Numerical Investigation of Electrostatic Charging on the Hydrodynamics of Gas-Solid Fluidized Beds

1. Introduction

Fluidized beds are used commonly in industry, for example for hydrocracking, polymer production, drying of minerals, foods and pharmaceuticals, and many more applications. A fluidized bed consists of a bed of particles suspended in a gas flow from below, termed the emulsion phase, which behaves as a fluid. Through the emulsion phase, gas bubbles form at the injector, and rise through the bed. These bubbles are responsible for the creation of solids circulation throughout the equipment, which results in very good heat and mass transfer characteristics. The minimum fluidization velocity is a key parameter, which determines many other hydrodynamic parameters and is central to the design of fluidized bed reactors.

In gas-solid fluidized beds, the emulsion phase is usually dense, and many collisions occur between particles and between particles and the walls (Hendrickson 2006; Sowinski, Miller, and Mehrani 2010). This causes particles to gain electrostatic charge, a phenomenon called triboelectrification or contact electrification. These charges cause additional inter-particle and particle-wall forces which may result in detrimental phenomena, such as wall sheeting and particle agglomeration.

How triboelectrification affects the minimum fluidization velocity, and thereby the hydrodynamic behavior, is however not fully understood. Carrying out experiments to investigate the effect of electrostatics on the hydrodynamics of gas-solid fluidized beds has proven rather difficult, especially related with the difficulties associated with the determination of the charge distribution over the particles. Without detailed information on the charge distribution, it will be very difficult to draw quantitative conclusions. Therefore, in this work a modelling study has been carried out to elucidate the effects of triboelectrification on the hydrodynamic behavior of gas-solid fluidized beds, particularly focusing on the minimum fluidization velocity, the solids circulation patterns and bubble behavior in beds with electrostatically charged particles.

2. Model Description

In this work an Euler-Lagrange model, referred to as CFD-DEM or the Discrete Particle Model (DPM), has been used to study the hydrodynamics of a fluidized bed with charged particles. The DPM allows for a fine-grained investigation on the particle-level, but is restricted to relatively small system sizes because of the required calculation times. Basically, every particle with its own individual properties such as mass, velocity, and charge, is tracked individually using Newton’s law of motion, while the gas flow is solved on the Eulerian (background) mesh. The inter-phase momentum coupling is performed by a mapping term in the momentum balance, corresponding to the drag force term in the equations for the particle motion.

The Cundall and Strack linear spring/dashpot soft-sphere model is used to describe the contact collision force of particles (Cundall and Strack 1979). The electrostatic interaction between particles is calculated by Coulomb’s law, assuming that the charge is distributed uniformly over the particle surfaces and that the calculation can be based on point charges. The electrostatic force consists of particle-particle and particle-wall interactions.

F_{electrostatic}= F^e_p-p + F^e_p-w 1

It is assumed that the system wall has no charge and the interaction between particles and the conducting wall is due to the induction of charge at the wall (image charge).

F^e_p-p = q_iq_j n_ij/4πε₀r_ij² r_ij≤ r_cut 2

F^e_{p-w =} q_iq_i n_ij/4πε₀(2r_ij)²r_ij≤ r_cut 3

where and represent the charge of particle i and j, the distance between them, the vacuum permittivity (equal to ) and the unit vector.

The consideration of all the electrostatic interactions between all particle combinations quickly becomes computationally prohibitive. Considering only the most significant interactions (i.e. nearby particles) can be an effective way of reducing the required computation time. In this work a neighbor list, or Verlet list, has been used, storing for each particle a list of nearest-neighboring particles (Cal et al. 1967), for which the electrostatic interactions have been calculated.

3. Results

• Minimum fluidization and minimum bubbling velocity

To determine the minimum fluidization velocity, the same pressure-drop procedure has been used as is standard in experimental works. The simulations are started with a bed consisting of Geldart B type particles (either charged and uncharged, depending on the case), which is subjected to a slowly linearly increasing superficial velocity from nihil till a velocity where bubbles have started to appear, and subsequently, the gas flow rate is linearly decreased again. During the simulation, the pressure drop over the bed is logged. Our simulations have shown that in charged systems the appearance of bubbles is delayed, while the system starts to fluidize earlier. Helped by the electrostatic forces, the bed starts to fluidize and expand already at lower superficial velocities, since the particles repel each other. Moreover, more energy is needed to push particles into densified zones and form bubbles in the bed. Thus, the minimum fluidization velocity decreases and the minimum bubbling velocity increases with the degree of electrification of the particles.

• Bubble injection

To better understand the effect of electrostatic forces on the hydrodynamics, a single bubble was injected into the bed. The rise velocity and bubble shape of a system with uncharged and charged particles were compared. Results show that in a system of uncharged particles, the bubble is clearly visible, whereas in a system with charged particles, the bubble experiences more excessive particle raining from the roof of the bubble and the bubble starts to disappear in the middle of the bed. Due to the electrical repulsion between the particles, the bubble start to fill with particles already as soon as it starts to rise through the emulsion phase, making a detailed analysis of the bubble rise velocity impossible. The extent of particle raining has been investigated as a function of the particle charge for different particle properties (size and density).

• Circulation patterns

By comparing the solids circulation patterns of charged and uncharged systems, it is clear that a bed with charged particles exhibits more homogeneity and due to the image charge of the walls the particles show a tendency to stick to the system walls. Calculations have shown that even 10% charge of the maximum charge can already cause serious wall sheeting in a gas-solid fluidized bed consisting of polymer particles. Due to smaller size of the bubbles in charged fluidized beds, the solids circulation is decreased significantly. Also this effect is quantified as a function of the particle charge for different particle systems.

4. Conclusions

The DPM was extended to model gas-solid fluidized beds in the presence of mono-charged particles. It was found that that the minimum fluidization velocity decreases, while the minimum bubbling velocity increases significantly in fluidized beds with charged particles. Moreover, a charged system shows more homogeneous fluidization with smaller bubbles suffering from heavy particle raining, causing significantly reduced solids circulation in the bed. These effects are quantified as a function of the particle charge for different particle systems. Future work will focus on the extent of fouling in polymer fluidized beds and its effect on the bed-to-wall heat transfer rates.

References

Cal, P. Y. S. I., R. E. Evi, Properties Lennard, and Jones Molecules. 1967. “Computer Experiments on Classical Fluids. I. Thermodynamical Properties of Lennard–Jones Molecules.” Physical Review 159(1):98.

Cundall, P. A. and O. D. L. Strack. 1979. “A Discrete Numerical Model for Granular Assemblies.” Géotechnique 29(1):47–65. Retrieved (http://www.icevirtuallibrary.com/doi/10.1680/geot.1979.29.1.47).

Hendrickson, Gregory. 2006. “Electrostatics and Gas Phase Fluidized Bed Polymerization Reactor Wall Sheeting.” Chemical Engineering Science 61(4):1041–64.

Sowinski, Andrew, Leigh Miller, and Poupak Mehrani. 2010. “Investigation of Electrostatic Charge Distribution in Gas-Solid Fluidized Beds.” Chemical Engineering Science 65(9):2771–81.