PARTICLE MIXING IN GAS-SOLID BUBBLING BED
K. SAVOLAINEN AND R. KARVINEN
Department of Energy and Process Engineering
Tampere University of Technology, Finland
Kai.savolainen@tut.fi, Tel. +358 40 8490882
ABSTRACT
The goal of the study is to increase the understanding of a mixing process in a bubbling
bed. Mixing of solid particles in a 1360x420-mm room-temperature gas-solid bubbling
fluidized bed was studied. Air at room temperature was used with plastic particles of 3.3
mm diameter and the particle density was equal to 1300 kg/m3. The minimum fluidization
velocity of the particles is 0.85 m/s and the actual fluidization velocity used in the
experiments was from 1 to 2.5 m/s. White and black particles were used and the particle
concentration was measured in the bed by taking samples from the bed at different times.
White and black particles in each sample were separated, counted and weighted. The
diffusivity coefficient of particles in the bed was obtained from an analytical equation,
which governs the concentration as a function of time.
Keywords: Particle mixing, Gas-solid fluidization, Bubbling bed, Cold model
1. INTRODUCTION
Mixing of particles is an important factor in fluidized bed combustors. The horizontal
mixing of fuel particles affects the performance of the beds. The mixing has a great
influence on the distribution of heat release from the fuel. In a bubbling fluidized bed the
particle movement is caused by rising bubbles. Bubbles transport particles upwards in their
wakes and particles flow downwards in the places, where there are no bubbles. An
important factor in the operation of a fluidized bed combustor is how the fuel particles are
mixed with the bed particles. In bubbling beds the particle concentration is high, which
makes the horizontal mixing of coal or any fuel difficult. According to the literature the
horizontal convective mixing of particles occurs mainly at the bed surface, where bubbles
burst (Mostoufi et al. 2001). In the regions, where velocity gradients are high, also the
diffusive mixing contribute to the process. The vertical mixing is many times larger than
the lateral one, and contribute more effectively to the bed mixing (Kunii & Levenspiel,
1977).
2. REVIEW OF MIXING STUDIES
2.1. Radioactive tracking technique
Mostoufi et al. (2000) studied the diffusivity of solid particles in a 152-mm gas-solid
fluidized bed with 38-μm sand and 70-μm FCC particles. The column was made of a plexi
glass-pipe with 1500 mm height. The gas was air at room temperature and at atmospheric
pressure. Superficial gas velocities were from 0.5 to 2.8 m/s for sand, and from 0.44 to 0.9
m/s for FCC, respectively. The initial height of the bed was 0.22 m for all the experiments.
Movement of a tracer was observed by radioactive particle tracking technique. The tracers
were made of a mixture of gold powder and epoxy resin. Tracer sizes of 420, 500 and 600μm were used. They were being activated in a nuclear reactor to each experiment. The
produced isotope 198Au, emitting γ-rays, can be found by detectors. In each experiment, a
single tracer was placed into the bed to move freely among the bed particles. The
movement of the tracer was monitored for 5 hours, during which about 820 000 points were
acquired.
Stein et al. (2000) observed particle motion in a 3-D bubbling fluidized bed at atmospheric
pressure. Positron emission particle tracking (PEPT) was used to observe particle trajectory
and solids velocity. Two acrylic columns were employed: a small one with a 70mm
diameter and the height of 430 mm, and a large one with a 141 mm diameter and the height
of 600 mm. Distributor plates were made of a metal containing 80-130 holes with 0.5-1.55
mm diameter. During the experiment, the column was placed between two γ-ray detectors.
Resin beads with 0.55-0.75 mm in diameter and a density of 1100 kg/m3 were used. The
minimum fluidization velocity of these particles is 0.11 m/s. The tracers used were resin
beads (660-μm) selected from the bulk. An ion exchange technique was employed in order
to produce 18F (half life=110 min.), and tracer particles were activated by ion exchange
with the radioactive water produced.
2.2. Thermal tracking technique
Glicksman et al. (2008) used a thermal tracking method in order to study mixing
charasteristics in a ¼-scale model (0.85x2.1 m) of a pressurized bubbling fluidized bed
combustor. The model was at room temperature and pressure. Particles cooled by liquid
nitrogen, were injected into the bed in the same way as pulverized coal is injected. An array
of thermistors was mounted inside the bed. Thermistors were used to trace the path of the
cooled particles when they are mixed with the other bed particles. It was assumed that heat
transfer to the air was negligible during the short time period detected (10 s.). After a short
period of time the bed returns to its initial temperature and another test can be performed.
Multiple runs at the same test conditions were made. For each thermistor, the temperature
results at each time were averaged.
2.3. Wall effect
Liu et al. (2007) studied the wall effect in micro fluidized beds (MFB). They measured the
minimum fluidization and minimum bubbling velocities of silica sand particles in air-blown
micro beds. Three different particle sizes were used: 96.4, 242.1 and 460.6-μm. The
particle density is 2600 kg/m3 in any case. Beds of 120 mm high and with inner diameters
of less than 32 mm were studied. Static bed heights varied from 20 to 50 mm. The
fluidization characteristics in MFBs should be different from those in the ordinary-size
fluidized beds due to strong wall effect.
Experiments were carried out in three cylindrical quarts-glass columns with a height of
120mm and inner diameters of 12, 20 and 32 mm, respectively. A sintered plate of 5 mm in
thickness made from 150-μm silica sand particles was used as a gas distributor.
2.4. Phosphorescent tracking technique
Pallarès and Johnsson (2006) applied a phosphorescent particle tracer to study the mixing
of fuel particles in fluidized beds. The technique is based on capturing the phosphorescence
of a single particle by a video recording with a digital image analysis in a 2-dimensional
fluidized bed with a transparent front wall. The experimental rig used is a cold riser with a
cross section of 0.02x0.4 m and a height of 2.15 m, having a perforated plate as an air
distributor. The front side of the riser is made of transparent Perspex. Since the solids
mixing in the bottom region was the focus of the work, only the first 0.85 m of the riser was
video recorded. A recording time of 20 min per run was chosen, because it was noticed,
that recordings longer than 15 min provided no additional information.
Glass beads with the size and the density similar to those of sand particles typically used in
fluidized bed boilers were used as a bed material: dp=330 μm and ρp=2600 kg/m3. Particles
belong to the group B in the Geldard classification and have a minimum fluidization
velocity umf=0.12 m/s and a terminal velocity of ut=1.76 m/s under ambient conditions.
Several fluidization regimes were included in the runs: bubbling, turbulent, circulating and
pneumatic. The height of the dense bottom bed varied from 0 to 0.69 m.
Tracer particles used were cylindrical capsules made of transparent plastic filled with a
self-phosphorescent solution. The reference particle had a large size and a lower density
simulating a fuel particle in a fluidized bed boiler. In order to study the influence of the size
and the density, two types of tracer particles were used: one type smaller in size and the
other with a higher density similar to that of the bed solids. The method of evaluation is
based on the tracking a single particle and it was assumed that interactions between fuel
particles do not influence their mixing process.
2.5. Possibilities of numerical modeling
Numerical modeling of the fluid flow has increased rapidly as a result of computer
development. The movement of a single bubble in a bed has been solved though it requires
plenty of computational capacity and there are problems to fix boundary conditions and to
take into account the interaction between particles. The modeling of very small scale units
can be performed, but the numerical calculation of a real bubbling bed is not possible in the
near future (Huang, 2007).
3. MIXING EXPERIMENTS IN PLASTIC PARTICLE MODEL
The experimental arrangement is shown in Figure 1. The test rig consists of an air blower
(not shown in the figure), an air chamber, a grate and a reactor with transparent walls. Air
at room temperature was blown into the air chamber (a) below the grate (b). A thick sieve
was placed above the grate in order to prevent particles falling down into the air chamber.
Air volume flow rate was measured with an orifice. The air flows into the reactor through
the grate with 30 holes with diameters equal to 102 mm. The grate geometry, i.e., the
number and size of grate holes, was chosen according to test results without the grate
showing the structure of the free bubbling bed. In a bubbling bed, in which the air was
blown through the sieve, the locations of bubbles are chancing arbitrarily. When a grate
with fixed holes was used, bubble locations were permanent. In the bed, plastic white and
black particles with diameters equal to 3.32 and 3.86 mm were used. Particle densities were
1300 and 950 kg/m3, respectively. The bed height was 125 mm. The minimum fluidization
velocity of the bed particles in the study is umf=0.85 m/s and the actual fluidization velocity
used in the experiments varied from 1 to 2.5 m/s. Particle properties in the study are shown
in Table 1.
Table 1. Particle properties.
Particle
color
Particle
diameter
Ø [mm]
Particle
volume
[mm3]
Particle
density
[kgm-3]
Particle
bulk density
[kgm-3]
Particle
mass
[g]
White
3,32
19.2
1300
900
0.025
Black
3.86
30.1
950
630
0.029
The study is based on the collection of particles from the bed at different times. Particles
with two different colors were used. White particles were used as the bed particles and
black particles were tracer particles. At the beginning of an experiment black particles were
located in the center of the reactor (Figure 1c). The width of the black particle region was
100 mm. When the air flow from the blower was fed into the reactor by opening the valve
of the blower, the mixing started. After a fixed period of time, the valve was closed and the
Reactor
Bubbling bed
420
Thick sieve
hole Ø 102 mm
10 columns
3 rows
a bubble
145
Air tube from blower
1360 mm
Air chamber
Grate hole size and distribution (a part of grate)
(a)
(b)
y
x
125
Black particles
White particles
White and black particles mixed
(c)
(d)
Sample gap
Pipe (plastic)
y
z
Particle distribution (y-z-plane)
(e)
Piston shaft (aluminum)
Handle
(f)
Figure 1. Test rig: bubbling bed (a), grate hole distribution (b), experiment initial condition (c), mixed
condition of particles (d), vertical and horizontal mixing condition (e), sample probe (f).
bubbling was finished. Particle samples consisting of a number of black and white particles
were taken from the bed at different locations with a sample probe, which is shown in
Figure 1f. The white and black particles in each sample were separated, counted and
weighted. The volume fraction of black tracer particles was calculated.
The concentration profile of black particles in the bed is governed by a type of equation
similar to the heat conduction equation, namely
∂C
∂ 2C
=a 2
∂t
∂x
(1)
in which C is the particle concentration and a the diffusivity.
The solution of the problem in Figure 1c can be found by using the Laplace transform
technique (see Appendix 1)
2
⎞
⎛ x
C = C0 e (βx + aβ t )erfc⎜⎜
+ β at ⎟⎟
⎠
⎝ 2 at
(2)
β is the coefficient depending on the thickness of the black zone in Figure 1(c). The
diffusivity coefficient a can be found from Eq. (2), when the concentration C is known on
the basis of measurements in a fixed location and at the known instant of time.
4. RESULTS
Particle samples taken from one run with the sample probe are shown in Figure 2. The
samples were taken from the bed at the location y=60 mm and z=0. The vertical and
horizontal distribution of particles is shown in Figure 1(e). The Figure shows that the
mixing in the y direction and in the z-direction is homogenous, because the tracer particles
are uniformly distributed. Samples were taken at five different x-locations, namely x=0,
150, 250, 350 and 450 mm. The result of one sample is shown in Table 2. Fluidization
velocity used was equal to 1.7 m/s. The diffusion coefficient appears to be larger when t=10
s and x=250 mm. The bubble dimension in the bed is db= 100 mm. It is obvious that the
first bubbles, when bubbling begins, throw black particles from the centerline of the bed.
These particles drop on the bed surface at this location. When the bubbling continues, the
coefficient approaches the same value, which is valid everywhere in the bed.
t2= 21 s
t1= 10 s
X=0 mm
150
250
350
450
Figure 2. Particle samples taken from bubbling bed with probe.
Table 2. Typical particle sample.
Sample
probing time
t [s]
uf=1.7 ms-1
Sample
probing
location
x [mm]
Sample
mass
m [g]
Black
particle
volume fraction
[m3/m3]
Diffusion
coefficient
a [m2/s]
10
10
10
10
10
0
150
250
350
450
47.5
53.6
65.1
76.9
69.2
0.216
0.119
0.0810
0.0206
0.0049
0.00172
0.00183
0.00293
0.00153
0.00156
21
21
21
21
21
0
150
250
350
450
34.6
68.2
53.3
69.0
67.1
0.156
0.109
0.0966
0.0552
0.0285
0.00168
0.00189
0.00212
0.00194
0.00176
5. CONCLUSIONS
The particle mixing in a bubbling fluidized bed cold-model was measured by taking tracer
particle samples from the bed. In the measurements concentration changes of tracer
particles were recorded in fixed locations. The experimental arrangement was such that
one-dimensional assumption can be made. The mixing is governed by the equation similar
to the heat conduction, and its solution can be found analytically. The effective diffusion
coefficient of tracer particles can be obtained by solving the inverse diffusion problem.
It was observed that the mixing in a horizontal direction is very uniform when the tracer
and bed particles have almost the same size and density. In that case the effective diffusion
coefficient of lateral mixing is also constant.
References
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APPENDIX 1
Mixing in a semi-infinite domain is shown in a figure below. Initial black particle
concentration in the white domain is C(x, t=0)=0.
Black
particles
∞
C(0,t)
C(x, t)
0
White
particles
C(∞,t)=0
∞
x
δ
The governing equation of mixing is
∂C
∂ 2C
=D 2
∂t
∂x
(1)
Diffusivity, boundary and initial conditions are
δ
∂C (0, t )
∂C (0, t )
=D
∂t
∂x
(2)
C(∞, t) = 0, C(0, t=∞) = 0
By using Laplace transformation: L[f] =
d 2C s
− C=0
dx 2 k
∫
∞
0
fe − st dt = f , equation (1) and (2) give
(3)
sδ C (0, s ) − δ = D
d C (0, s )
dx
(4)
The solution of which is
C=
1
e − qx ,
sδ + Dq
q=
s
D
(5)
The inverse transformation of (5) is
2
⎛ x
⎞
C = C 0 e (βx + Dβ t )erfc⎜⎜
+ β Dt ⎟⎟
⎝ 2 Dt
⎠
(6)