(448ad) Study of Solid-Liquid Fluidized Bed Using Electrical Impedance Tomography

Introduction:

Liquid fluidization has many applications in industrial
processes, such as particle classification, adsorption and ion exchange, and in
wastewater treatment¹. Additionally, a solid-liquid fluidized bed can
operate over a wide range of particle and fluid properties (e.g. solids
concentration, particle size, density, and fluid viscosity) and therefore
provides ideal conditions to study the dynamic behaviour of solid-liquid
systems. Specifically particle-particle, particle-fluid, and particle-wall
interactions can be investigated by studying liquid fluidization².

The turbulent nature of fluidization results in the
fluctuations of the velocities and volume fractions of both the solid and
liquid phases^3,4. Experimental investigations with the aim of understanding the nature
and magnitude of these fluctuations are necessary since: 1) these fluctuations
are directly responsible for the high level of mixing taking place in the
fluidization process, which in turn produces effective heat and mass transfer³;
2) such investigations are beneficial for the characterization of the dynamic
behaviour of other solid-liquid flow systems such as two-phase flows in pipelines;
and 3) measurements of the solid concentration fluctuations can be used to
validate and improve available numerical simulations.

Solid concentration fluctuations can be classified in two categories:
Large global fluctuations resulting from the bulk behaviour of the bed (i.e.
circulation); and small-scale fluctuations mainly produced by the local
hydrodynamics, and by particle-particle and particle-fluid interactions³.
Buyevich and Kapbasov³ were the first to provide a mathematical
model for prediction of the magnitude of small-scale fluctuations as a function
of bulk solid concentration. Zenit and Hunt⁴ then measured the
magnitude of small-scale fluctuations at different fluidization conditions and
for different particle properties. Their results showed that in addition to the
bulk solid concentration, particle size and density are contributing factors⁴.
In this study, for the case of inertial particles (particles with the largest
Stokes number tested), the measured values of the Root Mean Square (RMS)
fluctuations were close to the values predicted by the Buyevich and Kapbasov
model⁴. However, for the other particles tested (lower Stokes
numbers) the magnitude of fluctuations measured by Zenit and Hunt where 3 to 10
times lower than the values predicted by the model³, depending on
the particle terminal Stokes number⁴. The particle
terminal Stokes number can be expressed as St_t = (ρ_s /ρ_f)(Re_t/9), where ρ_s and ρ_f are solid and fluid
density, respectively, and Re_t is the particle Reynolds number at
the particle terminal settling velocity.

In 2010, Gevrin et al.⁵ conducted a numerical study of
the dynamic behaviour of a liquid fluidized bed and showed nonuniform
distributions of instantaneous local solid concentration in both
the vertical and radial directions. However, since the experimental data available
from Zenit and Hunt’s study was limited to values averaged over the
cross-section, Gevrin et al. were only able to validate their numerical
solutions for cross-sectional averaged concentration fluctuations. This indicates that the magnitude of the
local instantaneous distribution of particles and local concentration
fluctuations must still be measured. In 2013, Hashemi⁶ measured the
local solid concentration fluctuations for selected particles using high-speed
EIT. Results from this work which were limited to particles with moderate
Stokes numbers (glass beads) showed
that the RMS fluctuations was not uniformly distributed over the bed cross-section
(being higher in the near-wall region)⁶.

Based on the results of previous studies of the
small-scale fluctuations, there are multiple mechanisms involved in their
production, including particle-fluid interactions⁴, direct particle
collisions^3,4 and particle-wall interactions⁶. More
studies are required to investigate the relative magnitude of these mechanisms
at different fluidization conditions and for different particle properties. The
focus of this study is to measure the local instantaneous concentration distribution
of particles in a liquid fluidized bed and calculate the RMS fluctuations based
on those measurements. These localized measurements are conducted for a wide
range of particle properties (i.e. Stokes numbers) at different bulk
concentrations. Here we only present the results for particles having
relatively low Stokes numbers (St = 122).

Methods:

The solid-liquid fluidized bed used in this study had an
internal diameter of 10.16 cm. Mono-sized spherical Nylon particles (d = 6 mm, ρ
=1150 kg/m³) were used as the solid phase and a dilute salt solution
(C_NaCl = 0.85 g/L) was the liquid phase. The fluid was circulated
through the bed at different superficial velocities using a centrifugal pump.
Fluid flow rate and temperature were measured upstream of the entrance to the
bed. A high-speed EIT instrument (Z8000, Industrial Tomography Systems) was
used to obtain the instantaneous solid concentration distribution recorded at a
sampling rate of 1160 frames per second. Electrical tomography is a robust
noninvasive technique with the unique ability of providing local concentration
fluctuations even for opaque concentrated mixtures^7,8. This
technique utilizes an array of sensors to measure the electrical impedance of
the medium which will then be used to deduce solid concentration using
Maxwell’s equations⁷. The measurements conducted by EIT are used to produce
a solid concentration map of the bed cross-section with 316 pixels.

Results:

At each bulk solid concentration, C̅, 8000 instantaneous
solid concentration maps were obtained. From these maps, the magnitude of the
RMS of the solid concentration fluctuations, C̅ʹ, was then calculated for each
pixel. Time-averaged solid concentration maps, such as those shown in Figures 1a,
1c, and 1e, indicate that, on average, the particles are uniformly distributed over
the bed cross-section for all the bulk concentrations tested here. The
fluctuations, on the other hand, are not uniform. Figures 1b, 1d, and 1f show that
C̅ʹ in the near-wall region are 2 to 4 times higher than that
measured in the center of the bed. Greater values of C̅ʹ in the near-wall
region were also observed for spherical glass particles with moderate Stokes
numbers (153 ≤ St ≤ 480)⁶, and spherical Delrin
particles with low Stokes numbers (St = 94)⁹.

At the lowest bulk solid concentration tested (C̅ = 0.05),
the magnitude of the RMS of fluctuations falls within the range of C̅ʹ
= 0.005 to 0.022. By increasing the bulk solid concentration to 0.27, the range
of the fluctuations increases to C̅ʹ = 0.01 to 0.038. When the bulk
solid concentration is increased from 0.27 to 0.38, the magnitude of the
fluctuations does not change appreciably. Further increase in the bulk solid
concentration (up to C̅ = 0.52) decreases the range of the fluctuations to
C̅ʹ = 0.01 to 0.028. Similar trends for the changes in the magnitude
of C̅ʹ with the change in the bulk solid concentration were obtained
for particles with lower Stokes numbers (Delrin, St = 94)⁹.

By increasing the Stokes number from 94 (Delrin) to 122
(Nylon), the magnitude of the RMS of fluctuations increases. The magnitude of
fluctuations for both of these particles is smaller than that of particles with
moderate Stokes number (Glass, St = 480)⁶. This finding is in agreement
with the experimental results of Zenit and Hunt⁴, which showed that by
increasing the Stokes number the magnitude of the fluctuations increases and approaches
the values predicted by the Buyevich and Kapbasov model³.

Conclusions and future work:

The results of this study demonstrate the non-uniform
distribution of the local solid concentration fluctuations over the bed cross-section
for Nylon particles (St = 122). The magnitude of the fluctuations in the near-wall
region was found to be 2 to 4 times greater than that of the center of the bed.
These results, along with the previous work for Delrin particles (St = 94) confirm
the importance of local instantaneous concentration measurements. Future
experiments will focus on particles with higher Stokes numbers (800 < St <
3600). Collectively, these results can be used to create more accurate models for
prediction of the magnitude of local concentration
fluctuations. They can also be used to validate and improve numerical models of
fluidization.

References:

[1] Epstein, N., Applications of Liquid-Solid Fluidization, Int.
J. Chem. React. Eng., vol. 1, no.1, 2002.

[2] Gevrin, F., Masbernat, O., and Simonin, O., Granular
pressure and particle velocity fluctuations prediction in liquid fluidized
beds, Chem. Eng. Sci., vol.63, no.9, pp.2450–2464, May 2008.

[3] Buyevich, Y.A., and Kapbasov, S.K., Random fluctuations in
a fluidized bed, Chem. Eng. Sci., vol.49, no.8, pp.1229–1243, Apr. 1994.

[4] Zenit, R., and Hunt, M.L., Solid fraction fluctuations in
solid–liquid flows, Int. J. Multiph. Flow, vol.26, no.5, pp.763–781, May
2000.

[5] Gevrin, F., Masbernat, O., and Simonin, O., Numerical study
of solid–liquid fluidization dynamics, AIChE J., vol.56, no.11, pp.2781–2794,
Nov. 2010.

[6] Hashemi, S.A., Velocity and concentration fluctuations
in concentrated solids-liquid flows, PhD thesis, University of Alberta,
Edmonton, Canada, 2013.

[7] Dyakowski, T., Jeanmeure, L.F.C. and Jaworski, A.J.,
Applications of electrical tomography for gas–solids and liquid–solids flows —a
review, Powder Technol., vol.112, no.3, pp.174–192, Oct. 2000.

[8] Norman, J.T. and Bonnecaze, R.T., Measurement of Solids
Distribution in Suspension Flows using Electrical Resistance Tomography, Can.
J. Chem. Eng., vol.83, no.1, pp.24–36, 2005.

[9] Marefatallah, M. and Sanders, R.S., Solid Volume Fraction
Fluctuations in a Liquid Fluidized Bed, Proceedings of the 9th International
Conference on Multiphase Flow, Firenze, Italy, 2016.