An exact and vigorous kinetic Monte Carlo simulation to determine the properties of bimodal HDPE synthesized with a dual-site metallocene catalyst

A vigorous and progressed Monte Carlo strategy was developed to precisely simulate the ethylene and 1-butene copolymerization within the presence of hydrogen by dual-site metallocene catalyst. The results showed up that the ethylene and 1-butene consumption rates at the second catalyst site were approximately 5 times higher than at the first site, and hydrogen transfer rates at the first catalyst site were over 3 times more rapid than at the second site. It was found that the most elevated molar percentage of 1-butene inside the copolymers synthesized from the second site was around 12% and within the copolymers gotten from the first site was around 2%. At a steady hydrogen concentration, with 8 times increase in the 1-butene concentration within the initial feed, the overall weight average molecular weight (M‾w) and an overall number average molecular weight (M‾n) extended by approximately 50% and 40%, respectively. Besides, at a consistent 1-butene concentration, with 8 times increase in the concentration of hydrogen, M‾w and M‾n diminished by approximately 18% and 22%, separately. Due to the synthesis of two groups of chains with distinct molecular weights, the overall dispersity (Đ) was slightly higher than the dispersity resulting from each catalyst site (1.5-2.1). With increasing 1-butene concentrations, the overall bimodal molecular weight distribution (MWD) widened, and the peak sizes grew smaller and moved towards higher molecular weights. As hydrogen concentration increased, peaks became taller and move toward shorter chain lengths. It was observed that the first site created chain lengths between 102 and 103 while the second site generated chain lengths between 102 and 106. As the concentration of 1-butene was increased in the initial feed, the number of short chain branching per 1000 carbon atoms (SCB/1000C) increased from 10 to 50. Compared to the first site, there were 5 times as many SCBs at the chains produced from the second site. By diminishing the ratio of ethylene to 1-butene, the melt index (MI) tended towards smaller numbers (0.2≤MI≤2). With an increase in the ratio of ethylene to 1-butene and ethylene to hydrogen, the weight fraction of crystals raised from 67.4 to 69.5% and diminished from 71 to 69.5%, respectively. At last, increasing the temperature led to a diminish in molecular weight, a narrowing of the bimodal MWD, an increment within the thickness and weight fraction of crystals, and an increment within the density of HDPE.

Experiments on liquid film thickness around Taylor finger

Taylor finger is characterized by a single elongated air bubble that grows upward during the drainage of liquid from closed top vertical tubes. The characteristic of the Taylor finger is similar to the Taylor bubble commonly observed in gas–liquid two-phase flow. During the upward growth of the Taylor finger, liquid from the tube drains as a thin film around it. The exact prediction of film thickness is important in several engineering designs and process calculations such as the design of contacting devices, two-phase flow through porous media, boiling in tubes, and monolith reactors. The present study proposes an experimental technique to estimate the thickness of the draining liquid film. Based on experiments an empirical model has been proposed for non-dimensional film thickness in the inviscid region. The proposed model agrees well with the experimental data and equation proposed in published literatures (Davies, R. M., and G. Taylor. 1950. “The Mechanics of Large Bubbles Rising Through Extended Liquids and Through Liquids in Tubes.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 200, 375–90; Dukler, A. E., and J. Fabre. 1994. “Gas-Liquid Slug Flow.” Multiphase Science and Technology 8: 1–4; Fabre, J., and A. Liné. 1992. “Modeling of Two-Phase Slug Flow.” Annual Review of Fluid Mechanics 24: 21–46).

Multi-objective optimization of an industrial slurry phase ethylene polymerization reactor

Slurry polymerization processes using Zeigler–Natta catalysts are most widely used for the production of polyethylene due to their several advantages over other processes. Optimal operating conditions are required to obtain the maximum productivity of the polymer at minimal cost while ensuring operational safety in the slurry phase ethylene polymerization reactors. The main focus of this multi-objective optimization study is to obtain the optimal operating conditions corresponding to the maximization of productivity and yield at a minimal operating cost. The tuned reactor model has been optimized. The single objective optimization (SOO) and multi-objective optimization (MOO) problems are solved using non-dominating sorting genetic algorithm-II (NSGA-II). A complete range of Pareto optimal solutions are obtained to obtain the maximum productivity and polymer yield at different input costs.