance equations have particularly been developed to describe solid properties during crystallization [8][9][10] or precipitation processes [11][12], as well as for granulation [13], coagulation and sintering processes [14] or even more recently to describe the depolymerization of branched polymers [15].…”

Analysis of Slurry‐Phase Co‐Polymerization of Ethylene and 1‐Butene by Ziegler–Natta Catalysts Part 1: Experimental Activity Profiles

“…Although the modeling and simulation of polyolefin reactors has received significant attention in the literature, and in particular by the group of Kiparissides, there have been relatively few publications describing methods to obtain kinetic parameters to describe the activity of the catalysts and the properties of the polymer products . Kinetic studies of Ziegler–Natta catalysts have generally been conducted to obtain an understanding of the mechanisms involved, rather than to extract parameters for process simulation .…”