Influence of particle size, fluidization velocity and relative humidity on fluidized bed electrostatics

Journal of

ELECTROSTATICS ELSEVIER Journal of Electrostatics 37 (1996) 1-20

Influence of particle size, fluidization velocity and relative humidity on fluidized bed electrostatics

Jesfis G u a r d i o l a , V i c t o r R o j o , G u a d a l u p e R a m o s *

Dept. de Ingenieria Quimica, F. Ciencias, Universidad de Alcalh, Alcalit de Henares, 28871 Madrid. Spain

Received 9 August 1995; accepted after revision 18 December 1995

Abstract

The influence of particle size, dp, fluidization velocity, Ur, and relative humidity, RH, on the degree of electrification reached by a fluidized bed of glass beads has been studied. The static electrification of the bed was measured by means of the potential difference observed between an electric probe and the metallic distributor. The effect of relative humidity appears to be complex and is connected with the quality of fluidization- bubbling or slugging - existing in the bed. A characteristic curve for electrification vs. humidity has been proposed that consists of five zones. The results show that when the value of the relative humidity is lower than a critical value (RH¢), the static electrification of the bed cannot be measured accurately because the adhesion of particles to the probe leads to irreproducible voltage values. Also, the degree of electrification increases with particle size and air velocity. The relationship between the average solid circulation velocity and electrification is studied.

Keywords: Fluidized beds; Triboelectrification; Relative humidity; Fluid bed filters; Particle charging; Particle electrification

1. Introduction

The static electrification of solids (triboelectrification) in fluidized beds was first reported some 50 years ago when several researchers began to notice anomalous electric behaviour in different studies using fluidized beds. The mechanism that generated the static charge was apparent ly quite complex. Briefly, when two bodies come into contact electrons transfer f rom one to the other forming an "electrical double layer" that consists of two layers of charge of opposite sign. These layers are located on or near each surface and the distance between them is only a few molecular diameters. If the bodies are suddenly pulled apart, the original electronic equilibrium cannot be re-established and one of the surfaces retains more electrons than before the

* Corresponding author. Tel.: (91) 885 49 74; Fax: (91) 885 50 88; e-mail: [email protected]

0304-3886/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved PII S 0 3 0 4 - 3 8 8 6 ( 9 6 ) 0 0 0 0 2 - 2

2 J. Guardiola et al./Journal of Electrostatics 37 (1996) 1-20

contact was first established and the other will present a deficit. Obviously, the total charge of the two surfaces concerned remains constant, although if one of the surfaces loses the charge obtained (for instance, because it is a better conductor or is earthed) the global result of the phenomenon is to generate an electrical charge. The above is of course a very simple approach to the phenomenon of static electrification. A more complete description of the whole process can be found in [1-4].

The nature of fluidization processes produces continuous motion and rubbing among bed particles, thus generation of a static charge is almost unavoidable when the particles are made of an insulating material.

The first references to static electrification in fluidized beds appeared as comments by authors on a certain anomalous bed behaviour that they had encountered in experiments on subjects as diverse as heat transfer [-5], solids elutriation [,6], type of fluidization [-7] or fluid dynamics [8].

How electric charge is built up in a fluidized bed and how it is influenced by the operational variables is of interest for two contrasting reasons: (1) the need to reduce charge generation - avoid sparks or explosions, facilitate material handling in operations such as drying, etc.; and (2) the need to boost static electrification in industrial operations

- solid separation in binary mixtures, dust removal in industrial gas currents, etc. The variables that control the amount of charge generated when two bodies are

brought into contact is very high: bulk chemical composition of the bodies, condition of both surfaces, size and shape, state of electric charge before contact, relative velocity of bodies, are only a few. This, together with the complexity of the fluidization phenomenon, is probably one of the reasons for the relative lack of papers on static electrification in fluidized beds (see Table 1 [-9-23]) as compared with the large number of papers related to other topics in the field of fluidization.

Experimental work to understand the phenomenon requires measuring the degree of electrification in a fluidized bed and the following variables: column diameter, bed height, fluidization velocity, relative humidity and particle diameter. The work must also consider an additional variable: the height of the electric probe used for measuring the degree of static electrification. The influence of variables related to the geometry of the system - column diameter, bed height and probe height - has already been reported [24].

The aim of the present work is to study the influence of the remaining variables: relative humidity, fluidization velocity and particle diameter.

The results show that at relative humidity values below a critical value (RHc), the static electrification of the bed cannot be measured accurately by means of the probe-distributor voltage technique because the adhesion of particles to the probe leads to irreproducible voltage values. In addition, there is a limiting value of humidity beyond which static electrification is no longer observable in the fluidized bed. A characteristic curve consisting of five zones is proposed to explain the influence of relative humidity.

Studying the influence of the particle size and the air velocity shows that the degree of electrification increases with increasing values of both variables, and that the effect of air velocity is related to the quality of fluidization. The level of bed electrification increases with increase of the average solid circulation velocity.

J. Guardiola et al./Journal of Electrostatics 37 (1996) 1-20 3

Table 1 Experimental studies on static electrification in fluidized beds

Reference Bed Column

Material d r Hmf Material Dc (gm) (mm) (mm)

uf RH (cm/s) (%)

[9] Dylene-polystyrene, 297-420 19-25 Lucite 38 nylon 149-297

[10] Sand, sugar, sulphur 150 200 50-100 Glass 46 marble, iron, aluminium

[11] Vinylpolyacetate, 490-750 - - Glass 60 polystyrol, sand 400-490

300-400 [12] Hydroquinone, - - - - Glass - -

polyarcylonitrile ammonium sulphate

[13] Lead glass ballotini 100-800 600

[14] Glass ballotini 170 210 - - [15] Polystyrene 375 25-200 [ 16] Polyethylene - - 80 - 300 [17] Polystyrene 420-590 22-88

297-420 210-297 105-210

[ 18] Porcelain 2000 260 [19] Glass beads, 200, 250 - -

neobeads, PMMA and 540

[20] Glass ballotini

[21] Polystyrene, polystyrene with aluminium powder or sodium chloride

[22] Glass ballotini steel

[23] Glass ballotini

350 420 35-162 297-350 250-297 475 200

Perspex 500 or (2D) glass Metal 32 Glass 50 Glass 50-400 Perspex 44

15-58 64 - 10.7 a

71 78

10 43 0 12 ~

50-115 4 12.5"

15 80

40-110 30-65 8.4 12

2-60 10-90

Plastic 50 92-125 20-46 Perspex 67 21 50 10-65 or iron Perspex 35-54 11 66 5 80

200 x 200 - - ¢).70

500-590 5-50 Perspex 35-54 11-66 5 40 420-500 350-420 35-162 Perspex 35 54 11-66 0-80 297-350 250-297

"Absolute humidity (g/kg).

2. Experimental

2.1. Apparatus and materials

T h e a p p a r a t u s u s e d h e r e is a bas i c s o l i d - g a s f l u i d i z a t i o n i n c o r p o r a t i n g an e l ec t ro -

s ta t i c v o l t m e t e r to m e a s u r e e lec t r ic i ty (Fig. 1). T h e air s u p p l y f r o m the c o m p r e s s o r (A)

4 J. Guardiola et al./Journal of Electrostatics 37 H996) 1-20

%

Fig. 1. Experimental apparatus (schematic).

was divided into three streams at B: the first was humidified by bubbling the air through water, the second was untreated and the third was dried by means of a molecular sieve. The humidity of the mixed stream was measured at C by a Hy- grotest probe, with a meter covering the range of relative humidity from 5% to 98%. A four-way valve (D) permitted the flow of air at controlled velocity and humidity through the bed in the opposite direction to the normal fluidization run, so that the fixed bed could be conditioned at the desired humidity before the experiment started. The air flow rate was measured by a rotameter (E) before entering the fluidization column (F), made of Perspex tubing (44 mm inside diameter) and comprising three zones: (1) A calming zone. (2) The column itself containing the bed to be fluidized; the bed was supported on a stainless steel screen with an opening size of 80 ram and 36% of open area. This distributor model does not produce good fluidization, but it does (a) reduce electrically charged particle adherence to the distributor, as will be explained later in the section on relative humidity influence (zone A); and (b) will give results that could be used in a fluidized bed filter for industrial gas currents with minimal aerosol retention in the distributor. (3) An expanded freeboard. Extreme electrical isolation measures were taken (screened fluidization equipment, silicone coating for the column holding the bed and the electric wires). The upper and lower ends of zone 3 were fitted with two guides, to permit a metallic probe to be placed along the fluidization column. The probe (G) was made of a copper bar of 5 mm diameter and coated with silicone rubber (5 × 8 mm diameter), except the lower 10 mm of the bar which was left bare to contact the bed. In order to get high potential difference values and to ensure the necessary direct contact between probe and bed during fluidization, the probe was placed parallel to the column axis at a height above

J. Guardiola et al,/Journal of Electrostatics 37 (1996) 1 20

Table 2 Characteristics of glass beads

d v (lam) Umf rXmf (cm/s)

250- 297 7.6 0,41 297 350 9.0 0.38 350 420 19.0 0.41

the distributor equal to the bed height at incipient fluidization. A differential water manometer (H) measured the gas pressure drop through the bed.

The degree of electrification reached by the bed during fluidization was measured indirectly - with a model ESH-29 Sensitive Research, electrostatic voltmeter - (I) through the potential difference between the electric probe in touch with the bed and the earthed distributor bed.

The bed particles consisted of the three different sizes of glass beads (ballotini) characterized in Table 2, all belonging to group B of Geldart's classification [25]. The three fluidization velocities used with each size fraction were equivalent to 1.5, 2.5 and 3.5 times the minimum ftuidization velocity, respectively. For each fluidization velocity the relative humidity of the fluidizing air was varied from very low values (5 10%) to values high enough to block bed electrification. All experiments were performed at room temperature and pressure, using a constant incipient fluidization bed height of 88 ram.

2.2. The measurement of the degree of bed electrification

Performances and limitations of the system used for measuring the degree of bed electrification have been described elsewhere [24] and only those aspects related to the study reported in the present work are outlined below.

When the degree of electrification is measured by means of the probe-distributor voltage, curves like those shown in Fig. 2 are obtained. As can be seen, the voltage rises continuously until a stationary value (Vs) is reached. The variation of voltage with time shown in Fig. 2 is typical of capacitor charging so the probe--bed-distributor system is considered as a conical capacitor, where the probe and distributor are the plates and the bed is the dielectric medium.

Capacitance by a parallel-plate capacitor with equal circular plates is given as

capacitance = charge on the plates

voltage between plates

. . . . rt/4 (plate diameter) z = electric length between plates permlttlvlty


22

20

18

~6

w > 10

8

o ~ - o 0 0 o o

g'V

0 0 0 0

2

0 0 2 4 6 IS 10 12 B 16 18 20 22 2& 26 28 30 32 3& $6 38 &O &2 && &6 &8 50

! [min)

Fig. 2. Variat ion of p robe-d i s t r ibu tor voltage with time for d o = 350-420 pm and uf/umr = 2.5.

capacitance by the conical capacitor can be expressed as

Q (~/4)DcDe C = ~ = e.f He ' (1)

where Dc and De are, respectively, the column and probe diameters, He is the probe height, and Ef is the effective permittivity of the fluidized bed.

Bed electrification can be quantified by two variables from Eq. (1), Q or V. The electric charge, Q, represents the state of the electric capacitor, and is, therefore, the variable used in this study. It is a function of:

(1) The geometric characteristics of the equipment (De = 44 ram, De = 5 mm and He = 88 mm).

(2) Effective bed permittivity, ef, is a value for which Jones 1-26] proposed correla- tions that did not differ by more than 5% for normal fluidized bed voidages. The best permittivity for a voidage close to 0.5 is

- - ~ E p - - g O g'f EO -- (1 -- ~J , (2) 3e f 2e f -}- gp

% ( = k%) is the fluidizing material permittivity and So is the free space permittivity. ~ is the bed voidage and represents the non-geometric properties of the fluidized system. If


we solve for ~f we find

( 2 k - 3 ~ k + 3 ~ - 1 ) + ~ / ( 2 k - 3 : ~ k + 3 ~ - 1) 2 + 8 k ~ ' f ~ ~-~0 4

= ~:o[f(~,k)], 13)

in whichf(~, k) is the function for voidage and permittivity; k = 5 since glass is being fluidized here.

(3) V, the experimentally measured voltage. Thus Eq. (1) becomes

Q = ~ So [ f (~ , k)] V. /4)

On the other hand, the degree of fluidized bed electrification increases with time (see Fig. 2) so the selected voltage value must allow comparison of the results of experiments performed in different conditions. The voltage rises to a limiting stationary voltage (Vs) which was the value chosen for comparisons. The value V s for each experiment was obtained by fitting the data of time and voltage to the equation

V = V,[1 - e x p ( - K t ) ] (5)

by means of a non-linear regression method.

2.3. Procedure

Before each electrification experiment, air was passed downwards through the bed at a surface velocity equal to the fluidization velocity that was going to be used in the experiment and with a relative humidity of 80% - to remove any possible static charge built up during bed handling. Humidity was then set at the value corresponding to the experiment and air was passed downwards for another 10 min in order to ensure equilibrium between bed humidity and air humidity from the beginning of the fluidization.

After that, the bed was fluidized and voltage was measured on a regular basis until a stationary value was reached. At this time, fluidization was stopped and air - at the same velocity and humidity as those used during fluidization - was passed downwards once again and the voltage measured as a function of discharge time.

For each size of glass bead tested, the same sample of material was used throughout the work. To avoid the influence of the surface state of fresh material, the whole portion of each size to be used was fluidized for 24 h before beginning the first run, and the experiments were undertaken in a randomly established order.

3. Results and discussion

Tables 3-5 show the specific conditions used in the three series of experiments carried out. In addition, these tables include the mean values of V, and K, obtained

8 J. Guardiola et aL/Journal of Electrostatics 37 (1996) 1-20

Table 3 Charge generation experiments for dp = 250-297 lain

Uf/Umf Hf ~ RH No. Vs 95% c.l. K 95% c.l. Type of (mm) (%) of (V) ( _+ % of Vs) (min- ~) ( _+ % of K) fluidization

points

10 15 6468 4.9 0.01 8.3 1.5 94 0.45 20 25 2451 2.8 0.12 19.7 Bubbling

30 10 866 6.0 2.44 42.0

5 47 13 888 4.4 0.02 9.5 10 34 10634 0.8 0.09 2.7

2.5 110 0.53 20 16 4828 2.5 0.10 6.8 Bubbling 30 25 2776 2.6 0.98 18.4 35 17 955 9.2 2.43 91.8

5 18 16438 3.0 0.13 19.0 10 23 12286 9.7 0.03 21.4

3.5 120 0.57 15 46 13 380 7.2 0.03 24.6 Bubbling 20 22 7300 1.6 0.89 7.0 25 26 6073 2.7 0.76 14.0

For RH i> 40% bed electrification was no longer observed.

Table 4 Charge generation experiments for dp = 297-350 ~tm

udume Hf ~ RH No. Vs 95% c.l. K 95% c.1. Type of (mm) (%) of (V) ( + % of Vs) (rain- ') ( _+ % of K) fluidization

points

10 33 4916 6.4 0.15 32.5 1.5 95 0.43 20 54 10360 2.3 0.23 12.8 Bubbling

25 26 2359 3.1 1.21 25.2 30 8 931 6.8 0.85 35.4

10 23 6939 5.0 0.54 21.9 15 25 10281 2.5 0.57 11.0

2.5 110 0.50 20 35 12 399 1.4 0.68 7.3 Bubbling 25 30 6120 3.0 1.73 22.7 30 9 958 5.9 0.60 27.8

15 35 6662 4.3 0.96 28.4 3.5 125 0.56 20 32 8327 3.1 3.20 46.9 Onset of

25 44 6994 3.9 3.04 41.7 slugging 30 20 2095 - - 35.0 - -

For RH/> 40% bed electrification was no longer observed.

after fitting the data of time and voltage to Eq. (5), as well as the range - expressed as a percentage of the mean value of Vs and K - within a 95% confidence level. As an example, Fig. 2 shows both data and fitting lines corresponding to several of the experiments done with the size dp = 350-420/am.

J. Guardiola et al./Journal of Electrostatics 37 (1996) 1-20

Table 5 Charge generation experiments for dp = 350-420 lam

I.tf/Umf Hf ~ RH NO. of Vs 95% c.1. K 95% c.l. Type of (mm) (%) points (V) ( + % of V~) (rain-') ( + % of K) fluidization

10 39 9853 6.0 0.03 17.8 20 41 11 349 1.0 0.07 3.4 30 46 11926 2.0 0.09 9.2

1.5 95 0.45 40 30 8977 1.3 0.12 5.0 50 21 8334 1.3 0.21 4.7 60 20 5272 3.6 0.41 13.8 70 16 1898 4.0 2.39 36.5

10 52 16647 4.4 0.17 19.8 20 52 20882 1.3 0.21 7.4 30 43 23 838 1.1 0.32 5.4 40 46 21 372 1.6 0.40 8.6

2.5 115 0.55 50 47 21509 0.9 0.26 3.9 55 35 18 507 0.8 0.48 3.4 60 27 7666 2.0 1.19 11.9 65 17 4746 5.4 1.93 30.5 70 15 2249 5.8 11.47 132.2

10 41 5047 3.9 1.65 33.2 20 39 11 314 2.1 0.90 13.8 30 59 21 336 0.8 0.42

3.5 135 0.62 40 41 20425 0.9 0.50 50 42 21 143 1.1 0.43 55 23 19615 3.1 1.03 60 22 14 225 2.3 1.30 70 18 4108 3.3 6.15

Bubbling

Onset of slugging

5~1 4.7 Slugging 5.0

16.9 11.9 35.3

For RH t> 75% bed electrification was no longer observed.

3.1. Influence of relative humidity

The influence of the relative humidity of the fluidizing air on the maximum degree of electrification reached by the fluidized bed can be seen in Tables 3-5 which include the results obtained with all the fluidization velocities and particle diameters tested.

The influence of the relative humidity can be clarified with the aid of the characteristic curve proposed in Fig. 3. This general curve is valid for any velocity, particle size or fluidization velocity; as will be shown below, the curves for the variation of Qs with RH corresponding to some particular cases can be obtained from the plot in Fig. 4 by suppressing one or more of the stretches from the curve. The values of charge on the capacitor plates for stationary generation (Qs) appearing in the ordinate axis can be calculated with Eq. (4) using the Vs values in Tables 3-5.

At increasing values of relative humidity, the following zones can be observed in Fig. 3:

Zone A: For low values of relative humidity - below a critical value (RHc) - bed particles stick strongly to the column wall and to the electric probe so that direct

Qs (A) (C)

I I I I I I I I I I

RHc

(B)

RHmax


I

(D) ] IE) I I I I I I I I I I I I I I I I I I I

RH T RH%

Fig. 3. Generalized characteristic curve for the variation of the charge on the capacitor plates with relative humidity.

w o

Fig. 4. Example of voltage variation with time for RH < RHc.

TIME

contact between the probe and the rest of the bed is hindered. Under these conditions - as indicated by the potential difference measured by the voltmeter the bed "charges" and "discharges" spontaneously one or more times before reaching a stationary voltage (Fig. 4). Although the strong adhesion of particles to wall and probe

J. Guardiola et al./Journal o f Electrostatics 37 (1996) 1 20 11

indicates a very high level of bed electrification, the stationary voltage measured in these experiments is usually very low and always unstable (any action causing detachment probe particle - knocks to the column or vibrations, for instance - sets off a new series of "charge" and "discharge" processes in the bed that eventually lead to a new stationary voltage value that is different from the one reached before).

The values for Vs and K shown in Tables 3-5 for the experiments carried out in this zone of relative humidity have been obtained by fitting the data of time and voltage from the final charge process to Eq. (5). The values for Qs do not seem to be a reproducible measurement for bed electrification level when calculated on the basis of these Vs values.

Zone B: Relative humidity has very little or no effect on the stationary charge, Adhesion of particles to either the probe or the wall is not observed and thus the Qs value can be used to measure the degree of electrification. Humidities within this range produce the highest levels of bed electrification.

Zone C: Relative humidity has a strong influence on the degree of electrification and small increases in humidity produce sharp drops in the generated charge. Particle adhesion is not observed in this zone, either.

Zone D: For relative humidities greater than a certain value (RHmax), charge generation is not observed at all during fluidization.

Zone E: At high humidities above RHT the bed water content becomes so high that fluidization is impossible (wet quenching) because glass hydrophilicity [-27] leads to the formation of an ultrathin liquid layer around the particles that strengthens their mutual cohesion [28]. Preliminary experiments run with smaller glass beads (dp = 177-210 ~tm) determined the RHx value as 70%; for the three particle sizes studied here RHv > 85%.

The curve proposed in Fig. 4 can help explain the notorious difficulty in fluidizing very small particles (group C of Geldart's classification). Since the RHx value seems to decrease with particle size, zones B, C and D would be extremely small in group C powders (i.e. RHc ~ RHT) and fluidization will become difficult at any RH value due to the very high cohesion forces resulting from the electrostatic effect (for RH < RHc) and/or the bed moisture effect (for RH > RHx).

3.2. Influence of fluidization velocity

Bed electrification is related to the type of fluidization and the fluidization velocity as shown in Tables 3-5.

Two series of additional experiments with glass beads of 350-420 ~tm and two air velocities of 2 and 3 times the minimum fluidization velocity were conducted. Bubbl- ing and slugging were respectively produced at these respective velocities. The results obtained in these series are shown in Fig. 5.

If only that part of the curve corresponding to zone C shown in Fig. 5 is considered, there are two conclusions:

(1) The degree of electrification increases with fluidization velocity. (2) This increase is lower when the velocity is close to the value at which slugging

begins.

12 J. Guardiola et al./Journal o f Electrostatics 37 (1996) 1-20

9

8

7

4

3

2

1

0 20 40 60 80 100 RH(%)

Fig. 5. Influence of fluidization quality on the degree of electrification at dp = 350-420 pm.

This influence can be explained considering the type of fluidization and information from other papers.

In bubbling beds, bubbles rise through the tube, increasing in size and velocity, and reach the free bed surface as individual bubbles. When the bed is deep enough, bubbles can grow as wide as the column diameter and become slugs, which rise more slowly than the free bubbles with the same air volume that rise through a bubbling bed [29].

Boland and Geldart [13] studied the relationship between bubble size and degree of electrification by measuring the static electricity around the bubbles in gas fluidized beds. They found that the amount of the charge generated increases with bubble diameter because bigger bubbles rise more quickly, provoking more motion on the particles around them than do smaller bubbles.

Finally, the frequency of bubble formation at the distributor of a fluidized bed seems to be roughly constant to the increasing air flow rate which means that bubbles placed at a constant bed height become bigger as fluidization velocity increases 1-30, 31].

Thus, the increasing electrification that is observed with increasing fluidization velocities can be explained in the following terms: the increase in the air flow rate produces the formation of bigger bubbles that cause increasing motion of bed particles and therefore increase the levels of static electrification; this trend is limited by the onset of slugging fluidization when bubbles grow so wide that they become slugs which reduce particle motion.

As shown in Tables 3-5, the same Uf/Umf ratio yields either bubbling or slugging fluidization depending on the particle size tested because the minimum slugging

J. Guardiola et aL /Journal of Electrostatics 37 (1996) 1-20 13

velocity (urns) is proportional to d~, (a ranging from 0.5 to 0.6; see [32]) whereas the minimum fluidization velocity is proportional to d 2 (for Rep < 20; see [33]). Thus, the Ums/Umf ratio is proportional to dbp (b < 0), so a decrease in the value of the particle diameter will increase the umJUmf ratio and this will increase the range of the uf/umf ratio which will lead to bubbling fluidization.

The interaction of the effects produced by fluidization velocity and particle diameter will be analysed later.

3.3. Influence of particle diameter

The level of bed electrification increases with particle size (see Tables 3-5), but establishing a quantitative relationship between particle diameter and the level of static electrification reached in the bed is hampered by interaction between relative humidity, air velocity and type of fluidization, which makes it difficult to select RH and uf values that would allow result comparison. With regard to humidity, results might be compared by means of the degree of electrification obtained at RH = RHc, since this humidity level leads to the highest level of static charge for both bubbling and slugging fluidization. With regard to air velocity, the problem is identifying the fluidization velocity that would provoke the same degree of particle motion in beds of different particle size; neither the Uf/Umf ratio nor the excess gas velocity (uf - Umf) can be used for this proposal because in both cases a constant value for this parameter will produce either bubbling or slugging fluidization, depending on the size of particle considered.

Thus, the smallest tested particle sizes generate the lowest degree of static charge although they give the largest total bed surface. This is caused by the result of the increase with particle diameter in the number of contacts among particles - and thus charge build-up - during fluidization, as can be seen in the works of Graham and Harvey [34] and Cheylan and LeGoff [35].

3.4. Interaction between the influences of fluidization velocity and particle size

Both variables Ur and dp respectively together are responsible for the degree of particle motion in the bed that creates electrification. This is why the phenomenon can be analysed with the help of the solid circulation model [36, 37]. The average solid circulation velocity given by the inviscid model of Viswanathan [37] is

I °4 Uc=ubr gDc 2u3r [ , {6)

where the rising velocity of an isolated bubble, Ubr, as a function of the frontal diameter of the bubble, db, is

b/br ~ / ~ V 2 "

(7)


Bubble size can be calculated starting from the formulae of Darton [38],

deq 0 .54(uf u ,O.4hO.8 -0 .2 = - - mf) Y ,

Mori and Wen [39],

d ex / - 0.3 h'~ deq ~--- deq,m - ( d e q , m - eq,O) P ~ x ~ ) '

deq,m = 0.374 [rcD 2 (ur - - U m f ) ] 0 " 4 ,

deq.0 --- 3.76 × 10-3 (u f - - Urnf) 2,

and Rowe [40],

db= (uf - Umf)°'Sh°:Sg -°'25.

(8)

(9)

(9a)

(9b)

rio)

The values for deq obtained in Eqs. (8) and (9) are transformed to bubble size, db (db=deq/0.6 U3 [37]). The data from these three papers give an average size of bubble - d b in Table 6 - which can be used to calculate Ubr in Eq. (7).

Finally, as indicated in Table 6, the values for the average solid circulation velocity were obtained. When the size of the bubble, db, is just or slightly lower than the column diameter - 44 m m - the bed is in bubbling; if db were wider slugging would appear but the values for U¢ were not calculated. In all cases, the maximum height that the bubbles can reach in the bed was considered equivalent to the average bed height during fluidization, Hr.

Table 6 Estimation of the average solids circulation velocity

d v Uf llf///mf h d b Uhr /3 c (~m) (cm/s) (ram) (cm) (cm/s) (cm/s)

19.1 11.4 1.5 94 1.4 26.4 27.9

250 297 19.0 2.5 110 2.6 35.8 33.2 26.6 3.5 120 3.5 41.5

13.5 1.5 95 1.5 27.5 20.3 22.5 2.5 110 2.8 37.2 29.6

297 350 31.5 3.5 125 3.9 43.8 a 35.2 ~

28.5 1.5 95 2.2 32.5 26.4 38.0 2.0 105 3.2 39.4 33.6

350-420 47.5 2.5 115 4. l 44.6 ~ 38.5 ~ 57.0 3.0 125 4.9 ~-- 66.0 3.5 135 5.8

a They concern the values of db, slightly lower than the bed diameter.

J. Guardiola et aL/Journal of Electrostatics 37 (1996) 1-20 15

Table 6 shows that when the motion of bed particles increases - the average solid circulation velocity - bed electrification also increases. Although the Uc values reflect the restrictions resulting from the use of Eqs. (8)-(10) for beds with the type of distributor employed in the present work, they allow an approximation to the phenomenon. Earlier considerations on variations in particle surface and the number of inter-particle collisions as a function of size must not be forgotten, since both also affect electrical charge generation.

To sum up, the advantage of this approach is based on a single expression - Eq. {6) - which integrates the main variables in the process, namely

Uc --f(Ubr, De, uf, Umf ) (1 1)

or else

Uc = qo(h, De, uf, dp) (12)

in which h and D, express bed geometry, uf the system dynamics and dp the surface that is exposed to friction.

3.5. Loss o f electric charge

Once voltage had reached a stationary value at the end of each electrification experiment fluidization was stopped, and air - with the same superficial velocity and relative humidity as during fluidization - was passed downwards through the fixed bed and the voltage decay was noted through time. Voltage decay is due to the loss of the electric charge either by conduction through the tube wall - leakage - or by the effect of air humidity - dissipation - and it can be expressed by a first-order kinetic process (see Fig. 6):

-- (dV /d t ) = k'aV, (13)

where k~ is the kinetic constant for electric charge loss. Integration of Eq. (13) with the boundary conditions V = Vo for t --- 0 and V = V for t = t yields

V = Vo exp( - k'dt). (14)

Obviously the values of k~ obtained from these experiments - and fitting the data of voltage and time to Eq. (14) - will not be equal to the values for the charge loss constant corresponding to the bed that has been fluidized just before under the same conditions, since both porosity and contact surface between bed and column are different. However, it would seem reasonable that the qualitative conclusions on the influence of the variables drawn from these fixed bed experiments can be applied to the fluidized bed.

The influence of the air velocity and relative humidity on the kinetic constant for electric charge loss can be observed in Fig. 7. As explained above, experiments in which RH < RH~ were disregarded to avoid misinterpretation of the results. The k~ values were not obtained at the two smallest particle sizes because the rate of voltage decay was too fast - almost instantaneous for high RH and Uo values - and its

16 J.. Guardiola et al./Journal o f Electrostatics 37 (1996) 1-20

30

2O

15

I " I ' I ' I ' I

KEY RH(%I

• 30 o 40

• 50

10 I 1 , I , I i I , I 0

0 2 /, 5 8. 10 12

Time {mini

Fig. 6. Variation of voltage decay with time at dp = 350-420 lam and Uo = 47.5 cm/s.

measurement became impossible (the same thing happened at dp = 350-420 ~tm and RH > 60%).

As shown in Fig. 7, the charge loss constant increases with air velocity and relative humidity. This result evidences the strong effect that fluidization velocity exerts in promoting friction among bed particles since the increase of u~ increases the amount of charge generated, although it also increases, at the same time, the rate of electric charge loss.

4. C o n c l u s i o n s

The effect of relative humidity was found to be complex and to depend on the type of fluidization. A characteristic curve consisting of five zones is proposed to explain the variation of bed electrification with relative humidity. For any given particle size and air velocity there is a range of relative humidity - zone C - in which a small increase in humidity causes a sharp decrease of the level of electrification. It is worth noting that the characteristic curve proposed in the present work is likely to be valid only for those materials that, like glass, exhibit hydrophilic behaviour. Hydrophobic

J. Guardiola et al. /Journal of Electrostatics 37 (1996) 1-20 17

'c

10-1 8

5

' I ' I ' I

10" 20 70

f /

/ / /

/ /

R.= ///// / / /

/ / , / / / / /

2.5

I 3.5 I i t L I J I '

30 ~0 5O 50

RH (%1

Fig. 7. Variat ion of the fixed-bed charge loss constant with relative humidity and air velocity for dp = 350-420 Hm.

materials such as polyethylene, polystyrene, nylon or polymethyl-methacrylate might not follow this type of curve.

The results show that for relative humidity values lower than a critical level (RHc), the static electrification of the bed cannot be measured by means of the probe-distr ibutor voltage technique because the adhesion of particles to the probe produces non-reproducible voltage readings. Furthermore, the existence of a limiting value of humidity beyond which no static electrification is observed in the fluidized bed has been shown.

As for the effects of particle size and air velocity, the degree of electrification was found to increase with increasing values of both variables, the effect of the latter being connected with the type of fluidization - bubbling or slugging - existing in the bed. In the same way, from a qualitative point of view, the bed electrification level increases with the increase in the average solids circulation velocity - motion of fluidized particles.

18 J. Guardiola et aL /Journal of Electrostatics 37 (1996) 1-20

Additional fixed bed experiments have clarified the important role played by air velocity in promoting rubbing between bed particles; this variable increases the degree of electrification reached by the fluidized bed although it also simultaneously increases the rate of electric charge loss.

Nomenclature

C db deq deq,o

deq,m dp D~ D~ f(a,k) h He Hf Hmf k~, K Q Qs RH RH¢ RHmax RHx t Ubr Uf Umf Ums U0 uc V Vo Vs

capacitance of the probe-bed-distributor capacitor, F frontal diameter of bubble, cm equivalent volume diameter of bubble, cm initial equivalent bubble size, cm maximum equivalent bubble size attainable by coalescence, cm particle diameter, ktm inside diameter of column, mm electric probe diameter, mm function for bed voidage and permittivity as defined in Eq. (3) distance above distributor, mm height of electric probe above distributor, mm average height reached by bed during fluidization, mm bed height at incipient fluidization, mm kinetic constant for electric charge loss with fixed bed, min-1 kinetic constant of charge generation, min- electric charge of capacitor, C electric charge of capacitor for stationary generation conditions, C relative humidity of fluidizing air relative humidity at critical point relative humidity beyond which electrification is no longer observed relative humidity beyond which wet quenching occurs time, min rising velocity of an isolated bubble, cm/s fluidization velocity, cm/s minimum fluidization velocity, cm/s minimum slugging velocity, cm/s superficial velocity of gas in fixed-bed experiments, cm/s average solids circulation velocity, cm/s potential difference between probe and distributor, V initial potential difference in electric charge loss experiments, V stationary potential difference, V

Greek letters

void fraction of fluidized bed ~mf void fraction of bed at incipient fluidization


gf

go gp

effective permittivity of fluidized bed, F/m effective permittivity of free space, F/m effective permittivity of particles, F/m

Acknowledgements

Our gratitude to Ms. C.F. Warren of the Instituto de Ciencias de la Educaci6n of the University of Alcalfi de Henares for linguistic assistance.

References

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Influence of particle size, fluidization velocity and relative humidity on fluidized bed electrostatics

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