(133c) Investigation of Particle Sheeting of Monodisperse Particles with an Euler-Euler Two-Fluid Model Incorporating Electrostatic Charging Effects

Electrostatic charging of particles is a disruptive phenomenon commonly encountered in gas-solid fluidization. In commercial applications such as catalytic polymerization of polyethylene, such events lead to particle aggregation as well as “sheeting” on the reactor wall. The sheets lead to halting the production process for reactor clean up and in turn results in large revenue losses.
Computational Fluid Dynamic (CFD) modeling has received interest over the past few years to predict the occurrence and magnitude of charging in gas-solid fluidized beds. Rokkam et al. (2013) had carried out CFD simulations using fixed particle charge densities to demonstrate the effect of the electrostatic forces in influencing the hydrodynamics of fluidization and wall sheeting. The model used three types of particles, namely wall, dropped and fines. The size and charge density of each of these types was based on the average values of these variables as observed in the fluidization experiments carried out by Sowinski (2012). It was shown that at the end of fluidization, a small layer of highly charged particles sticks to the wall in a similar way to that observed in experiments. The goal of the present work is the extension of Rokkam’s work to include a model for charge generation and transport. To this purpose, two phenomena need to be described by the model: charging due to particle-wall collisions, and charging due to particle-particle collisions. The model for particle-wall charging hypothesized by Matsusaka et al. (2000) and Matsusaka and Masuda (2003) was used to obtain a boundary condition describing particle charging due to contact with the wall. The methodology based on the kinetic theory of the granular flow described by Johnson and Jackson (1987) was used to derive this boundary condition.
The charging model of Matsusaka et al. (2000) was used to describe charging due to particle-particle collisions by determining the rate of change of charge due to collisions through the solution of the appropriate collision integral, as defined in accordance to the kinetic theory for monodisperse granular spheres (Jenkins and Savage, 1983). Consequently, expressions for the charge transport coefficient due to particle-particle collisions and charge flux due to particle-wall collisions are found. The model was implemented into an Euler-Euler two-fluid model with kinetic theory closures (Jenkins and Savage, 1983) to describe the properties of the particulate flow. The resulting model was applied to the simulation of gas-solid fluidized beds.
The domain size and initial conditions used to perform the numerical simulations reproduce the experimental conditions of Sowinski (2012). The fluidized bed was 0.1 m in diameter and the particles had a diameter of 300 μm. The fluidization velocity was varied between 1.5 and 4 times the minimum fluidization velocity, encompassing both bubbling and slug flow regimes. For the electrostatic properties, work function values of 4.4 eV and 5.6 eV (Masuda et al., 2006) were used for the reactor wall (carbon steel) and polyethylene particles respectively. A saturation charge density of 117 μC/kg, based on experimental observations was used. The bed was fluidized until a steady state of electrification was observed. The gas flow was then interrupted, and particles were allowed to settle at the bottom of the bed. Results of the simulations showed that the profile of charge density had its highest value near the wall, and decreased towards the center of the fluidized bed. A force balance was used to determine regions where particles would stick to the wall if the distributor plate was removed and the particles be allowed to fall. The radial component of the electrostatic force predicted by the model was significantly larger than its axial counterpart, and its magnitude also declined rapidly with distance from the wall. It was determined that the particles within a 2 mm thickness layer on the wall would not drop, in agreement with experimental observation in Mehrani’s group. The average charge density within this layer was 47 μC/kg while it was 70 μC/kg for a thickness layer of 0.5 mm on the wall. The results are in agreement with the experimental observations obtained by Sowinski (2012).

References

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Johnson, P.C., Jackson, R., 1987. Frictional–collisional constitutive relations for granular materials, with application to plane shearing. Journal of Fluid Mechanics 176, 67. doi:10.1017/S0022112087000570

Masuda, H., Higashitani, K., Yoshida, H. (Eds.), 2006. Powder technology handbook, 3rd ed. Taylor & Francis

Matsusaka, S., Ghadiri, M., Masuda, H., 2000. Electrification of an elastic sphere by repeated impacts on a metal plate. Journal of Physics D: Applied Physics 33, 2311–2319

Matsusaka, S., Masuda, H., 2003. Electrostatics of particles. Advanced Powder Technology 14, 143–166. doi:10.1163/156855203763593958

Rokkam, R.G., Sowinski, A., Fox, R.O., Mehrani, P., Muhle, M.E., 2013. Computational and experimental study of electrostatics in gas–solid polymerization fluidized beds. Chemical Engineering Science 92, 146–156. doi:10.1016/j.ces.2013.01.023

Sowinski, A., 2012. The study of reactor wall fouling in gas-solid fluidized beds caused by electrostatic charge generation (Thesis dissertation). University of Ottawa