Fluidization XVI
Numerical and Experimental Study of Electrostatic Charge in Gas-Solid Fluidized Bed
Authors
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:
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(1) |
where αg is the gas volume fraction, αpβ is the volume fraction
on the βth solid phase, N is the number of solid phases
in the mixture, εm and ε0 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:
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(2) |
This electric field induces an electrostatic force Fqpβ:
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(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:
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(4) |
where χpc= https://proceedings.aiche.org/sites/default/files/aiche-proceedings/con…" class="documentimage"> is the average charge per mass unit. αp and ρp are, respectively, the volume fraction and the density of the pth phase. Up,i is the ith component of the pth phase velocity. Dχ is the diffusion coefficient. ψp,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).
Hendrickson, G. Electrostatics and gas phase
fluidized bed polymerization reactor wall sheeting. Chemical
Engineering Science, Vol 61(4), 1041–1064 (2006)
Sowinski, A., Mayne, A. & Mehrani P. Effect of
fluidizing particle size on electrostatic charge generation and
reactor wall fouling in gas-solid fluidized beds. Chemical
Engineering Science, Vol 71, 552–563 (2012)
Fotovat, F., Alsmari, T. A., Grace, J. R. & Bi X. T.
The relationship between fluidized bed electrostatics and
entrainment. Powder Technology, Vol 316, 157–165 (2017)
Rokkam, R. G. & Fox, R. O. & Muhle, M. E.
Computational fluid dynamics and electrostatic modeling of
polymerization fluidized-bed reactors. Powder Technology,
Vol 203(2), 109–124 (2010)
Lindell, I. V., Sten, J. C.-E. & Nikoskinen, K. I.
Electrostatic image method for the interaction of two
dielectric spheres. Radio Science, Vol 28(3), 319–329 (1993)
Ali, F. S., Ali, M. A., Castle, G. S. P. & Inculet, I. I.
Charge exchange model of a disperse system of spherical
powder particles. In The 1998 IEEE Industry Applications
Conference, 1998. Thirty-Third IAS Annual Meeting, Vol 3,
1884–1891 (1998)
Laurentie, J. C., Traoré, P. & Dascalescu, L. Discrete
element modeling of triboelectric charging of insulating
materials in vibrated granular beds. Journal of Electrostatics,
Vol 71, 951–957 (2013)
Kolehmainen, J., Ozel,
A., Boyce, C. M. & Sundaresan,S. Triboelectric charging of
monodisperse particles in fluidized beds. AIChE Journal, Vol
63, 1872–1891 (2016)
Kolehmainen, J., Ozel, A. & Sundaresan, S. Eulerian
modelling of gas-solid flows with triboelectric charging.
Journal of Fluid Mechanics, Vol 848, 340–369 (2018)
Hamidouche, Z., Masi, E., Fede, P., Ansart, R., Neau,
H., Hemati, M. & Simonin, O. Numerical simulation
of multiphase reactive flows. Advances in Chemical Engineering, Vol 52, 51–124 (2018)
Sowinski, A., Miller, L. & Mehrani, P. Investigation of electrostatic charge distribution in gas-solid fluidized beds. Chemical Engineering Science, Vol 65(9), 2771–2781 (2010)