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Electrostatic effects on entrainment from a fluidized bed
Powder
Technology,
57 (1987) 55 - 67
55
‘Electrostatic Effects on Entrainment from a Fluidized Bed T. BARON The ~niversi~
of Western Ontario,
Faculty
of Engineering Science, London,
Ont. N6A 539 (Canada)
C. L. BRIENS, M. A. BERGOUGNOU Ins~tut
Francais du Petrol-ENSPM,
1 ti 3 avenue du Bois Prkau, 92500 Rueil Mu~maison {France)
and J. D. HAZLETT IX&-ion of Chemistry,
NRC, Ottawa,
Oat. KlA
OR9 ~Canada~
(Received April 24, 1987)
SUMMARY
Effects of electrostatics on entrainment from a gas-solid f~uidi~ed bed were studied in a 0.61-m I.D. column with silica sand. The flux of particles en~ained above the transport disengaging height almost doubled when the relative hum~ity of gas was increased from 10% to 30% and then stabilized when humidity was further increased. However, neither the average bubble gas ~act~n nor the flux ejected from the bed surface were affected by humidity. Electrostatic effects did not promote particle agglomeration in the freeboard, since the same proportion of clusters was measured in ejected fluxes at low and high humidity (around 10%) and at high hum~ities (super~r to 30%). The electrostatic pressure drop in the freeboard, however, accounts for around 50% of the total pressure drop at low gas humidity. By adapting an entrainment model based on a choking load model to take this elect~static pressure drop into account, a 26% decrease in the flux entrained above the TDH was predicted. The effect of electrostatics on entrainment is thus primarily caused by the increase in the pressure drop in the freeboard which results from electrostatic interactions between the column wall and the particles.
INTRODUCTION
Entr~nment of particles from fluidized bed reactors is an important area to consider in their design. The ability to predict the variation of the flow rate of entrained solids and their size distribution is required for the
design of cyclones which can effectively limit particulate loss. As bubbles break at the surface of the fluidized bed, particles are ejected from the bed surface and are entrained by the upward flowing gas stream. Gas bubbles bursting at the surface of a fluidized bed are analogous to intermittent jets imposing a highly irregular velocity profile across the column. The jets are eventually dissipated to the superficial gas velocity at some equilib~um height above the bed surface referred to as the transport disengaging height (TDH) . The entrainment then becomes relatively constant and presumably equal to the maximum or saturation dilute-phase particle-carrying capacity of the gas stream at its superficial velocity if there is enough material ejected from the bed. Above the TDH, the column therefore operates as a dilute-phase vertical pneumatic transport line. Thus, it is clear that entrainment is subject to the same electrostatic phenomena as gas-solid transport even if in general the vessel diameter is larger and wall effect weaker in the freeboard of fluidized beds. Geldart and Wong [1] studied the effect of humidity of the fluidizing gas on the flux of particles entrained above the TDH of an &cm I.D. fluidized bed in the slugging regime. They tested a variety of group A and C powders according to Geldart’s powder classification [2]. They found that the entrainment flux was reduced when the relative humidity of the ~uidizing gas was increased. They attributed these results to the increase in the cohesivity of the powder with the relative humidity of the fluidizing gas. This increase in powder cohesivity was @ Elsevier Sequoia/Printed in The Netherlands
56
confirmed by bed expansion measurements. As non-porous fine powders become more cohesive with increased humidity, fluidization is poorer and the bed expansion is reduced. They commented that electrostatic forces, which are affected by humidity, had only a minor role to play in their system. Preliminary experiments conducted at the University of Western Ontario in a 0.61-m dia. fluidization column indicated that gas humidity had a significant effect on the entrainment flux. The first objective of this study was therefore to quantify the effect of humidity and electrostatics on the entrainment of solids from large fluidized beds. The second objective was to establish whether the humidity effect could be attributed to changes in the behaviour of the dense fluidized bed or to electrostatic forces acting on the particles in the freeboard.
PRESENTATION
OF
ELECTROSTATIC
PHE-
NOMENA
Importance
of electrostatic
square of the particle radius and that highly asymmetric charging of dust clouds led to charge segregation and ultimate sparking. Masuda et al. [6] have also studied static electrification in gas-solid pipe flow, especially with respect to particle-wall collisions. They introduced a contact time concept in their analysis and gave a simplified expression for the wall-current. They paid particular attention to the fundamentals of charge transfer and classified a number of materials as to composition and size. More recently, Smeltzer et al. [7] studied a Plexiglass-glass system in dilute-phase transport to examine the individual particle interactions with the confining wall at relative humidities varying from 25 to 65%. At constant loadings, greater electrostatic effects were seen for small particles than for large particles due to the high particle number density and thus increased interactions for the smaller particles. Higher loadings at low relative humidities also produced increased electrostatics effects. Ally [S] expanded this type of analysis to the dense-phase regime.
phenomena
The phenomenon of electrification in gassolid transport is often neglected in the analysis of many processes. However, the electrification of particles can be extensive in a gas-solid system, since only one unit of electronic charge per 10’ surface atom needs to be transferred to cause electrical breakdown of the surrounding air, according to Klinzing [ 31. The large charges on small particles are related to the large surface-to-volume ratio that is characteristic of these fine materials. Often these electrostatic effects are difficult if not impossible to duplicate, causing much frustration to the experimenter. Some parameters of importance are humidity and temperature of the gas, moisture content of the solids, and surface conditions of the flowing solids and of the wall. Flow rates of the solid and gas stream, loading of the stream, particle size and shape are other important factors in electrostatics or gas-solid flow systems. Soo [4] has been a pioneer in electrostatic analysis, presenting a rational approach to analysis through solid mechanics. Kunkel [ 51 experimentally studied the dust-charging mechanism. He found that the average charge increased somewhat more slowly than the
Lessening
electrostatic
charging
In most cases, electrostatics present very troublesome conditions in the handling of gas-solids systems. Elimination of the phenomenon would often simplify system design considerably. The primary safety procedure toward reducing the deposition of material is proper grounding of the column and of the cyclones to avoid the charging and eventual sparkover. This is necessary but not sufficient. The most common way to reduce electrostatic charging is to raise the relative humidity of the carrier gas. It has been demonstrated experimentally that electrostatic effects can be totally eliminated at relative humidities greater than 75%. This was shown in two experiments performed by Peters [9] on the flow of glass beads in a plastic tube (see Figs. l(a) and l(b)). The pressure drop data were converted to friction factor values by subtracting gravity, and acceleration effects were subtracted and the difference between the values of the ratio of two-phase friction factor to single-phase friction factor f,/fg can be attributed to electrostatic forces. The procedure of humidifying the air to eliminate charging is relatively simple and can be closely
51
Re =
14x
0
1.9 x 104
A26x
1
0.00,
104
0
IO’
I
i
0002
0003
1
0004
0005
I
0.006
I
0007
0008
controlled. In most temperate climates, the dry winter air conditions generally set the stage for large electrostatic effects in gas-solid flows according to Klinzing’s directions [3]. Loeb [lo] measured charge reductions of 50% at 15% relative humidity and complete reduction to zero at 60% relative humidity at standard temperature and pressure. Soo [ll] correlated data from Turner and Balasubramanian [ 121 to give the distribution of charge to mass ratio of 83 pm glass particles at various humidities and showed that the alteration of particle charging is greatly affected by humidity control as reported in Fig. 2. Use of humidity for the reduction of electrostatic charging must, however, be checked against condensation and frost formation. Humidity control is also not suitable for a hygroscopic material. In this case, grounding and reduction of particle loading are left as the basic means of charge control.
t_ 95
h
t
v h;=19%rh. a h2 =28%rh. 0 h3 =38X r.h. b
Dato.Tumer,el 01.
Charge to Mass Ratlo, C/kg-
i 4
0.3
0. I
Re=
1 4 x IV
0
18X
4
104
EXPERIMENTAL
1 1
(b)
0
I
1 I
0.001 0.002 0003
Fig. 2. Cumulative percentage of particles with charge to mass ratio equal to or greater than a certain value (from [ll]).
I
0004
0.005 0.006 0 007 0008
w,. kg/s
Fig. 1. Effect of humidity on friction factor from [9]. (a), Ratio of two-phase friction factor to singlephase friction factor as a function of bead feed rate for 25pm beads in silastic tube (relative humidity = 25%); (b), ratio of two-phase friction factor as a function of bead feed rate for 25-pm beads in silastic tube (relative humidity = 80%).
The fluidized bed used in this study was 0.61 m in diameter, 7.5 m high, and equipped with static pressure taps at numerous positions along the column height. As shown in Fig. 3, it consisted of a Plexiglass windbox, a carbon steel bed section, three Plexiglass freeboard sections, and two carbon steel sections above the TDH at the top of the column. Static pressure measurements allowed the evaluation of bed height, bed density and other properties of the operating bed. The air distributor consisted of a
58
desired bed conditions had been established, the bed was allowed to operate for 2 h to reach steady state before entrainment data were collected. The bed material was unground silica sand, grade F-140 supplied by the Ottawa Silica Sand Company. Its apparent particle density is 2650 kg/m3. The sand had been sieved using a 150-mesh (105~pm) stainless steel screen on a Rotex Model 11 GP shaker in order to reduce its Sauter mean diameter to 82 pm. These solids were charged to the column and elutriated until the bed size distribution stabilized. The bed particle size distribution is given in Table 1. TABLE
A,
High-pressure
(Chinese
hat);
air; 6, air from D, windbox;
port; G, pressure J, elliptical cone sections; primary
M,
rotameter;
E, grid
plate;
C, conical F, solids
baffle
cyclone
cyclone; R. diverter dipleg; U. pneumatic
P,
inlet
extension;
pressure
control
valve; S, Plexiglass lift line; V, ejector.
Fig. 3. Fluidization
N,
manual
valve;
0.
sections;
from
Largest diameter size cut
in
Coulter
Counter
analysis
Cumulative volume
%
(Pm)
discharge
taps; H, sampling ports; I, pneumatic seal; collector; K, flexible vent hose; L. metallic
cyclone;
1
Bed composition
hoist;
0,
secondary T, cyclone
column.
12.7-mm aluminum plate fitted with 16 conical top, acrylic tuyeres on a 114-mm square pitch. Each tuyere provided four 6.35-mm diameter openings inclined with a downward angle of 45” to the horizontal, resulting in a fractional grid open area of 0.7%. Fluidizing air of controlled humidity was used. Superheated steam was injected downstream of the rotameter to control the humidity of the air entering the column. Low-pressure steam (150 kPa absolute) passed through a pipe wrapped with electrical heating tape. The steam system was run on bypass (discharging into the lab) until the steam temperature indicated that the steam superheat was 30 to 40 “C. The flow of steam was controlled manually and the fluidizing air relative humidity measured by a wet bulb/dry bulb hygrometer mounted in parallel to the main flow. The mixing was so rapid that no fog or condensation was observed in the air line or in the column. Humidity of the outlet air was measured to check that there was no retention of water in the column. Once the
6.35 8.00 10.08 12.7 16.0 20.2 25.4 32.0 40.3 50.8 64.0 80.6 101.6 128.0 161.0 203.0
0 0 0.09 0.18 0.30 0.36 0.40 0.42 1.23 5.08 20.32 50.03 87.49 97.29 99.42 100.00
Entrained particles were recovered by a pair of cyclones mounted in series. Solids collected by the primary cyclone returned to the bed via a dipleg. A valve between the two cyclones allowed manual control of the column pressure. The secondary cyclone collected a negligible quantity of solids during the experiments described here. Entrainment fluxes were measured by using a movable semi-elliptical cone which could be raised or lowered to change the height of the freeboard space above the bed. The gas-solid mixture thus collected was sent to the primary cyclone. The flux of solids recovered by the primary cyclone was determined by diverting the particles which flow through the dipleg
59
into a container for a given duration and by weighing them. The flux of solids escaping the primary cyclone was negligible, as determined by the amount of solids collected by the high-efficiency secondary cyclone. As the cone approaches the bed surface, the flow will no longer be capable of turning to accommodate the cone profile and the impaction of solids on the surface of the cone should increase. This will result in lower measured fluxes than those actually present. Thus, the cone is always at least 70 cm above the bed surface. Size analyses were performed using a Model TAII Coulter Counter with population accessory. Samples were characterized by their Sauter mean diameter. Standard riffling techniques were used to obtain an appropriately small sample for the Coulter Counter.
EXPERIMENTAL
RESULTS
The relative humidity of the fluidizing gas has a strong effect on the entrainment of particles, above the TDH, as demonstrated in Figs. 4(a) - (d). At all gas velocities, the flux 50
F, of particles entrained above the TDH increased by a factor of 2 when the relative humidity was increased from 7% to 30%. Above a relative humidity of 30%, a plateau was reached and further increases in humidity had no further effect. A relative humidity of the inlet gas of more than 30% thus prevents any electrostatic phenomena in the fluidization column. Vertical profiles of the flux of collected particles were therefore measured in the column at low humidity and at high humidity. ‘Low humidity’ means that no steam was added in the inlet gas. The relative humidity of the inlet air was then around 10% and electrostatic phenomena occurred in the column. ‘High humidity’ means that superheated steam was injected in the inlet gas and the controlled relative humidity was well above 30%, i.e., between 40% and 60%. Values from a typical experiment are reported in Table 2. The accuracy on the entrained flux was around 5% above the TDH and 15% near the bed surface. Figure 5 shows two entrainment profiles obtained at exactly the same conditions except that one run was carried out at a relative humidity of 48.3% and the other at a relative humidity of 11.4%. The run at low humidity gave significantly lower entrained fluxes all along the freeboard.
30 20 z VI “E ;
10
6
w
4
:
3
y :
2
=i
1
Typical
entrainment
Cone height above grid
% 2
2 profile
run
Superficial gas velocity (m/s) Inlet air conditions: Temperature (“C) Pressure (kPa) Relative humidity (‘%) Bed characteristics from pressure balance: Bed height (m) Bed density (kg/m3) Bed voidage
c” s
TABLE
0.5
(m)
03
4.65 3.89 3.28 2.36 2.21 2.06 1.91 1.75 1.60 1.45
2
0.2
01 0
10
20 HUMIDITY
30 OF
40 INLET
50 GAS
Fig. 4. Effect of humidity on entrainment TDH, (m), Us = 0.15 m/s;(@), Ug= 0.20 U, = 0.25 m/s; (x 1, Up = 0.30 m/s.
60
(%I
above the
m/S;(.),
70
Average
fiux
Standard
(g/(m’s))
(g/(m2s))
4.04 3.82 3.88 4.39 4.93 5.14 7.27 9.31 24.15 30.11
0.22 0.14 0.11 0.21 0.35 0.73 0.84 0.87 2.12 3.78
0.201 28.2 20 48.3 0.774 1236.5 0.5334 deviation
60
x
0
05
1
15
HEIGHT
Fig. 5. Entrainment ities.
2
25
ABOVE
3 THE
profile
35
4
GRID
45
E-
-
B-
Gnf
(31
1 - f,f
The bed voidage cmf and the gas velocity U,, at the minimum fluidization conditions were measured in a small column. Their values were: iJmf = 9.8 1O-3 m/s and cmf = 0.480. A good agreement with this value was obtained by using the aerated particle density determination technique given by Geldart and Abrahamsen [14], which yielded emf = 0.475. Figure 6 shows that there is no significant effect of the gas humidity or superficial gas velocity on the bubble volume fraction. An average value for xB of 0.10 can be retained for the present experimental conditions.
5
lm)
at low and high humid-
Experiments at various velocities ranging from 0.15 to 0.30 m/s were carried out in the fluidization column to establish whether the humidity effect could be attributed to changes in dense fluidized bed behaviour or to electrostatic effects on particles in the freeboard.
SE
0.12
;
I .
n
HIGH
0
LOW
HUMIDITY
0
30%1
c< 30%)
HUMIDITY
0
0.11
0
ANALYSIS
OF DENSE
Two basic experimental results were used to characterize the dense bed behaviour: the bed expansion and the flux of particles ejected from the bed surface. Bed expansion teristics
and bubble
phase
The bed voidage is determined from the bed pressure drop:
E=l-Pbed
@bed -
H bed
0 -------
_-__ 0.10
g
0
L
0 15
t
0.18
0.20
Fig. 6. Effect of humidity volumetric bubble fraction.
(-2)
According to the two-phase theory [ 131, the fluidized bed can be separated into the bubble phase and the emulsion phase and the dense phase voidage is independent of the gas velocity and equal to e,f, the bed voidage at minimum fluidization conditions. If E is the overall bed voidage at operating conditions, the bed volume fraction xB occupied by the gas bubbles can be obtained:
.
t
SUPERFICIAL
(1)
8 .
m
0.10
directly
Is= ,102 _----
AVERAGE
1
0.09L
where =
w i m 2
charac-
Ps
Pbed
0
z I&
BED BEHAVIOUR
GAS
0
“,
I
0.25 VELOCITY
0.30
w
(m/51
and gas velocity
on
An estimation of the average bubble size in the dense fluidized bed can also be determined from the two-phase theory, which gives as flow rate through the bubble phase QB = AUBXB = A(U,
-
urn,)
(4)
Thus, u,
=
u, -
Ulnf
(5)
xB
An estimation of the diameter of the sphere of bubble equivalent volume can be obtained from Hilligardt and Werther’s expression [ 151:
61 UB = ,g(u,
-
U,,)
+ 0.71e(gds)“~5
(6)
where ,$ and 8 are correction factors which depend respectively on the Geldart group to which the powder belongs and on the column diameter. In our case (Group A powder, D, = 0.61 m) the corresponding values are
8 = 3.2
(7)
Dco*33= 2.71 which yield da = 0.0275[&
- 0.8(U, - &,,)I*
(8)
It should be noticed that using the standard equation for bubble velocity, which does not take the bed diameter into account (4 = 8 = l), leads to erroneous values for the bubble diameter. At high gas velocities, the bubble diameters thus estimated were larger than the column diameter. Figures 7(a) and 7(b) show that the bubble diameter increased the same way at low and high humidities. Thus, it seems that gas humidity had no effect on bubble behaviour. Estimation of the total flux ejected from the bed surface A higher flux of particles ejected into the freeboard because of a change in dense bed behaviour could also explain an increase in the flux of particles entrained above the TDH. To compare the values of the ejected flux F, at low and high humidities, a new method for the determination of the ejected flux based on cluster flux measurements which had been proposed by Baron et al. [16] was used. Clusters are agglomerates or ‘pieces of the bed’ projected into the freeboard by bubble eruptions at the bed surface. Their size can be assumed to range from 1000 average particle volumes to 10% of the bubble volume at the bed surface according to George and Grace [ 171, who observed that only 40% of the solids present in the wake of the bubble is effectively ejected in the freeboard. As the maximum height that non-entrainable individual particles ejected from the bed can reach in the freeboard is always very small (less than 0.15 m under our experimental conditions), practically all the non-entrainable particles present below the TDH belong to
u,
(a)
GAS
VELOCITY
lm/sI
0.25
G
0.05
0 0
(b)
0.05
0.10
d,
HIGH
0.15
0.20
HUMIDITY
(ml
0.25
Fig. 7. Effect of humidity at various gas velocities on bubble diameter. (a), Effect of gas velocity; (b), effect of humidity.
clusters. Thus, the maximum height that clusters reach can be considered as the TDH. At low freeboard heights, the cluster flux becomes predominant and the individual particle flux negligible and the cluster flux ejected from the bed surface can thus be considered equal to the total flux F, ejected from the bed surface. It has also been shown experimentally [ 161 that cluster flux varies according to the exponential decay law and can be expressed as F, = F, exp(-aJ)
(9)
while the total flux is given by F = F,.+ F, exp(-aZ)
(10)
where 2 is the height above the bed surface. Figure 8 shows typical axial profiles of the total flux, the cluster flux and the individual particle flux.
62 34
-
3000
= en1000;
“E ;
700-
.?
500
-
: ;; z ? 3 0 .A
300
c
100 70
/ . .
.
I -
/‘_
30-
2 I
“I
0 .25
1
I
A.
I
I
I_
3
2 HEIGHT
I_,
ABOVE
THE
4
BE0
(ml
10
Fig. 8. Typical entrainment profile.
p
3000
-
2000
-
1000
-
700
-
500
-
400
-
300
-
200
-
100
-
70
-
50
-
LO
-
30
-
20
-
0.10
30
I
I1111111
100
Fe HIGH
A new linear regression method which uses both the total flux and the cluster flux experimental data yields a more accurate extrapolated value of the ejected flux by doubling the number of experimental points [16]. Figure 9 shows the variation of ejected flux with gas velocity at both low and high humidities. Figure 10 represents directly the 4000
I I I11111 10
300 HUMIDITY
0.15
0.18
.20
0.25 GAS
VELOCITY
0.30
0 35 (m/s1
Fig. 9. Evolution of the ejected flux with gas velocity (95% confidence intervals are shown).
3000
(g/(d,Il
Fig. 10. Effect of humidity on ejected flux (the rectangles represent the 95% confidence intervals).
effect of humidity on the ejected flux. Since the 95% confidence intervals for the ejected flux at different humidities overlap for each gas velocity (Fig. 9), it can be concluded that the flux ejected from the bed is not significantly affected by the gas humidity. This result confirms that the bubble size was unaffected by the gas humidity. Electrostatic effects on the dense bed behaviour thus seem to be negligible. This appears reasonable as the energy of jets and bubbles at gas velocities of around 20 U,, is much larger than the cohesion energy of the particles which might be affected by an electric field.
ANALYSIS OF FREEBOARD
SUPERFICIAL
1 1111111
1000
BEHAVIOUR
Comparison of cluster fluxes in the freeboard The cluster flux was measured at various freeboard heights [ 161. The evolution of the mean diameter of entrained particles at various freeboard heights was not affected by gas humidity. It was found that the values of the cluster flux well above the bed surface were slightly smaller at low humidity but that the percentage of clusters in the total entrained flux was not significantly affected by gas humidity. Similar results were obtained for gas velocities ranging from 0.15 to 0.30 m/s [18]. Agglomeration of particles in the
63
freeboard cannot therefore account for the observed effects of electrostatics on the entrained flux. This conclusion was confirmed by considering the TDH. The TDH can be predicted from the following equation, which was derived from a model for the cluster trajectories [ 191: TDH=
(2.llJ,)2
(11)
%
Since the gas humidity does not significantly affect the bubble velocity U, as demonstrated in Fig. 7, the TDH should therefore be independent of the gas humidity. Another equation for the estimation of the TDH [16]
(12) leads to the same conclusion since F, and a, are not significantly affected by the gas humidity. Effect of the electrostatic pressure drop in the free board Importance of the electrostatic pressure drop The measurement of energy losses by pressure drop in systems where electrostatic effects are present is sparse. Often, increases in pressure drop due to static electrification effects were noted according to Richardson and McLennan [20] and Clark et al. [21]. More recently, Morikawa et al. [22] found that the pressure drop through a horizontal acrylic pipe was doubled when compared with a grounded brass pipe because of electrostatic effects in pneumatic conveying. In general, the overall pressure drop for an electrostatic system can be measured and the analysis of the overall pressure drop can be interpreted in a similar manner to the simple two-phase flow case as AP = (1 -e)p,g L
+
2fgPgUg2 D
C
gravitational
fluid
term
term
+ fA41
- wg2
friction
+
APei L
20, solid
friction
term
electrostatic term
(13)
with the solid friction term expressed according to Jones [ 231. According to Klinzing [ 31, the electrostatic contribution to the pressure drop is given by L
(14)
ms
where E is the electric field, q the charge of the particle, and m, the mass of the particle. Analyses have been performed on data taken in Klinzing’s laboratory by Weaver [ 241. Figure 11 is a plot of the electrostatic pressure drop produced in a system consisting of a Selastic tube with glass beads at low relative humidities. The electrostatic pressure drop is the pressure drop measured over and above that predicted by eqn. (13), not including the last term attributable to the electrostatic effect. As would be expected, the smaller the diameter of the flowing particle, the greater the electrostatic charge that is generated. A reduction in particle size by a factor of 2 resulted in an increase in generated charges by nearly an order of magnitude.
25 pm particles, low humidity
-25%
,:/ y
0.010
0.020 K
0.030
0 w IO
1k/s
Fig. 11. Electrostatic pressure drop per unit length versus bed flow rate from [24].
Estimation of the electrostatic pressure drop Ally and Klinzing [25] studied the interaction of electrostatic charging and pressure drop in pneumatic transport. They observed that the electrostatic pressure drop decreases linearly with the moisture-solid ratios in a logarithmic representation. They tested various particle-tube systems and found in particular that the Plexiglass tube retains its
64
charge over a wider range of moisture ratios than copper or glass tubes. Using a loading ratio of solids to gas mass flow rates equal to 100, they found for a similar gas-particle system (7 5-l.trnspherical glass beads in a Plexiglass tube, absolute humidity around lop2 kg water/kg air) the following expression for the electrostatic pressure drop:
me, = -0.38
1
In -
t L
In x + 4.935
(15)
where APJL is the electrostatic pressure drop per unit length in N/m3 and x is the absolute gas humidity in kg water/kg air. This formula has been used to compute the electrostatic pressure drop at various absolute humidities in the fluidization column by assuming that the electrostatic effects were comparable in both our system and Ally and Klinzing’s. Ally and Klinzing’s loading ratio was PsWp
MS -= M!3
PP(l - c,)Ug = 100
(16)
with
=
u, - u,
(17)
As the solid holdup E, was very small (E, Q 1) and U, was very small compared with U, for the small particles entrained above the TDH (U, S U,), eqn. (16) can be rewritten as
MS - = 100 M,
Z-E
PS s
f-32 Thus, 1OOPg e,= PS
= 0.0453 Equation (14) can also be expressed as
@e,
(18)
-=Ke, L
where K = Eqp,/m,
is the electrostatic coefficient
Using both eqns. (16) and (15), this coefficient can be computed at various humidities from K = 0.0453~ exp(-0.38
lnx + 4.935)
(19)
Under the operating conditions of this study, the electrostatic pressure drop can then be expressed as @,I L
=KE, = &exp(-0.38
lnw + 4.935)
(20)
where e, is the solid concentration in the freeboard and x the absolute humidity of the fluidization gas. Prediction of the electrostatic effects on entrainment A new entrainment model developed by Brienset al. [26 - 281 has been adapted to take the electrostatic phenomena into account. The flux entrained above the TDH is predicted from the fluidized bed characteristics and from the total flux ejected from the bed surface F,. This model also assumes that the freeboard above the TDH can be described as a vertical pneumatic transport line. The flux of solids entrained above the TDH is thus limited by the choking load, i.e., the maximum flux of particles which can be carried by a gas flowing at a certain velocity. A simple physical model which assumes that a stationary annulus forms along the pipe wall at low velocities [27] is used to predict the onset of choking which occurs when this annulus occupies 25% of the total pipe crosssectional area. An electrostatic pressure term calculated from eqn. (18) can be used in the choking load calculation to take electrostatic phenomena into account for low humidity experiments. Electrostatic effects are assumed to be negligible at high humidity where they were not observed. This model was used to predict the effect of electrostatics on the flux entrained above the TDH. Table 3 summarizes the results obtained at low and high humidities for five gas velocities. A decrease of approximately 45% of the flux entrained above the TDH was observed experimentally in the column when the gas relative humidity was reduced from values superior to 30% to values around 10%.
65 TABLE 3 Comparison of experimental and calculated effects of gas humidity on flux F, of particles entrained above the TDH
ug
(m/s)
FO
(g/(m2s))
Relative humidity
AF’totd (Pa/m)
aPel F
Experimental F
tm
@I @I
W(m2s))
dP Wm)
F exP
Calculated Fn-FL
F,
-
W(m2s))
dP 0.W
79
18
122
20
278
25
400
30
957
12.2 67.9 14.6 33.0 11.4 48.3 10.4 38.2 9.3 32.5
0.07 0.04 0.10 0.07 0.19 0.12 0.28 0.20 0.58 0.41
51 0 50 0 52 0 52 0 55 0
0.49 0.89 1.5 2.3 1.6 3.9 4.6 8.6 9.5 16.5
The model predicts an average decrease of 26%. The predicted trend thus agrees well with the experimental values when one takes into account the limited quantitative information from which the electrostatic pressure drop can be evaluated. Moreover, although the prediction of the average particle diameter is not excellent, both experimental and calculated data show that electrostatic effects have no effect on the average size of the entrained particles. The electrostatic pressure drop is found to account for 50% of the total pressure drop at low humidity and similar
34 33 37 37 36 36 41 38 41 42
44
35 58 46 42
Fcal
FH (%I
FH @I
15
FH-FL
0.36 0.44 0.64 0.82 1.39 1.78 2.46 3.55 6.17 9.36
15 17 l6 19 l6 19 18 23 19 24
lg 22 22 3l 34
1.3 2.0 2.3 2.8 1.1 2.1 1.8 2.4 1.5 1.7
values have been observed in pneumatic transport [ 211. The model is quite sensitive to the total flux ejected from the bed surface F, and the 95% confidence interval on the ejected flux represents around 50% of its value. Thus, the predicted values of the flux entrained above the TDH have been determined for the minimum and the maximum values of the ejected flux. The value of the ejected flux has no significant effect on the predicted decrease of the flux entrained above the TDH with the gas humidity, shown in Table 4,
TABLE 4 Effect of F, on humidity effect determination Ug = 0.15 m/s Experimental values: FL= 0.49 g/(m2s) at h = 12.2% (low humidity) FH = 0.89 g/(m’S) at h = 67.9% (high humidity)
FO W(m2s))
Relative humidity (%)
F exP
(F-J,1 (g/(m2s))
FCd (%I
Average 79.0 Minimum 36.0 Maximum 270
12.2
0.36
67.9
0.44
12.2
0.19
1.3 19
2.0 2.5
21 67.9 12.2
0.24 1.02
67.9
1.20
3.7 0.5 15 0.8
66
for a gas velocity of 0.15 m/s. The experimental value of the flux entrained above the TDH is within the range of values predicted from the minimum and the maximum values of the ejected flux. This demonstrates the validity of the model.
FH FL
FO
Eh CONCLUSION
Electrostatic effects on the entrainment of fine particles of sand from a fluidized bed have been studied. The relative humidity of the fluidizing gas has to be greater than 30% to suppress the electrostatic phenomena. Entrainment of particles above the TDH decreases by 45% when the gas relative humidity falls from 30% to 10%. The analysis of the dense fluidized bed behaviour shows that it is not significantly affected by electrostatic effects. Agglomeration of particles in the freeboard which might result from electrostatic forces does not occur. The electrostatic pressure drop in the freeboard, however, accounts for around 50% of the total pressure drop at low gas humidity. By adapting an entrainment model based on a choking load model to take this electrostatic pressure drop into account, a decrease in the flux entrained above the TDH of 26% was predicted. The effect of electrostatics on entrainment is thus primarily caused by the increase in the pressure drop in the freeboard which results from electrostatic interactions between the column wall and the particles.
4 QB
TDH UB u mf
u, us Ut WS X
xB
z f EnIf
P LIST OF SYMBOLS
a a, da d!? D, ; L
fs
F, F exp F Cd
constant in eqn. (lo), m-l constant in eqn. (ll), m-r bubble diameter, m particle diameter, m column diameter, m electric field, V fluid friction factor mixture friction factor solid friction factor flux of particles entrained above the TDH, kg/(m*s) experimental value of the flux entrained above the TDH, kg/(m*s) calculated value of the flux entrained above the TDH, kg/(m*s)
i3
h;, K
PP PS
flux entrained above the TDH at high humidity, kg(m*s) flux entrained above the TDH at low humidity, kg/(m*s) total flux of particles ejected from bed surface, kg/(m*s) gravitational constant, m*/s relative humidity, % electrostatic factor = EqpJm, VC/m3 particle mass, kg solids to air mass loading ratio pressure drop per unit length, N/m3 electrostatic drop per unit length, N/m3 particle charge, C bubble flow rate, m3/s transport disengaging height,‘m bubble velocity, m/s gas velocity at minimum fluidization, m/s superficial gas velocity, m/s particle slip velocity, m/s particle terminal velocity, m/s solids flow rate, kg/s absolute humidity of inlet gas, kg water/kg air bed volume fraction occupied by bubbles height above bed surface, m bed voidage bed voidage at minimum fluidization bed density, kg/m3 gas density, kg/m3 solid density, kg/m3
REFERENCES D. Geldart and A. C. Y. Wong, paper presented at AIChE Annual Meeting, Chicago, Nov. 10 - 15, 1985. D. Geldart, Powder Technol, 7 (1973) 285. G. E. Klinzing, Gas Solid Transport, McGraw-Hill Chemical Engineering Series, McGraw-Hill, New York, 1981, p. 122. S. L. Soo, Fluid Dynamics of Multiphase Systems, Blaisdell, Waltham, MA, 1967. W. B. Kunkel, J. Appl. Phys., 21 (1950) 829. H. T. Masuda, T. Komatsu and K. Iinoya, AZChE J., 22 (1976) 558. E. E. Smeltzer, M. L. Weaver and G. E. Klinzing, Powder TechnoZ., 33 (1982) 31.
67 8 M. R. Ally, Ph.D. Dissertation, Univ. of Pittsburg (1981). 9 L. K. Peters, Ph.D. Thesis, Univ. of Pittsburg (1971). 10 L. B. Leob, Static Electrification, Springer Verlag, New York, 1958. 11 S. L. Soo, Pipelines, 1 (1981) 57. 12 G. A. Turner and J. Balasubramanian, Electrostatics, 2 (1976) 85. 13 R. F. Toomey and H. F. Johnstone, Chem. Eng. Progress, 48 (1952) 220. 14 D. Geldart and A. R. Abrahamsen, AZChE Symp. Series, No. 205, 77 (1981) 160. 15 K. Hilligardt and J. Werther, Ger. Chem. Eng., 9 (1986) 215. 16 T. Baron, C. L. Briens and M. A. Bergougnou, AZChE J., (1987) to be published. 17 S. E. George and J. R. Grace, AZChE Symp. Ser., No. 176, 74 (1978) 67. 18 T. Baron, Ph.D. Thesis, Institut Francais du P&role (1987).
19 T. Baron, C. L. Briens and M. A. Bergougnou, Can. J. Chem. Eng. (1987) to be published. 20 J. F. Richardson and M. McLennan, Trans. Inst. Chem. Eng., 38 (1960) 257. 21 R. H. Clark, D. E. Charles, J. F. Richardson and N. E. Newitt, Trans. Inst. Chem. Eng., 30 (1952) 209. 22 Y. Morikawa and S. Sakamoto, Bulk Solids Handling, 5 (1985) 647. 23 J. H. Jones, W. E. Braun, T. E. Daubert and H. D. AIlendorf, AZChE J., 13 (1967) 608. 24 M. L. Weaver, M.S. Thesis, Univ. of Pittsburg (1979). 25 M. R. Ally and G. E. Klinzing, Powder Technol., 44 (1985) 85. 26 C. L. Briens, T. Baron and M. A. Bergougnou, Powder Technol., (1987) to be published. 27 C. L. Briens and M. A. Bergougnou, Can. J. Chem. Eng., 64 (1986) 196. 28 C. L. Briens and M. A. Bergougnou, AZChE., 32 (1986) 233.
Technology,
57 (1987) 55 - 67
55
‘Electrostatic Effects on Entrainment from a Fluidized Bed T. BARON The ~niversi~
of Western Ontario,
Faculty
of Engineering Science, London,
Ont. N6A 539 (Canada)
C. L. BRIENS, M. A. BERGOUGNOU Ins~tut
Francais du Petrol-ENSPM,
1 ti 3 avenue du Bois Prkau, 92500 Rueil Mu~maison {France)
and J. D. HAZLETT IX&-ion of Chemistry,
NRC, Ottawa,
Oat. KlA
OR9 ~Canada~
(Received April 24, 1987)
SUMMARY
Effects of electrostatics on entrainment from a gas-solid f~uidi~ed bed were studied in a 0.61-m I.D. column with silica sand. The flux of particles en~ained above the transport disengaging height almost doubled when the relative hum~ity of gas was increased from 10% to 30% and then stabilized when humidity was further increased. However, neither the average bubble gas ~act~n nor the flux ejected from the bed surface were affected by humidity. Electrostatic effects did not promote particle agglomeration in the freeboard, since the same proportion of clusters was measured in ejected fluxes at low and high humidity (around 10%) and at high hum~ities (super~r to 30%). The electrostatic pressure drop in the freeboard, however, accounts for around 50% of the total pressure drop at low gas humidity. By adapting an entrainment model based on a choking load model to take this elect~static pressure drop into account, a 26% decrease in the flux entrained above the TDH was predicted. The effect of electrostatics on entrainment is thus primarily caused by the increase in the pressure drop in the freeboard which results from electrostatic interactions between the column wall and the particles.
INTRODUCTION
Entr~nment of particles from fluidized bed reactors is an important area to consider in their design. The ability to predict the variation of the flow rate of entrained solids and their size distribution is required for the
design of cyclones which can effectively limit particulate loss. As bubbles break at the surface of the fluidized bed, particles are ejected from the bed surface and are entrained by the upward flowing gas stream. Gas bubbles bursting at the surface of a fluidized bed are analogous to intermittent jets imposing a highly irregular velocity profile across the column. The jets are eventually dissipated to the superficial gas velocity at some equilib~um height above the bed surface referred to as the transport disengaging height (TDH) . The entrainment then becomes relatively constant and presumably equal to the maximum or saturation dilute-phase particle-carrying capacity of the gas stream at its superficial velocity if there is enough material ejected from the bed. Above the TDH, the column therefore operates as a dilute-phase vertical pneumatic transport line. Thus, it is clear that entrainment is subject to the same electrostatic phenomena as gas-solid transport even if in general the vessel diameter is larger and wall effect weaker in the freeboard of fluidized beds. Geldart and Wong [1] studied the effect of humidity of the fluidizing gas on the flux of particles entrained above the TDH of an &cm I.D. fluidized bed in the slugging regime. They tested a variety of group A and C powders according to Geldart’s powder classification [2]. They found that the entrainment flux was reduced when the relative humidity of the ~uidizing gas was increased. They attributed these results to the increase in the cohesivity of the powder with the relative humidity of the fluidizing gas. This increase in powder cohesivity was @ Elsevier Sequoia/Printed in The Netherlands
56
confirmed by bed expansion measurements. As non-porous fine powders become more cohesive with increased humidity, fluidization is poorer and the bed expansion is reduced. They commented that electrostatic forces, which are affected by humidity, had only a minor role to play in their system. Preliminary experiments conducted at the University of Western Ontario in a 0.61-m dia. fluidization column indicated that gas humidity had a significant effect on the entrainment flux. The first objective of this study was therefore to quantify the effect of humidity and electrostatics on the entrainment of solids from large fluidized beds. The second objective was to establish whether the humidity effect could be attributed to changes in the behaviour of the dense fluidized bed or to electrostatic forces acting on the particles in the freeboard.
PRESENTATION
OF
ELECTROSTATIC
PHE-
NOMENA
Importance
of electrostatic
square of the particle radius and that highly asymmetric charging of dust clouds led to charge segregation and ultimate sparking. Masuda et al. [6] have also studied static electrification in gas-solid pipe flow, especially with respect to particle-wall collisions. They introduced a contact time concept in their analysis and gave a simplified expression for the wall-current. They paid particular attention to the fundamentals of charge transfer and classified a number of materials as to composition and size. More recently, Smeltzer et al. [7] studied a Plexiglass-glass system in dilute-phase transport to examine the individual particle interactions with the confining wall at relative humidities varying from 25 to 65%. At constant loadings, greater electrostatic effects were seen for small particles than for large particles due to the high particle number density and thus increased interactions for the smaller particles. Higher loadings at low relative humidities also produced increased electrostatics effects. Ally [S] expanded this type of analysis to the dense-phase regime.
phenomena
The phenomenon of electrification in gassolid transport is often neglected in the analysis of many processes. However, the electrification of particles can be extensive in a gas-solid system, since only one unit of electronic charge per 10’ surface atom needs to be transferred to cause electrical breakdown of the surrounding air, according to Klinzing [ 31. The large charges on small particles are related to the large surface-to-volume ratio that is characteristic of these fine materials. Often these electrostatic effects are difficult if not impossible to duplicate, causing much frustration to the experimenter. Some parameters of importance are humidity and temperature of the gas, moisture content of the solids, and surface conditions of the flowing solids and of the wall. Flow rates of the solid and gas stream, loading of the stream, particle size and shape are other important factors in electrostatics or gas-solid flow systems. Soo [4] has been a pioneer in electrostatic analysis, presenting a rational approach to analysis through solid mechanics. Kunkel [ 51 experimentally studied the dust-charging mechanism. He found that the average charge increased somewhat more slowly than the
Lessening
electrostatic
charging
In most cases, electrostatics present very troublesome conditions in the handling of gas-solids systems. Elimination of the phenomenon would often simplify system design considerably. The primary safety procedure toward reducing the deposition of material is proper grounding of the column and of the cyclones to avoid the charging and eventual sparkover. This is necessary but not sufficient. The most common way to reduce electrostatic charging is to raise the relative humidity of the carrier gas. It has been demonstrated experimentally that electrostatic effects can be totally eliminated at relative humidities greater than 75%. This was shown in two experiments performed by Peters [9] on the flow of glass beads in a plastic tube (see Figs. l(a) and l(b)). The pressure drop data were converted to friction factor values by subtracting gravity, and acceleration effects were subtracted and the difference between the values of the ratio of two-phase friction factor to single-phase friction factor f,/fg can be attributed to electrostatic forces. The procedure of humidifying the air to eliminate charging is relatively simple and can be closely
51
Re =
14x
0
1.9 x 104
A26x
1
0.00,
104
0
IO’
I
i
0002
0003
1
0004
0005
I
0.006
I
0007
0008
controlled. In most temperate climates, the dry winter air conditions generally set the stage for large electrostatic effects in gas-solid flows according to Klinzing’s directions [3]. Loeb [lo] measured charge reductions of 50% at 15% relative humidity and complete reduction to zero at 60% relative humidity at standard temperature and pressure. Soo [ll] correlated data from Turner and Balasubramanian [ 121 to give the distribution of charge to mass ratio of 83 pm glass particles at various humidities and showed that the alteration of particle charging is greatly affected by humidity control as reported in Fig. 2. Use of humidity for the reduction of electrostatic charging must, however, be checked against condensation and frost formation. Humidity control is also not suitable for a hygroscopic material. In this case, grounding and reduction of particle loading are left as the basic means of charge control.
t_ 95
h
t
v h;=19%rh. a h2 =28%rh. 0 h3 =38X r.h. b
Dato.Tumer,el 01.
Charge to Mass Ratlo, C/kg-
i 4
0.3
0. I
Re=
1 4 x IV
0
18X
4
104
EXPERIMENTAL
1 1
(b)
0
I
1 I
0.001 0.002 0003
Fig. 2. Cumulative percentage of particles with charge to mass ratio equal to or greater than a certain value (from [ll]).
I
0004
0.005 0.006 0 007 0008
w,. kg/s
Fig. 1. Effect of humidity on friction factor from [9]. (a), Ratio of two-phase friction factor to singlephase friction factor as a function of bead feed rate for 25pm beads in silastic tube (relative humidity = 25%); (b), ratio of two-phase friction factor as a function of bead feed rate for 25-pm beads in silastic tube (relative humidity = 80%).
The fluidized bed used in this study was 0.61 m in diameter, 7.5 m high, and equipped with static pressure taps at numerous positions along the column height. As shown in Fig. 3, it consisted of a Plexiglass windbox, a carbon steel bed section, three Plexiglass freeboard sections, and two carbon steel sections above the TDH at the top of the column. Static pressure measurements allowed the evaluation of bed height, bed density and other properties of the operating bed. The air distributor consisted of a
58
desired bed conditions had been established, the bed was allowed to operate for 2 h to reach steady state before entrainment data were collected. The bed material was unground silica sand, grade F-140 supplied by the Ottawa Silica Sand Company. Its apparent particle density is 2650 kg/m3. The sand had been sieved using a 150-mesh (105~pm) stainless steel screen on a Rotex Model 11 GP shaker in order to reduce its Sauter mean diameter to 82 pm. These solids were charged to the column and elutriated until the bed size distribution stabilized. The bed particle size distribution is given in Table 1. TABLE
A,
High-pressure
(Chinese
hat);
air; 6, air from D, windbox;
port; G, pressure J, elliptical cone sections; primary
M,
rotameter;
E, grid
plate;
C, conical F, solids
baffle
cyclone
cyclone; R. diverter dipleg; U. pneumatic
P,
inlet
extension;
pressure
control
valve; S, Plexiglass lift line; V, ejector.
Fig. 3. Fluidization
N,
manual
valve;
0.
sections;
from
Largest diameter size cut
in
Coulter
Counter
analysis
Cumulative volume
%
(Pm)
discharge
taps; H, sampling ports; I, pneumatic seal; collector; K, flexible vent hose; L. metallic
cyclone;
1
Bed composition
hoist;
0,
secondary T, cyclone
column.
12.7-mm aluminum plate fitted with 16 conical top, acrylic tuyeres on a 114-mm square pitch. Each tuyere provided four 6.35-mm diameter openings inclined with a downward angle of 45” to the horizontal, resulting in a fractional grid open area of 0.7%. Fluidizing air of controlled humidity was used. Superheated steam was injected downstream of the rotameter to control the humidity of the air entering the column. Low-pressure steam (150 kPa absolute) passed through a pipe wrapped with electrical heating tape. The steam system was run on bypass (discharging into the lab) until the steam temperature indicated that the steam superheat was 30 to 40 “C. The flow of steam was controlled manually and the fluidizing air relative humidity measured by a wet bulb/dry bulb hygrometer mounted in parallel to the main flow. The mixing was so rapid that no fog or condensation was observed in the air line or in the column. Humidity of the outlet air was measured to check that there was no retention of water in the column. Once the
6.35 8.00 10.08 12.7 16.0 20.2 25.4 32.0 40.3 50.8 64.0 80.6 101.6 128.0 161.0 203.0
0 0 0.09 0.18 0.30 0.36 0.40 0.42 1.23 5.08 20.32 50.03 87.49 97.29 99.42 100.00
Entrained particles were recovered by a pair of cyclones mounted in series. Solids collected by the primary cyclone returned to the bed via a dipleg. A valve between the two cyclones allowed manual control of the column pressure. The secondary cyclone collected a negligible quantity of solids during the experiments described here. Entrainment fluxes were measured by using a movable semi-elliptical cone which could be raised or lowered to change the height of the freeboard space above the bed. The gas-solid mixture thus collected was sent to the primary cyclone. The flux of solids recovered by the primary cyclone was determined by diverting the particles which flow through the dipleg
59
into a container for a given duration and by weighing them. The flux of solids escaping the primary cyclone was negligible, as determined by the amount of solids collected by the high-efficiency secondary cyclone. As the cone approaches the bed surface, the flow will no longer be capable of turning to accommodate the cone profile and the impaction of solids on the surface of the cone should increase. This will result in lower measured fluxes than those actually present. Thus, the cone is always at least 70 cm above the bed surface. Size analyses were performed using a Model TAII Coulter Counter with population accessory. Samples were characterized by their Sauter mean diameter. Standard riffling techniques were used to obtain an appropriately small sample for the Coulter Counter.
EXPERIMENTAL
RESULTS
The relative humidity of the fluidizing gas has a strong effect on the entrainment of particles, above the TDH, as demonstrated in Figs. 4(a) - (d). At all gas velocities, the flux 50
F, of particles entrained above the TDH increased by a factor of 2 when the relative humidity was increased from 7% to 30%. Above a relative humidity of 30%, a plateau was reached and further increases in humidity had no further effect. A relative humidity of the inlet gas of more than 30% thus prevents any electrostatic phenomena in the fluidization column. Vertical profiles of the flux of collected particles were therefore measured in the column at low humidity and at high humidity. ‘Low humidity’ means that no steam was added in the inlet gas. The relative humidity of the inlet air was then around 10% and electrostatic phenomena occurred in the column. ‘High humidity’ means that superheated steam was injected in the inlet gas and the controlled relative humidity was well above 30%, i.e., between 40% and 60%. Values from a typical experiment are reported in Table 2. The accuracy on the entrained flux was around 5% above the TDH and 15% near the bed surface. Figure 5 shows two entrainment profiles obtained at exactly the same conditions except that one run was carried out at a relative humidity of 48.3% and the other at a relative humidity of 11.4%. The run at low humidity gave significantly lower entrained fluxes all along the freeboard.
30 20 z VI “E ;
10
6
w
4
:
3
y :
2
=i
1
Typical
entrainment
Cone height above grid
% 2
2 profile
run
Superficial gas velocity (m/s) Inlet air conditions: Temperature (“C) Pressure (kPa) Relative humidity (‘%) Bed characteristics from pressure balance: Bed height (m) Bed density (kg/m3) Bed voidage
c” s
TABLE
0.5
(m)
03
4.65 3.89 3.28 2.36 2.21 2.06 1.91 1.75 1.60 1.45
2
0.2
01 0
10
20 HUMIDITY
30 OF
40 INLET
50 GAS
Fig. 4. Effect of humidity on entrainment TDH, (m), Us = 0.15 m/s;(@), Ug= 0.20 U, = 0.25 m/s; (x 1, Up = 0.30 m/s.
60
(%I
above the
m/S;(.),
70
Average
fiux
Standard
(g/(m’s))
(g/(m2s))
4.04 3.82 3.88 4.39 4.93 5.14 7.27 9.31 24.15 30.11
0.22 0.14 0.11 0.21 0.35 0.73 0.84 0.87 2.12 3.78
0.201 28.2 20 48.3 0.774 1236.5 0.5334 deviation
60
x
0
05
1
15
HEIGHT
Fig. 5. Entrainment ities.
2
25
ABOVE
3 THE
profile
35
4
GRID
45
E-
-
B-
Gnf
(31
1 - f,f
The bed voidage cmf and the gas velocity U,, at the minimum fluidization conditions were measured in a small column. Their values were: iJmf = 9.8 1O-3 m/s and cmf = 0.480. A good agreement with this value was obtained by using the aerated particle density determination technique given by Geldart and Abrahamsen [14], which yielded emf = 0.475. Figure 6 shows that there is no significant effect of the gas humidity or superficial gas velocity on the bubble volume fraction. An average value for xB of 0.10 can be retained for the present experimental conditions.
5
lm)
at low and high humid-
Experiments at various velocities ranging from 0.15 to 0.30 m/s were carried out in the fluidization column to establish whether the humidity effect could be attributed to changes in dense fluidized bed behaviour or to electrostatic effects on particles in the freeboard.
SE
0.12
;
I .
n
HIGH
0
LOW
HUMIDITY
0
30%1
c< 30%)
HUMIDITY
0
0.11
0
ANALYSIS
OF DENSE
Two basic experimental results were used to characterize the dense bed behaviour: the bed expansion and the flux of particles ejected from the bed surface. Bed expansion teristics
and bubble
phase
The bed voidage is determined from the bed pressure drop:
E=l-Pbed
@bed -
H bed
0 -------
_-__ 0.10
g
0
L
0 15
t
0.18
0.20
Fig. 6. Effect of humidity volumetric bubble fraction.
(-2)
According to the two-phase theory [ 131, the fluidized bed can be separated into the bubble phase and the emulsion phase and the dense phase voidage is independent of the gas velocity and equal to e,f, the bed voidage at minimum fluidization conditions. If E is the overall bed voidage at operating conditions, the bed volume fraction xB occupied by the gas bubbles can be obtained:
.
t
SUPERFICIAL
(1)
8 .
m
0.10
directly
Is= ,102 _----
AVERAGE
1
0.09L
where =
w i m 2
charac-
Ps
Pbed
0
z I&
BED BEHAVIOUR
GAS
0
“,
I
0.25 VELOCITY
0.30
w
(m/51
and gas velocity
on
An estimation of the average bubble size in the dense fluidized bed can also be determined from the two-phase theory, which gives as flow rate through the bubble phase QB = AUBXB = A(U,
-
urn,)
(4)
Thus, u,
=
u, -
Ulnf
(5)
xB
An estimation of the diameter of the sphere of bubble equivalent volume can be obtained from Hilligardt and Werther’s expression [ 151:
61 UB = ,g(u,
-
U,,)
+ 0.71e(gds)“~5
(6)
where ,$ and 8 are correction factors which depend respectively on the Geldart group to which the powder belongs and on the column diameter. In our case (Group A powder, D, = 0.61 m) the corresponding values are
8 = 3.2
(7)
Dco*33= 2.71 which yield da = 0.0275[&
- 0.8(U, - &,,)I*
(8)
It should be noticed that using the standard equation for bubble velocity, which does not take the bed diameter into account (4 = 8 = l), leads to erroneous values for the bubble diameter. At high gas velocities, the bubble diameters thus estimated were larger than the column diameter. Figures 7(a) and 7(b) show that the bubble diameter increased the same way at low and high humidities. Thus, it seems that gas humidity had no effect on bubble behaviour. Estimation of the total flux ejected from the bed surface A higher flux of particles ejected into the freeboard because of a change in dense bed behaviour could also explain an increase in the flux of particles entrained above the TDH. To compare the values of the ejected flux F, at low and high humidities, a new method for the determination of the ejected flux based on cluster flux measurements which had been proposed by Baron et al. [16] was used. Clusters are agglomerates or ‘pieces of the bed’ projected into the freeboard by bubble eruptions at the bed surface. Their size can be assumed to range from 1000 average particle volumes to 10% of the bubble volume at the bed surface according to George and Grace [ 171, who observed that only 40% of the solids present in the wake of the bubble is effectively ejected in the freeboard. As the maximum height that non-entrainable individual particles ejected from the bed can reach in the freeboard is always very small (less than 0.15 m under our experimental conditions), practically all the non-entrainable particles present below the TDH belong to
u,
(a)
GAS
VELOCITY
lm/sI
0.25
G
0.05
0 0
(b)
0.05
0.10
d,
HIGH
0.15
0.20
HUMIDITY
(ml
0.25
Fig. 7. Effect of humidity at various gas velocities on bubble diameter. (a), Effect of gas velocity; (b), effect of humidity.
clusters. Thus, the maximum height that clusters reach can be considered as the TDH. At low freeboard heights, the cluster flux becomes predominant and the individual particle flux negligible and the cluster flux ejected from the bed surface can thus be considered equal to the total flux F, ejected from the bed surface. It has also been shown experimentally [ 161 that cluster flux varies according to the exponential decay law and can be expressed as F, = F, exp(-aJ)
(9)
while the total flux is given by F = F,.+ F, exp(-aZ)
(10)
where 2 is the height above the bed surface. Figure 8 shows typical axial profiles of the total flux, the cluster flux and the individual particle flux.
62 34
-
3000
= en1000;
“E ;
700-
.?
500
-
: ;; z ? 3 0 .A
300
c
100 70
/ . .
.
I -
/‘_
30-
2 I
“I
0 .25
1
I
A.
I
I
I_
3
2 HEIGHT
I_,
ABOVE
THE
4
BE0
(ml
10
Fig. 8. Typical entrainment profile.
p
3000
-
2000
-
1000
-
700
-
500
-
400
-
300
-
200
-
100
-
70
-
50
-
LO
-
30
-
20
-
0.10
30
I
I1111111
100
Fe HIGH
A new linear regression method which uses both the total flux and the cluster flux experimental data yields a more accurate extrapolated value of the ejected flux by doubling the number of experimental points [16]. Figure 9 shows the variation of ejected flux with gas velocity at both low and high humidities. Figure 10 represents directly the 4000
I I I11111 10
300 HUMIDITY
0.15
0.18
.20
0.25 GAS
VELOCITY
0.30
0 35 (m/s1
Fig. 9. Evolution of the ejected flux with gas velocity (95% confidence intervals are shown).
3000
(g/(d,Il
Fig. 10. Effect of humidity on ejected flux (the rectangles represent the 95% confidence intervals).
effect of humidity on the ejected flux. Since the 95% confidence intervals for the ejected flux at different humidities overlap for each gas velocity (Fig. 9), it can be concluded that the flux ejected from the bed is not significantly affected by the gas humidity. This result confirms that the bubble size was unaffected by the gas humidity. Electrostatic effects on the dense bed behaviour thus seem to be negligible. This appears reasonable as the energy of jets and bubbles at gas velocities of around 20 U,, is much larger than the cohesion energy of the particles which might be affected by an electric field.
ANALYSIS OF FREEBOARD
SUPERFICIAL
1 1111111
1000
BEHAVIOUR
Comparison of cluster fluxes in the freeboard The cluster flux was measured at various freeboard heights [ 161. The evolution of the mean diameter of entrained particles at various freeboard heights was not affected by gas humidity. It was found that the values of the cluster flux well above the bed surface were slightly smaller at low humidity but that the percentage of clusters in the total entrained flux was not significantly affected by gas humidity. Similar results were obtained for gas velocities ranging from 0.15 to 0.30 m/s [18]. Agglomeration of particles in the
63
freeboard cannot therefore account for the observed effects of electrostatics on the entrained flux. This conclusion was confirmed by considering the TDH. The TDH can be predicted from the following equation, which was derived from a model for the cluster trajectories [ 191: TDH=
(2.llJ,)2
(11)
%
Since the gas humidity does not significantly affect the bubble velocity U, as demonstrated in Fig. 7, the TDH should therefore be independent of the gas humidity. Another equation for the estimation of the TDH [16]
(12) leads to the same conclusion since F, and a, are not significantly affected by the gas humidity. Effect of the electrostatic pressure drop in the free board Importance of the electrostatic pressure drop The measurement of energy losses by pressure drop in systems where electrostatic effects are present is sparse. Often, increases in pressure drop due to static electrification effects were noted according to Richardson and McLennan [20] and Clark et al. [21]. More recently, Morikawa et al. [22] found that the pressure drop through a horizontal acrylic pipe was doubled when compared with a grounded brass pipe because of electrostatic effects in pneumatic conveying. In general, the overall pressure drop for an electrostatic system can be measured and the analysis of the overall pressure drop can be interpreted in a similar manner to the simple two-phase flow case as AP = (1 -e)p,g L
+
2fgPgUg2 D
C
gravitational
fluid
term
term
+ fA41
- wg2
friction
+
APei L
20, solid
friction
term
electrostatic term
(13)
with the solid friction term expressed according to Jones [ 231. According to Klinzing [ 31, the electrostatic contribution to the pressure drop is given by L
(14)
ms
where E is the electric field, q the charge of the particle, and m, the mass of the particle. Analyses have been performed on data taken in Klinzing’s laboratory by Weaver [ 241. Figure 11 is a plot of the electrostatic pressure drop produced in a system consisting of a Selastic tube with glass beads at low relative humidities. The electrostatic pressure drop is the pressure drop measured over and above that predicted by eqn. (13), not including the last term attributable to the electrostatic effect. As would be expected, the smaller the diameter of the flowing particle, the greater the electrostatic charge that is generated. A reduction in particle size by a factor of 2 resulted in an increase in generated charges by nearly an order of magnitude.
25 pm particles, low humidity
-25%
,:/ y
0.010
0.020 K
0.030
0 w IO
1k/s
Fig. 11. Electrostatic pressure drop per unit length versus bed flow rate from [24].
Estimation of the electrostatic pressure drop Ally and Klinzing [25] studied the interaction of electrostatic charging and pressure drop in pneumatic transport. They observed that the electrostatic pressure drop decreases linearly with the moisture-solid ratios in a logarithmic representation. They tested various particle-tube systems and found in particular that the Plexiglass tube retains its
64
charge over a wider range of moisture ratios than copper or glass tubes. Using a loading ratio of solids to gas mass flow rates equal to 100, they found for a similar gas-particle system (7 5-l.trnspherical glass beads in a Plexiglass tube, absolute humidity around lop2 kg water/kg air) the following expression for the electrostatic pressure drop:
me, = -0.38
1
In -
t L
In x + 4.935
(15)
where APJL is the electrostatic pressure drop per unit length in N/m3 and x is the absolute gas humidity in kg water/kg air. This formula has been used to compute the electrostatic pressure drop at various absolute humidities in the fluidization column by assuming that the electrostatic effects were comparable in both our system and Ally and Klinzing’s. Ally and Klinzing’s loading ratio was PsWp
MS -= M!3
PP(l - c,)Ug = 100
(16)
with
=
u, - u,
(17)
As the solid holdup E, was very small (E, Q 1) and U, was very small compared with U, for the small particles entrained above the TDH (U, S U,), eqn. (16) can be rewritten as
MS - = 100 M,
Z-E
PS s
f-32 Thus, 1OOPg e,= PS
= 0.0453 Equation (14) can also be expressed as
@e,
(18)
-=Ke, L
where K = Eqp,/m,
is the electrostatic coefficient
Using both eqns. (16) and (15), this coefficient can be computed at various humidities from K = 0.0453~ exp(-0.38
lnx + 4.935)
(19)
Under the operating conditions of this study, the electrostatic pressure drop can then be expressed as @,I L
=KE, = &exp(-0.38
lnw + 4.935)
(20)
where e, is the solid concentration in the freeboard and x the absolute humidity of the fluidization gas. Prediction of the electrostatic effects on entrainment A new entrainment model developed by Brienset al. [26 - 281 has been adapted to take the electrostatic phenomena into account. The flux entrained above the TDH is predicted from the fluidized bed characteristics and from the total flux ejected from the bed surface F,. This model also assumes that the freeboard above the TDH can be described as a vertical pneumatic transport line. The flux of solids entrained above the TDH is thus limited by the choking load, i.e., the maximum flux of particles which can be carried by a gas flowing at a certain velocity. A simple physical model which assumes that a stationary annulus forms along the pipe wall at low velocities [27] is used to predict the onset of choking which occurs when this annulus occupies 25% of the total pipe crosssectional area. An electrostatic pressure term calculated from eqn. (18) can be used in the choking load calculation to take electrostatic phenomena into account for low humidity experiments. Electrostatic effects are assumed to be negligible at high humidity where they were not observed. This model was used to predict the effect of electrostatics on the flux entrained above the TDH. Table 3 summarizes the results obtained at low and high humidities for five gas velocities. A decrease of approximately 45% of the flux entrained above the TDH was observed experimentally in the column when the gas relative humidity was reduced from values superior to 30% to values around 10%.
65 TABLE 3 Comparison of experimental and calculated effects of gas humidity on flux F, of particles entrained above the TDH
ug
(m/s)
FO
(g/(m2s))
Relative humidity
AF’totd (Pa/m)
aPel F
Experimental F
tm
@I @I
W(m2s))
dP Wm)
F exP
Calculated Fn-FL
F,
-
W(m2s))
dP 0.W
79
18
122
20
278
25
400
30
957
12.2 67.9 14.6 33.0 11.4 48.3 10.4 38.2 9.3 32.5
0.07 0.04 0.10 0.07 0.19 0.12 0.28 0.20 0.58 0.41
51 0 50 0 52 0 52 0 55 0
0.49 0.89 1.5 2.3 1.6 3.9 4.6 8.6 9.5 16.5
The model predicts an average decrease of 26%. The predicted trend thus agrees well with the experimental values when one takes into account the limited quantitative information from which the electrostatic pressure drop can be evaluated. Moreover, although the prediction of the average particle diameter is not excellent, both experimental and calculated data show that electrostatic effects have no effect on the average size of the entrained particles. The electrostatic pressure drop is found to account for 50% of the total pressure drop at low humidity and similar
34 33 37 37 36 36 41 38 41 42
44
35 58 46 42
Fcal
FH (%I
FH @I
15
FH-FL
0.36 0.44 0.64 0.82 1.39 1.78 2.46 3.55 6.17 9.36
15 17 l6 19 l6 19 18 23 19 24
lg 22 22 3l 34
1.3 2.0 2.3 2.8 1.1 2.1 1.8 2.4 1.5 1.7
values have been observed in pneumatic transport [ 211. The model is quite sensitive to the total flux ejected from the bed surface F, and the 95% confidence interval on the ejected flux represents around 50% of its value. Thus, the predicted values of the flux entrained above the TDH have been determined for the minimum and the maximum values of the ejected flux. The value of the ejected flux has no significant effect on the predicted decrease of the flux entrained above the TDH with the gas humidity, shown in Table 4,
TABLE 4 Effect of F, on humidity effect determination Ug = 0.15 m/s Experimental values: FL= 0.49 g/(m2s) at h = 12.2% (low humidity) FH = 0.89 g/(m’S) at h = 67.9% (high humidity)
FO W(m2s))
Relative humidity (%)
F exP
(F-J,1 (g/(m2s))
FCd (%I
Average 79.0 Minimum 36.0 Maximum 270
12.2
0.36
67.9
0.44
12.2
0.19
1.3 19
2.0 2.5
21 67.9 12.2
0.24 1.02
67.9
1.20
3.7 0.5 15 0.8
66
for a gas velocity of 0.15 m/s. The experimental value of the flux entrained above the TDH is within the range of values predicted from the minimum and the maximum values of the ejected flux. This demonstrates the validity of the model.
FH FL
FO
Eh CONCLUSION
Electrostatic effects on the entrainment of fine particles of sand from a fluidized bed have been studied. The relative humidity of the fluidizing gas has to be greater than 30% to suppress the electrostatic phenomena. Entrainment of particles above the TDH decreases by 45% when the gas relative humidity falls from 30% to 10%. The analysis of the dense fluidized bed behaviour shows that it is not significantly affected by electrostatic effects. Agglomeration of particles in the freeboard which might result from electrostatic forces does not occur. The electrostatic pressure drop in the freeboard, however, accounts for around 50% of the total pressure drop at low gas humidity. By adapting an entrainment model based on a choking load model to take this electrostatic pressure drop into account, a decrease in the flux entrained above the TDH of 26% was predicted. The effect of electrostatics on entrainment is thus primarily caused by the increase in the pressure drop in the freeboard which results from electrostatic interactions between the column wall and the particles.
4 QB
TDH UB u mf
u, us Ut WS X
xB
z f EnIf
P LIST OF SYMBOLS
a a, da d!? D, ; L
fs
F, F exp F Cd
constant in eqn. (lo), m-l constant in eqn. (ll), m-r bubble diameter, m particle diameter, m column diameter, m electric field, V fluid friction factor mixture friction factor solid friction factor flux of particles entrained above the TDH, kg/(m*s) experimental value of the flux entrained above the TDH, kg/(m*s) calculated value of the flux entrained above the TDH, kg/(m*s)
i3
h;, K
PP PS
flux entrained above the TDH at high humidity, kg(m*s) flux entrained above the TDH at low humidity, kg/(m*s) total flux of particles ejected from bed surface, kg/(m*s) gravitational constant, m*/s relative humidity, % electrostatic factor = EqpJm, VC/m3 particle mass, kg solids to air mass loading ratio pressure drop per unit length, N/m3 electrostatic drop per unit length, N/m3 particle charge, C bubble flow rate, m3/s transport disengaging height,‘m bubble velocity, m/s gas velocity at minimum fluidization, m/s superficial gas velocity, m/s particle slip velocity, m/s particle terminal velocity, m/s solids flow rate, kg/s absolute humidity of inlet gas, kg water/kg air bed volume fraction occupied by bubbles height above bed surface, m bed voidage bed voidage at minimum fluidization bed density, kg/m3 gas density, kg/m3 solid density, kg/m3
REFERENCES D. Geldart and A. C. Y. Wong, paper presented at AIChE Annual Meeting, Chicago, Nov. 10 - 15, 1985. D. Geldart, Powder Technol, 7 (1973) 285. G. E. Klinzing, Gas Solid Transport, McGraw-Hill Chemical Engineering Series, McGraw-Hill, New York, 1981, p. 122. S. L. Soo, Fluid Dynamics of Multiphase Systems, Blaisdell, Waltham, MA, 1967. W. B. Kunkel, J. Appl. Phys., 21 (1950) 829. H. T. Masuda, T. Komatsu and K. Iinoya, AZChE J., 22 (1976) 558. E. E. Smeltzer, M. L. Weaver and G. E. Klinzing, Powder TechnoZ., 33 (1982) 31.
67 8 M. R. Ally, Ph.D. Dissertation, Univ. of Pittsburg (1981). 9 L. K. Peters, Ph.D. Thesis, Univ. of Pittsburg (1971). 10 L. B. Leob, Static Electrification, Springer Verlag, New York, 1958. 11 S. L. Soo, Pipelines, 1 (1981) 57. 12 G. A. Turner and J. Balasubramanian, Electrostatics, 2 (1976) 85. 13 R. F. Toomey and H. F. Johnstone, Chem. Eng. Progress, 48 (1952) 220. 14 D. Geldart and A. R. Abrahamsen, AZChE Symp. Series, No. 205, 77 (1981) 160. 15 K. Hilligardt and J. Werther, Ger. Chem. Eng., 9 (1986) 215. 16 T. Baron, C. L. Briens and M. A. Bergougnou, AZChE J., (1987) to be published. 17 S. E. George and J. R. Grace, AZChE Symp. Ser., No. 176, 74 (1978) 67. 18 T. Baron, Ph.D. Thesis, Institut Francais du P&role (1987).
19 T. Baron, C. L. Briens and M. A. Bergougnou, Can. J. Chem. Eng. (1987) to be published. 20 J. F. Richardson and M. McLennan, Trans. Inst. Chem. Eng., 38 (1960) 257. 21 R. H. Clark, D. E. Charles, J. F. Richardson and N. E. Newitt, Trans. Inst. Chem. Eng., 30 (1952) 209. 22 Y. Morikawa and S. Sakamoto, Bulk Solids Handling, 5 (1985) 647. 23 J. H. Jones, W. E. Braun, T. E. Daubert and H. D. AIlendorf, AZChE J., 13 (1967) 608. 24 M. L. Weaver, M.S. Thesis, Univ. of Pittsburg (1979). 25 M. R. Ally and G. E. Klinzing, Powder Technol., 44 (1985) 85. 26 C. L. Briens, T. Baron and M. A. Bergougnou, Powder Technol., (1987) to be published. 27 C. L. Briens and M. A. Bergougnou, Can. J. Chem. Eng., 64 (1986) 196. 28 C. L. Briens and M. A. Bergougnou, AZChE., 32 (1986) 233.