# Numerical and Experimental Study of Electrostatic Charge in Gas-Solid Fluidized Bed

- Conference: Fluidization
- Year: 2019
- Proceeding: Fluidization XVI
- Group: General Paper Pool
- Session:
- Time: Monday, May 27, 2019 - 1:55pm-2:07pm

Electrostatic charges have been one of the major issues in gas–solid fluidized beds, including wall fouling due to particle accumulation on

the walls, defluidization, and security issues such as sparks and dust explosions. At a molecular scale, the particle–wall or

particle–particle contact generates electron transfer, inducing a charge on each particle. As a result, the surrounding gas carries an

electromagnetic field which results in an electromagnetic force known as the Lorentz force. The aim of this work is to model this force

and take its contribution into account in the particle-phase momentum balance. In this work, a tribocharging model, coupled with the

multi-fluid model, is proposed in an Eulerian approach to model the phenomenon. The numerical simulations are carried with

NEPTUNE_CFD to test the model. An experimental setup is build to develop an accurate database for comparison with simulations, and

to calibrate the model parameters.

In polymerization reactors, electrostatic charge generation can

cause the formation of larger granules, as well as reactor wall

fouling, which is the formation of layers of the particles on the

reactor wall. Hendrickson (2006) reviewed electrostatic effects

in polymerization fluidized-bed reactors and the causes of reactor

fouling, explained the charge distribution in fluidized beds,

and compared the effect of electrostatic forces with other

forces such as drag and gravity on particle entrainment.

Sowinski et al. (2012) studied the effect of particle size of a

polyethylene resin received directly from industrial reactors on

electrostatic charge generation and reactor wall fouling using a

Faraday cup. Regarding the effect of relative humidity on

electrostatic charge generation, Fotovat et al. (2016) performed

experiments at different values of relative humidity using a

mixture of glass beads as coarse particles and fine particles

of different materials. These experiments aimed to study

the relationship between fluidized bed electrostatics and

entrainment.

On the numerical side, many models have been proposed to

describe the phenomenon. Rokkam et al. (2010) developed an electrostatic model based on basic laws describing electromagnetic phenomena using an Eulerian approach. For tribocharging phenomenon, Lindell et al. (1993) analyzed the interaction of two dielectric spheres to find their reaction to external sources based on a static theory image. On the other hand, some authors proposed models based on the surface state theory (Ali et al. 1998; Laurentie et al. 2013). Kolehmainen et al. (2016) built a Lagrangian model on the same works and tested it on a miniaturized fluidized bed in a DEM simulation. More recently, Kolehmainen et al. (2018) proposed the same model in an Eulerian approach.

Building on the well-known Maxwell equations for an electromagnetic field, a Poisson equation is solved for the electric potential:

âˆ‡ â‹…(Îµmâˆ‡ Ï†) = ---Î²=1--pÎ²--pÎ² Îµ0 " src="https://www.aiche.org/sites/default/files/aiche-proceedings/conferences/..." class="documentimage"> |
(1) |

where α_{g} is the gas volume fraction, α_{pβ} is the volume fraction

on the β^{th} solid phase, N is the number of solid phases

in the mixture, ε_{m} and ε_{0} are the dielectric permittivity

of the mixture and the vacuum, respectively, and φ is the

electric potential. The walls are assumed to be grounded

(φ = 0). Note that the effect of magnetic field is neglected

here.

The gradient of the potential results in an electric field

E:

" src="https://www.aiche.org/sites/default/files/aiche-proceedings/conferences/..." class="documentimage"> |
(2) |

This electric field induces an electrostatic force F_{qpβ}:

" src="https://www.aiche.org/sites/default/files/aiche-proceedings/conferences/..." class="documentimage"> |
(3) |

Numerical simulations are carried with NEPTUNE_CFD, an

unstructured code using unsteady Eulerian multi-fluid approach

for dilute and dense particle-laden reactive flows (Hamidouche

et al. 2018). The coupling between the electrostatic model and

the multi-fluid was verified by simulating experimental results of

Sowinski et al. (2010). The weakness of this model is that

charges are fixed on particles, which does not take into account

the tribocharging phenomenon.

The triboelectric charging mechanism assumes that the charge

carried by the solid phase obeys to the following transport

equation:

Î±pÏp--p-+ --- Î±pÏpUp,iÏ‡cp = âˆ‚t âˆ‚xi ( c) -âˆ‚- Î±pÏpD Ï‡âˆ‚Ï‡p- + Ïˆp,q âˆ‚xi âˆ‚xi " src="https://www.aiche.org/sites/default/files/aiche-proceedings/conferences/..." class="documentimage"> |
(4) |

where χ_{p}^{c}=
mpp--" align="middle" src="https://www.aiche.org/sites/default/files/aiche-proceedings/conferences/..." class="documentimage"> is the average charge per mass unit. α_{p} and ρ_{p} are, respectively, the volume fraction and the density of the p^{th} phase. U_{p,i} is the i^{th} component of the p^{th} phase velocity. D_{χ} is the diffusion coefficient. ψ_{p,q} is a source term representing the charge generation due to collisions between particles of different solid phases. The transfer between particles inside the same solid phase is included in the diffusion coefficient. The boundary conditions are expressed by a charge flux from the wall towards the particles. This flux represents the charge generation due to the particles-wall collision.

The experiments are performed in a laboratory scale facility of 0.1 m inner diameter and 1 m height Plexiglass column. The electrostatic charges are measured by means of two Faraday cups connected to an electrometer. The distributor plate was welded in a valve attached to an actuator to allow particles to drop into the Faraday cup. Entrainment flux is captured via a box at the end of the cyclone. The box contains a Faraday cup placed on a balance to measure the evolution of charge and entrainment flux simultaneously. This facility is made of the same material (Plexiglass) starting from the distributor to the end of the cyclone in order to have the same effect of walls on particles. The effect of humidity is studied by means of a humidity generator. This generator ensure a constant relative humidity in a range up to 40% without heating the system. It is connected to the compressed air supplier.

The experimental work can be divided in two main parts. The first one is the study of a bubbling fluidized bed. The net charge of the particles is measured after each experiment. This aims to compare to literature findings and to estimate the saturation charge of the particles. The second part is the study of entrainment flux. The entrained mass and charge evolution are measured at the end of the cyclone. This allows to study the effect of electrostatic charges on entrainment flux. Both parts are performed at different relative humidity to highlight its effect. These experiments provide an accurate database to adjust the tribocharging model parameters depending on relative humidity and particles properties (size, material).

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