A Lagrangian-Eulerian hybrid model for the simulation of poly-disperse fluidized beds: Application to industrial-scale olefin polymerization

Abstract

We present a generalization of the Lagrangian-Eulerian hybrid model for the numerical assessment of poly-disperse gas-solid flows (Schneiderbauer et al., Pow. Tech., 2016) to olefin polymerization fluidized beds. The main idea of such a modeling strategy is to use a combination of a Lagrangian discrete phase model (DPM) and a coarse-grained two-fluid model (TFM) to take advantage of the benefits of those two different formulations. On the one hand, the DPM model unveils additional information such as the local particle size distribution, which is not covered by TFM. On the other hand, the TFM solution deflects the DPM trajectories due to the inter-particle stresses. Moreover, sub-grid drag corrections are applied to account for the impact of the small unresolved scales on the gas-solid drag force. This hybrid approach further enables the efficient evaluation of gas-solid reactions at a particle level using DPM. In particular, at each DPM trajectory we consider the olefin polymerization accounting for the catalyst profile (activity over time), the pressure driven solubility of the reaction gases in the polymer particles, the particles crystallinity and the corresponding reaction masses and reaction heat. These, in turn, are mapped to the TFM approach, where they appear as additional mass and energy source terms. The predictive capability and numerical efficiency of this reactive hybrid modeling approach is demonstrated in the case of (i) an inert bi-disperse fluidized bed and (ii) in the case of an industrial-scale olefin polymerization fluidized bed. The results show that the model is able to correctly predict segregation in poly-disperse gas-solid flows. In addition, the model is able to predict the particle growth in a fluidized bed reactor as well as its impact on the hydrodynamics of the bed. The results further give a closer insight about the temperatures and the crystallinity of the polymer particles.