Ind. Eng. Chem. Fundam. 1083, 22, 445-453
Bellman, R.; Kalaba, R. ”Quasillnearlzatlon and Nonlinear Boundary Value Problems”; American Elsevier: New York, 1965. Byrne, 0. D.; Hindmarch, A. C.; Jackson, K. R.; Brown, H. 0. Comput. Chem. Eng. 1977, 1 , 133. DonneHy, J. K.; Quon, D. Can. J. Chem. €ng. 1970, 48, 114. Edsberg, L. I n “Numerical Methods for Differential Systems”; Lapidus, L.; Schiesser, W. E., Ed.; Academic Press: New York, 1978; p 181. Enrlght, A. H.; Hull, T. !-I. I n “Numerical Methods for Dlfferentlal Systems”; Lapidus, L.; Schiesser, W. E., Ed.; Academlc Press: New York, 1976; p 45. Oarflnkel, D.; Chlng, D. W.; Adelman, M.; Clark, P. Ann. N . Y . Aced. Sci. 1966, 1054. Glowlnskl, J.; Stockl, J. A I M J. 1981, 27, 1041. Hindmarch, A. C.; Byrne, G. D. I n “Numerical Methods for Differential Systems“; Lapidus, L.; Schlesser, W. E.. Ed.; Academic Press: New York, 1978; p 147. Hougen, 0.; Watson, K. M. “Chemical Process Prlnciples”; Vol. 3, Wlley: New York, 1948. IMSL Llbrary, “Reference manual”, 8th ed.; tnternatlonal Mathematical and Statlstlcal Librarles Inc.: Houston, TX, 1980. Kalogerakis. N.; Luus, R. A I C M J. 1980, 26, 670. Kalogerakb, N.; Luus, R. Proceedings of 1982 American Control Conference,
445
Lawson, C. L.; Hanson, R. J. “Solving Least Squares Problems”; PrentlceHall: Englewcad Cllffs, NJ, 1974. Lee. E. S. ”Quasillnearlzatlon and Invariant Imbedding”; Academlc Press: New York. 1968. Levenberg, K. Quart. Appl. Meth. 1944, 2 , 184. Marquardt, D. W. J. Soc. Ind. Appl. Meth. 1963, 1 1 , 431. Nieman, R. E.; Fisher, D. 0. Can. J . Chem. €ng. 1972, 50, 802. Osbome, M. R. In "Numerical Methods for Nonlinear Optimization”; Lootsma, F. A.. Ed.; Academlc Press: New York, 1972; p 171. Ramaker, B. L.; Smith, C. L.; Mwlll, P. W. Ind. Eng. Chem. Fundam. 1970, 9 , 28. Reo, S. N.; Luus, R. Can. J. Chem. Eng. 1972, 50, 777. Robertson, H. H. I n “Numerical Methods”; Walsh, J., Ed.; Thompson: Washington, 1967; p 178. Seinfeid, J. H.; Gavalas. G. R. A I C M J . 1970, 16, 644. Strang, G. “Linear Algebra and Its Appllcatlons”; Academlc Press. New York, 1980. Vllladsen, J.; Michelsen, M. L. “Solution of Differential Equatlon Models by Polynomial Approxlmatlon”; Prentlce-Hall: Englewood ClMs, NJ, 1978. Wang, B. C.; Luus, R. Int. J . Control 1980, 3 1 , 947. Welmer. A. W.; Clough, D. E. AIJ. 1979, 25, 730.
Received for review September 20, 1982 Revised manuscript received June 10,1983 Accepted July 20,1983
Filtration of Airborne Dust in a Triboelectrically Charged Fluidized Bed Gabrlel Tardos’ and Robert Pfeffer Department of Chemical Englneerlng, The City College of The City Universlv of New York, New York, New York 10031
Mlchael Peters Department of Chemical Engineering and Envlronmental Engineering, Rensselaer Polytechnic Institute, Troy, New
York 1218 1
Thomas Sweeney Department of Chemical Engineering, The Ohla State University, Columbus, Ohla 43210
Experimental evidence is given to show that charges generated naturally on dielectric granules in a fluidized bed during the fluidization process can considerably increase the efficiency of such beds to remove micron and submicron airborne particles. The experimental work Includes both the measurement of electrostatic charges generated on fluidized granules wtth a modlfied Faraday cage, as well as the measurement of the filtration efficiency when such parameters as gas velocity and gas humidity are varied over a wide range. The experimentally obtained efficiencies are then compared to the predictions of a previous fluidized bed filtration model which took into account both the electrostatic charges on the bed granules and dust particles as well as the presence of bubbles in the bed. Furthermore, lt is demonstrated that a proper choice of fluidized particles can significantly increase the efficiency of the fluidized bed filter without an increase in bed thickness or a corresponding increase in pressure drop through the filter.
Introduction The filtration of dusts and aerosols from a gas stream is a common industrial problem. Many applications involve high temperatures, corrosive environments, arkd high particle loadings in which classical cleaning devices, such as electrostatic precipitation, venturi scrubbing, and fixed bed filtration, may not be well suited. The idea of using a fluidized bed to circumvent these difficulties has been
the subject of many investigations dating back to Meissner and Mickley (1949). The concept involves using the gas to be filtered as the fluidizing medium for a bed of collector particles. Because the collector particles are fluidized, they can be easily removed, cleaned, and replaced continuously (see, e.g., Sryvcek and Beeckmans, 1976). Recent reviews of studies on fluidized bed filtration may be found in the work of 0 1983 American Chemical Society
446
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Jackson (1974), Doganoglu et al. (1978), Tardos et al. (1978), Tardos and Pfeffer (1979a), and Peters et al. (1982a). Since high efficiencies are necessary, in general, for fine particle filtration devices, a major concern about fluidized bed filters lies in the bypassing of the dust or aerosol particles through the gas bubbles of the fluidized bed. Although this “bypassing effect” can be greatly reduced through the use of internal baffles, neutrally buoyant bubble breakers (Gbordzoe et al., 1981) or magnetic stabilization (Rosensweiget al., 1981)a great deal of emphasis has also been placed on increasing the particle removal efficiency of the dense phase. For example, Melcher and his co-workers (Johnson and Melcher, 1975; Zahedi and Melcher, 1976, 1977; Alexander and Melcher, 1977; Dietz and Melcher, 1978) have investigated the use of externally applied electric fields to enhance the efficiencies of fluidized bed filters. In this type of fluidized bed, the electric field induces positive and negative charges on the ends of the collectors. This induced polarization of charge has been shown to occur for both conductive as well as insulating type materials (Zahedi and Melcher, 1976). Since all particulates carry some residual charge, electrostatic collection is possible at the oppositely charged end of the collectors. These electrofluidized beds (EFB’s) have been shown to demonstrate very high efficiencies (see, e.g., Johnson and Melcher, 1975; Zahedi and Melcher 1976; Zahedi and Melcher, 1977; Dietz, 1981). A method of achieving electrostatic collection without the use of an external electric field is by frictional charging or triboelectrification of the bed medium collectors. This type of charging occurs naturally in a fluidized bed consisting of insulating and semiinsulating materials. The exact mechanism of frictional charging is not well understood (see, e.g., Harper, 1967 and Briggs, 1979). Charge transfer is thought to occur by three possible mechanisms: (1) transfer of electrons between surface levels; (2) transfer of electrolytic ions; (3) transfer of specks of charged material. With insulating materials electron transfer might be ruled out since there are no unoccupied energy levels for the electrons to go into. However, it is well-known that insulators do become charged when in contact with electrons, and this has been attributed to impurities and defects in the insulator (Cottrell et al., 1979). One can only conclude at this time that frictional charging in a fluidized bed is possible by all three mechanisms. Further mechanistic understandings await the results of surface analysis techniques (Briggs, 1979). There is also question concerning the distribution of the charges on the granules in the fluidized bed. Bafrnec and Bena (1972) have stated that, although any single granule may be charged mostly positively or negatively, the total charge of a greater number of granules of the bed will be zero. Zahedi and Melcher (1976) have stated that each individual granule may itself be on the whole neutral, giving rise to “micro” electric fields around the granules. Tardos and Pfeffer (1979b) gave theory for the trajectory of a small charged dust particle around a charged spherical collector, assuming a very low and uniformly distributed surface charge on the sphere. Their theory can be used to estimate the effects of frictional charging on the efficiency of fluidized bed filters, provided one has knowledge of the magnitudes of the charges involved. Although frictional charging of the bed medium collectors has been discussed since the introduction of fluidized bed filters, the literature has only recently seen more critical examinations of the phenomena. Ciborowski and Zakowski (1977) experimentally observed a direct corre-
Figure 1. Experimental setup for charge and filtration efficiency measurements: (1)Teflon insulator; (2) grounded vessel; (3) granules; (4) metal cover; (5) Teflon vessel; (6) sustaining screen (100 mesh); (7) Ni probe (2 mm); (8) bypass tube; (9) Corona charger; (10) a-ray aerosol neutralizer; (11)Keithley 610C electrometer (for current measurement); (12) Royco 220 aerosol analyzer; (13) vacuum pump; (14)aerosol generator; (15) manometer; (16) rotameter; (17) rotameter; (18) dryer; (19) filter; (20) compressed air supply; (21) Keithley 610C electrometer (for charge measurement); (22) granule removing tube.
lation between the fluidized bed filtration efficiency and the electrostatic charge intensity in a bed of dielectric granules. Those authors also found a considerable reduction in the filtration efficiency and a rapid dissipation of the electrostatic charge with increases in the relative humidity of the inlet gas. A similar effect was noted by Zahedi and Melcher (1976). Increased efficiencies in bubbling fluidized beds of dielectric granules were also reported by Balasubramanian et al. (1978),Figueora and Licht (1978), and Gutfinger and Tardos (1979). Tardos et al. (1979a) simultaneously measured the electric potential in the bed and the filtration efficiency at the onset of fluidization. They observed a significant increase in both the filtration efficiency and the electric potential when the bed collectors became fluidized. Their results provide conclusive experimental evidence that the fluidized bed filtration efficiencies can be greatly enhanced through frictional charging. In the present study, a more extensive analysis on the effects of triboelectrification is given by simultaneous experimental measurements of the collector surface charges and the fluidized bed filtration efficiencies. Since selfelectrification depends strongly on the nature of fluidized granules, the study includes experiments performed on different granules fluidized under different conditions. The experimental findings are also compared to a theoretical model which accounts for the bypassing of dust particles in the bubble phase and also includes the effect of electrostatic deposition in the bed due to attractive Coulombic forces between the dust particles and the granules. Apparatus and Experimental Procedure The experimental setup is shown schematically in Figure 1. I t is essentially a fluidized bed of granules contained in a 5-cm diameter, grounded copper (or Lucite) tube in which the granules are supported on a 100-mesh copper
Ind. Eng. Chem. Fundam., Vol. 22, No, 4, 1983
447
Table I. Characteristics of Fluidized Particles Poly -
granule material
units
shape
average equivalent diameter,
mm
material density, p s porosity packed bed, e o porosity of bed at minimum fluidization, E m f minimum fluidization velocity, Umf
g/cm3 cm/s
phenylene oxide rod
polyethylene rod
3.1 1.1 0.4 0.45 65
2.92 1.24 0.41 0.46 66
polystyrene spherical
0.45 1.03 0.37 0.38 10.5
screen. Fluidization air is provided at superficial air velocities up to 1.5 m/s and relative humidities between l and 90% at room temperatures. Latex aerosols 1.01 pm in diameter are generated in a Royco-256 generator and are introduced into the fluidization air through an a-ray aerosol neutralizer and a rod-in-cylinder corona charger. This enables one to use neutral or charged aerosols during the filtration experiment at will. The efficiency of the granular bed is measured during the experiment with both a Royco-220 and a Climet CI-210 aerosol analyzer. The efficiency of the bed for separation of the aerosol is then computed from 17 = 1 - NO"t/NO
(1)
where No and No, are the aerosol concentrations measured at the inlet and the outlet of the bed, respectively. The electric charging of the bed granules can be detected by two different techniques. One is by inserting a small nickel ball probe through the bed and into the granules and measuring the current to ground generated by the fluidized particles. The nickel probe, presented in Figure 2, is placed a t the center of the bed and held in position by a grounded metallic tube. The probe is identical with that used by Duckworth and Chan (1973) and Cheng and So0 (1970). The probe is connected to an oscilloscope and to a Keithley electrometer which measures the current generated on the sphere through a 10-MQresistance. The signal is then passed through an RMS meter (DISA 5535) and is displayed on a digital voltmeter (HP-3438A) and a digital printer (HP-5150A). There are two distinct mechanisms by which current is generated on the probe, namely, direct contact between charged granules and the nickel sphere and induction due to the passage of charged granules near the probe. The generated current, which is the sum of these two effects, is time-averaged by the RMS meter whose integration interval can be changed in such a way that the resultant current has relatively small fluctuations. The other technique is to measure the charge on the granules directly and is based on the well-known property of a fluidized bed which enables the removal of granules through any opening in the fluidizing vessel. The granule removing device is a long straight tube 3/a in. in diameter, mounted in the fluidized bed as shown in Figure 1. A lock enables granules to be removed from the fluidized bed through the open end of the tube at a central location at any desired time. These granules are caught below the fluidized bed in a Teflon vessel. This vessel serves as an electrically insulated part of a Faraday cage. The other wall of the Teflon vessel is metal-covered and is connected to a Keithley electrometer for electric charge measurement. To complete the Faraday cage, an external vessel is provided and connected to ground through a low resistance cable. A measurement is carried out as follows. After steady fluidization has been established at a given gas superficial velocity, the lock on the granule removing system is opened and particles are collected in the Faraday cage. The charge
PIPE WALL-'
Figure 2. The nickel probe for current measurement.
present on the granules induces an equal and opposite charge on the metallic cover of the Teflon vessel whose charge is subsequently measured by the electrometer. After a given time the lock is closed and the Teflon vessel is removed and the mass of collected granules is measured on an analytical balance. The average charge on the granules is obtained from the total charge and from the total weight of the granules. Details on the devices, the procedure, and the precision of the method are given in Tardos and Pfeffer (1980). At the same time the current generated on the nickel probe (RMS value) and the separation efficiency, 7, of the bed are also recorded. The experimental program was designed to simultaneously measure the efficiency of the granular bed, the average surface charge on the granules, and the current generated on the nickel probe. The parameters varied during the experiment were gas humidity and gas superficial velocity, so as to obtain both packed and fluidized conditions. The gas velokity was increased from zero to its maximum value in increments of 10-20 cm/s and subsequently decreased to zero. A t each gas velocity enough time was given for the granules to achieve a constant charge characteristic of the selected velocity. This time varied with the type of granule and also was a strong function of gas humidity. A constant charge was assumed to have been achieved when the current generated on the nickel probe remained constant for at least 2-5 min. At that time, the charge on the granules was measured by use of the Faraday cage. The granules used during the experiment are characterized in Table I.
Experimental Results Some typical experimental results are presented in Figure 3, where the filtration efficiency, 1,of a 1.1cm thick
Ind. Eng. Chem. Fundam., Vol. 22, No. 4, 1983
448
0.45rnrn POLYSTYRENE SPHERES1
[ 1.o
I
BRASS W A L L
i 0.71 PACKED B E D L -
L
i I
IO
15 G A S VELOCITY
u,
20 [cm/sec]
GAS V E L O C I T Y U,
Figure 3. Efficiency vs. gas velocity for polystyrene spheres 0.45 mm in diameter. Hu
0.45rnrn POLYSTYRENE SPHERES 1
1
BRASS W A L L
p/O]
,
10
[crn /tec]
/POLYETHYLENE OXIDE m~s1 Bed thickness LA= 17crn h
PACKED BED
1
RANGE OF
I
07
Hu
FCLIDIZATION
PACKED BED
-1-
1-
‘i
14
I
L
PACKED BED
A
y
O
~
Figure 6. Filter efficiency and surface charge vs. gas velocity for polyethylene oxide rods at a gas humidity of Hu = 30%.
kw
I
__
-RA_NGEOF FLUIDIZATION
LEGEND
: 60%,
I Hu
a
-
15 GAS VELOCITY
u,
i
80%
I
b
20 [crn/sec]
aw
I>
Figure 4. Mean specific charge vs. gas velocity for polystyrene spheres 0.45 mm in diameter.
25 35
55
75
95
115115
95
75
55
35 25
G A S V E L O C I T Y [cm/secl
Figure 7. Filter efficiency and surface charge vs. gas velocity for polyethylene rods a t a gas humidity of Hu = 17%.
0.45rnrn POLYSTYRENE SPHERES BRASS W A L L
POLYETHYLENE OXIDE RODS Bed thickness L o = 17cm
80
-SECOND RUN
GAS VELOCITY
uo [crn/sec]
Figure 5. Current generated on nickel probe vs. gas velocity for polystyrene spheres 0.45 mm in diameter.
layer of polystyrene spheres 0.45 mm in diameter, is given as a function of gas superficialvelocity, U,,at four different gas humidities. In figures 4 and 5 the mean specific charge, q, and the current, I, generated on the nickel probe (RMS value) are given for the same particles. During the experiment the gas velocity was increased from zero to about twice the minimuum fluidization velocity while the humidity was varied from 1% to 80%, at room temperature (22 “C). As seen in Figure 4, the surface charge generated on the granules at the highest humidity (Hu= 80%) is nearly zero, while the current generated on the nickel probe is also very low (Figure 5 ) . Examination of the efficiency variation in Figure 3 shows the high efficiencies obtained in the packed bed region (U, < U,) and a subsequent drastic decrease at high humidities once fluidization is reached. The efficiency drops
uww
LVO
a$K y WLZU 2
05-
4
2
1
1U m f ) 65
.
;
1
.Umf’65 )L,
: I&
I
I
1.
Ind. Eng. Chem. Fundam., Vol. 22, No. 4, 1983 449 q2,55!
P O L Y E T H Y L E N E RODS
T255p
FILTER THICKNESS i..= 4.4cm BRASS WALL
= 0.46 ps = 1.24
.Emf
w
u
,+ I
25 =2.92mrn
.8
P O L Y E T H Y L E N E RODS
@j8 FILTER THICKNESS ~ = 4 , 4 c m PLASTIC WALL
Umf
2;
=2.92mm = 0.41
HUMIDITY = 30%
,6[ 0
,
30
40
I
50
1
60
uo [cm/sec]
I
PACKED BED
0
1
70 80 90 G A S VELOCITY
100
-
INCREASING U, DECREASING U,
.6
0
, 30
FLUIDIZED BED
LEGEND
.
0
,
40
50
60
~,[cm/ssc]
70
, BO
90
INCREASING Uo DECREASING U,
100
GAS VELOCITY
Figure 9. Filter efficiency v8. gas velocity for polyethylene granules in a metal wall fluidized bed.
Figure 10. Filter efficiency vs. gas velocity for polyethylene granules in a Lucite wall fluidized bed.
tices of the bed and from the bubbles and force them to deposit on the granule's surface. Similar results were obtained for the case of polyethylene oxide rods of 3.1 mm equivalent diameter in a 17 cm thick packed and fluidized bed. These results are shown in Figures 6-8,where the efficiency, q, and the surface charge q are presented on the same figure as functions of gas velocity UD.During these experiments the velocity was first increased from zero to a maximum value and subsequently decreased. The initial experiment was carried at a gas humidity of Hu = 30% (Figure 6). The efficiency decreased somewhat in the bubbling regime and was high in the packed bed. A decrease in gas humidity to Hu = 17% yielded the data shown in Figure 7: an increase in surface charge by about a factor of 1.5 to 2 and an efficiency increase from about 80% to 85%. A subsequent experiment at a much higher gas humidity of Hu = 60% resulted in a marked decrease in efficiency (about 60%) while the average surface charge proved to be very low (Figure 8). A careful study of the results, especially those in Figure 9, reveals that the efficiency variation with gas velocity is different if the velocity is increasing or decreasing. A similar variation in the surface charge seems to indicate that residual charge on the granules is responsible for this behavior. Two separate runs are presented in Figures 6 to 8. The first set of data (crosses) was obtained by increasing the velocity to its maximum value and then decreasing the velocity back to zero using freshly washed granules. The second set of data (dots) was simply a repeat of this process without washing the granules. As seen in the figures both the filtration efficiency and the surface chage were somewhat higher during the second set. Subsequent runs using the same unwashed granules did not show further changes in either efficiency or surface charge. The hysteresis effect obtained by increasing and decreasing the velocity, Uo,in the granular filter is depicted more visibly in Figure 9 where the filtration efficiency, q, of a 4.4 cm thick layer of rod-like polyethylene granules is given as a function of gas superficial velocity. As seen in the figure, the filtration efficiency decreased slightly as the gas velocity was increased in the packed bed mode. This was due to the fact that the main mechanism by which aerosols are collected is by diffusion, which decreases as the velocity increases (Gutfinger and Tardos, 1979). The surface charge q on the granules measured at the same velocities is practically zero. As soon as fluidization conditions were reached an efficiency increase could be observed which decreased as the velocity was further increased. If one starts to decrease the gas velocity from its maximum value the measured efficiencies do not follow the reverse pattern, but rather follow a higher efficiency
path. This suggests that the electrostatic charge generated during fluidization had not dissipated, thus increasing the efficiency. For these dielectric granules the efficiency of the defluidized bed is shown to be higher than the corresponding efficiency of the packed bed at the same gas velocity. A similar experiment with a bed of identical granules and identical height as that presented in Figure 9 was performed by replacing the metal grounded wall of the fluidized bed with a dielectric lucite pipe of the same diameter. The results are given in Figure 10. As can be seen, the efficiencies were significantly higher than those given in Figure 9, thus showing that the effect of wall material is also very important in this kind of application. Theoretical Considerations and Discussion The analysis of fluidized bed filtration efficiencies is compounded by the complex mechanics of the gas-solid fluidization process. Particulates enter the fluidized bed through the bubbles and the surrounding dense phase, and thus experience the gas dynamical behavior in their journey through the bed. It is therefore necessary, a priori, to particle collection mechanisms, to have an accurate quantitification of the relative size, division of gas flow, and gas interchange between the bubble phase and the surrounding dense phases. For example, Peters et al. (1982a) have demonstrated that considerable error can be made in the calculation of fluidized bed filtration efficiencies if the two-phase theory is employed for evaluating the division of gas flow among the phases. This is due to the overprediction of the bubble phase flow rate in the bed. Concerning gas interchange between the bubble and surrounding dense phases, Grace and his co-workers (Chavarie and Grace, 1976; Sit and Grace, 1981) have shown that employing the Murray analysis of bubble motion (Murray, 1965) to calculate convective mass transfer contributions leads to reasonable agreement with experimentally determined gas interchange coefficients. These results can be particularly important in fluidized bed filtration since convective diffusion outweighs molecular diffusion of particulates (Doganoglu at al., 1978). The incorporation of the above observations into the prediction of the fluidized filtration efficiency has been recently given by Peters et al. (1981). In that model the well-known Bubble Assemblage Concepts of Kato and Wen (1969) were modified to give a more realistic view of the fluidization mechanics and to include the physical process of particulate removal. The basic features of that model have been given previously (Peters et al., 1981,1982a) and we only present a summary of the equations employed. A steady-state material balance on particulates over the nth compartment in the fluidized bed for all three phases
Ind. Eng. Chem. Fundam., Vol. 22, No. 4, 1983
450
Table 11. Parameter Estimations Summary
"IS
Bn D2n e
P O L Y E T H Y L E N E OXIDE RODS B e d thickness L0=17 cm
4
Bed thickness L o = 1 7 c m
i 0 L
t
F I t e r efficiency S p e c i f c surface charge
--Experimental
( f i t t e d line)
T h e o r e t i c a l l y predicted f i l t e r e f f ciency
l4
$
12 0
-10 w 001
w
t
F i l t e r efficiency
d
8 6
2:
:2
a:
w
k
d 06LL
- 4 2
4 $
-
x
1
05 10
1
20
-
i
30 40 50 60 GAS R E L A T I V E HUMID'TY Hu
-- _ _ 70
-
[XI
2; - 007 80
IO
20
-
30 40 50 60 70 GAS R E L A T I V E HUMIDITY Hu PA]
80
Figure 11. Comparison of experimental and theoretical filter efficiencies in a bed of polyethylene oxide rods at a gas velocity of 94 cm/s.
Figure 12. Comparison of experimental and theoretical filter efficiencies in a bed of polyethylene oxide rods at a gas velocity of 109 cm/s.
(i = 1,bubble phase; i = 2, cloud phase; i = 3, emulsion phase) may be written
where E*,ER,ED, and EG are single collector efficiencies due to inertial impaction, interception, diffusion, and gravity, respectively, and E,, represents a collection mechanism to account for the Coulombic force between a charged collector and a charged aerosol particle. Equations to predict the individual single collector efficiencies are given in Appendix I. Starting from the boundary conditions (4) Ni, = N2, = NSo = No
u,swvl"-l- Nl") + F(l,$+l)nvL"(Nl+ln - Nl) + 3 F(L-l,*)"v,"(N,-l" - Nl) = E,"Nt"U,S--(l - %)VI. (2) 20, where VI,is the average superficial gas velocity in phase i, F,, is a gas interchange coefficient between phase i and phase j , V ,is the absolute volume of phase i, and N , is the dust particle concentration in phase i. The quantity E, is the so-called "single collector efficiency" in phase i and can be computed from Tardos and Pfeffer (1979b),Tardos et al. (1979a)) and Nielsen and Hill (1976) as E, = 1 - (1- &)(1- E R ) (-~E D ) ( 1 - E G ) ( 1 - Eel) (3)
the implicit eq 2 were solved to obtain the dust concentration at the exit of the fluidized bed as
Ind. Eng. Chem. Fundam., Vol. 22, No. 4, 1983
Table 111. Single Collector Efficiencies at the Midpoint of the Bed in Figure 11
Hu,% E R 16 26 37
0.002 0.002 0.002
ED
E1
Eel
EG
0.001 0.001 0.001
0.000 0.000 0.000
0.107 0.083
0.000
0.058
0.000 0.000
Table IV. Single Collector Efficiencies at the Midpoint of the Bed in Figure 12
Hu,% E , 15 25 32
0.002 0.002 0.002
ED
E1
Eel
EG
0.001 0.001 0.001
0.000 0.000 0.000
0.119
0.000 0.000 0.000
0.098 0.090
The overall efficiency of the bed was then computed using eq 1. Estimation of the fluidization parameters appearing in eq 2 has, been previously given by Peters et al. (1981) and is summarized in Table 11. Note, however, that the gas interchange coefficient between the bubble and cloud phases has been modified slightly based on the recent multi-bubble work of Sit and Grace (1981). Extensions of the model to the two-phase region may be found in Appendix 11. In Figures 11 and 12 the theoretically computed efficiencies are compared to experimental results obtained in the 17 cm thick bed of polyethylene oxide rods. The experimental results were obtained from Figures 6-8 for two different gas superficial velocities, namely 94 and 109 cm/s and for different gas relative humidities. By inputing the values of the experimentally measured surface charge, corresponding to a given gas relative humidity, the filtration efficiencies were calculated. Further computational details are given in Appendix I. As can be seen in Figures 11and 12, the agreement between the experimental and theoretical results is very good. In Tables I11 and IV the single collector efficiencies in the emulsion phase at the midpoint of the bed are given corresponding to the calculated filtration efficiencies shown in Figures 11and 12, respectively. As is evident from the tables, the controlling mechanism is the Coulombic attractive force, which results in the drastic changes in the filtration efficiencies with relative gas humidity. Thus, the theory verifies the ability to compensate gas bypassing effects by increasing the efficiency of the dense phase in removing particulates. Furthermore, the calculations show that the magnitude of the charges brought about by natural electrification are sufficient in that respect. No attempt was made to simulate the efficiencies obtained in the 1.1 cm thick bed of 0.45-mm diameter polystyrene spheres since the theoretical model is not suitable. This is due to the fact that assumption of concentration homogeneity in each compartment is suspect for such shallow beds. Furthermore, in these very shallow beds the collection of aerosols is overwhelmingly influenced by the geometry of the distributor plate (Doganoglu et al., 1978; Knetting and Beeckmans, 1974).
Conclusions It appears from the present work that the filtration efficiency of fluidized beds made of dielectric granules is low in the bubbling regime at values of gas relative humidity greater than about 4040% due to the combined effect of bypassing of aerosols through the bed in the bubble phase and the weak collecting ability of chargeneutralized granules in the emulsion phase. At lower gas humidities gas bypassing effects are counterbalanced by strong electrostatic forces which result from the charge buildup on the granules due to their continuous agitation in the fluidized bed. For certain dielectric granules which
451
have the property to retain electric charge, the efficiency of a defluidized bed is higher than the efficiency of the initial packed bed at the same velocity. Increased efficiency may also be obtained by using dielectric walls (or baffles) in the fluidized bed to enhance the formation of electrostatic charge. The theoretical model based on bubble assemblage concepts accurately predicts the overall efficiency of the bubbling bed in collecting aerosols and is, therefore, useful for design of such beds. The model should not be used to predict the efficiency of very shallow fluidized bed filters where the collection is mainly due to jet penetration. However, one has to keep in mid that commercial applications of granular bed filters are necessarily “deep” beds to insure collection efficiencies over 99%.
Acknowledgment The experimental part of this research was supported by Grant ENG-77-25002 from the National Science Foundation. The authors also wish to thank Ms. E. Girardi, Mr. W. Cassidy, and Mr. D. Firnberg for their help in construction of the apparatus and in running the experiments. Appendix I. Single Collector Efficiencies The expression for the single collector efficiency Ei given in eq 3 Ei = 1- (1- EI) (1- ER) (1-ED) (1- EG) (1- Eel) (AI) can be approximated by
Ei
ER + E D + E1 + EG + E,,
(A2)
if the individual efficiencies are small as compared to unity. These quantities may be estimated by the following equations 3 ER = -R, (A3) ei
E1 = 4 . 0 5 6 + 0.853St for ei
+ 6.048St2 + 11.137St3
(A5)
0.4 and St L 0.05
EG =
GaSt 1 GaSt
+
E,, = 4.4K,O.” for ei
= 0.4, where
-
D~QAcQ~ 3 M UieD Equations A3 to A5 are taken from the work of Tardos et al. (1979b) and are based on potential flow analysis. Note that eq A5 is the result of a curve-fit of the theoretically computed values taken from Figure 7 of that paper. Similarly, eq A7, for the electrical deposition due to Coulombic interaction, was obtained from a curve-fit of the theoretically computed values taken from Figure 3 of Tardos and Pfeffer (1979b). Although eq A7 is strictly valid for Stokes flow around the collectors, its sensitivity to the flow field type is relatively small; consequently, it is employed for potential flow analysis as well. Furthermore, small deviations in the voidage, from ei = 0.4, are neglected in eq A5 and A7. Note that eq A8 for the gravitational efficiency is independent of the flow field. Also, since the flow is K, =
452
Ind. Eng. Chem. Fundam., Vol. 22, No. 4, 1983
always opposite to the direction of gravity, EG is taken as the negative of eq A6. The equations corresponding to (A3)-(A5) for Stokes flow have been previously summarized by Peters et al. (1981) as
y) 3
ER = 1.5(
E1 = -0.191
R:
+ 1.717St - 1.266St2 + 0.31680St3
(All)
for ti LZ 0.4 and St I0.12. Consistent with the flow field models used in the development of eq A3 to A l l the velocity employed is an assembly averaged velocity for each phase. For the multiphase situation that exists in the fluidized bed, this is given by the superficial or empty tower velocity divided by the phase volume fraction
and since the volume fraction of each phase varies throughout the bed so will the assembly average velocity. The average surface charge distribution on the aerosol particle, Qp, was taken to be 1.3 X 10-lo C/cm2 (Pontius, 1977). The collector charge, QAC,is an experimentally determined parameter and was computed from the measured surface charge q using qPPc
QAC =
6x10'0
Note that is is implicitly assumed that Q, and QAC are of opposite sign in eq A7. For nonspherical collectors, an equivalent, volume-based spherical diameter is employed for the value of D,. In Figures 11 and 12, and in Tables I11 and IV, the potential flow based expressions, eq A3 to A5, were employed. However, since the controlling mechanism is the electrostatic force, the use of the corresponding Stokes flow expressions, eq A9 to A l l , makes little difference and is not considered here. Appendix 11. Simplications for the Two-Phase Region and Additional Assumptions For values of the superficial gas velocity close to the minimum fluidization velocity, clouds may not exist in the entire fluidized bed,or the clouds may be so large that they overlap in a compartment. Simplifications of the model for these cases have been given previously (Peters et ai., 1982b) in which the entire two-phase region is treated as just bubble and dense phases. The material balance equation, eq 2 becomes ulsS(Nin-l - Ni,) + Fi3,Vin(N3, - Ni,) = 0 (A14)
where
In addition, as pointed out by Yacano et al. (19791, the invisible bubble flow or bubble throughput must be included in the evaluation of the superficial bubble phase velocity. Extending their analysis to the present model, it would be argued that, in reality, bubbles exist randomly at any given bed height. Thus,there is in general a transfer of bubble phase gas from compartment to compartment by invisible bubble flow under two-phase conditions. Employing the Murray model, the average gas velocity in the bubble phase relative to the bubbles is Ud (e.g., Lockett et al., 1967). However, the recent work of Sit and Grace (1981)would suggest an enhancement of the Murray prediction under multi-bubble conditions. Employing their suggested values, the expression for Ul, would become under two-phase conditions = (VI
+ 1.33ud)Ji
6419)
We note that under three-phase conditions where closed streamlines around bubble exist, the upward gas flow through the bubble is exactly canceled by the downward flow in the cloud region (Yacono et al., 1979),and thus the expression given in Table I1 is applicable under threephase conditions. At ratice of superficial to minimum fluidization velocities greater than three to five, local flow reversal of gas in the emulsion phase can occur (Peters et al., 1982b). In the present analysis the divisions of gas flow among the phases are based on average values, and thus are taken to be constant throughout the fluidized bed. Furthermore, only an average upward flow of gas in the emulsion phase is considered. It is assumed that the equations describing the flow of gas in the fluidized bed are also applicable to the flow of particulates, and that the particulates contacting a collector adhere to it and are not re-entrained by the gas flow. Relative changes in particle velocities due to the motion of the collectors in the fluidized bed are also neglected. Nomenclature a = collector radius = number of bubbles in the nth compartment B = average number of bubbles in a compartment C, = Cunningham factor = 1 + (A/r,) [1.257 + 0.4 exp(-1.10
e,,
r,/Nl
D, = collector diameter, cm DG = mulecular diffusion coefficient of particulate, cmz/s D, = particulate diameter, cm DR = fluid bed diameter, cm D1 = equivalent spherical bubble diameter having the same volume as that of a bubble, cm D 2= equivalent spherical cloud diameter, cm Ill = average equivalent spherical bubble diameter, cm Dz = average equivalent spherical cloud diameter, cm D1, = initial bubble diameter, cm D1, = maximum bubble diameter, cm Ei = net single collector efficiency in phase i ET,ER,ED,.EG,E,,= single collector efficiencies due to impaction, interception, diffusion, gravity, and electrostatic effects, respectively. F12= gas interchange coefficient between phase 1and phase 2 per unit volume of phase 1, l / s F13 = gas interchange coefficient between phase 1and phase 3 per unit volume of phase 1, l / s FZ3= gas interchange coefficient between phase 2 and phase 3 per unit volume of phase 1, l / s G = gravitational acceleration, cm/s2 h = height from distributor plate, cm Hu = gas relative humidity, % IRMs = RMS value of current, pA erg/molecule K K = Boltzmann constant, 1.38 X Kc = dimensionless characteristic particle mobility for Coulombic forces, (D,&A&,) / 3~Uiq)
Ind. Eng. Chem. Fundam., Vol. 22, No. 4, 1983
L = expanded bed height, cm Lmf= bed height at Ud, cm ND= number of orifice openings on the distributor Nil = concentration of particulates in the nth compartment in phase i, g/cm3 No = inlet particulate concentration, g/cm3 NOut = outlet particulate concentration, g/cm3 AP = pressure drop, cm H20 Pe = Peclet number, UiDc/DG q = measured surface charge on collectors, pC/kg Q A C = charge on collectors, C/cm2 Q, = charge on particles, C/cm2 R, = dimensionless interception parameter, D,/Dc S = cross-sectional area of bed, cm2 et = Stokes number, (1/ 9)(CP,U&,/MD,) .Yi = assembly averaged velocity of gas in phase i, cm/s yi = average linear gas velocity in bubble phase, cm/s Vi,= average superficial velocity of gas in phase i, cm/s Ud = minimum fluidization velocity, cm/s Uo = superficial gas velocity, cm/s yL= volume of phase i in a compartment, cm3 VI = average volume of bubble phase, cm3 Greek Symbols ai = volume fraction of bed occupied by phase i Bi = average bubble phase volume fraction tf = permittivity of free space, 8.85 X C2 dyn-cm2 t i = void fraction of gas in phase i emf = void fraction in bed at Umf 7 = fluidized bed filtration efficiency p = gas viscosity, g/cm s p = gas density, g/cm3 pc = collector density, g/cm3 p, = particle density, g/cm3 Subscripts i = phase n = compartment number Registry No. Polyphenylene oxide (SRU), 9041-80-9; polyethylene (homopolymer),9002-88-4; polystyrene (homopolymer), 9003-53-6. Literature Cited Alexander, J. C.; Melcher, J. R. Ind. Eng. Chem. Fundam. 1977, 76, 311. Bafmec, M.; Bena, J. Chem. Eng. Scl. 1972, 2 7 , 1181. Balasubramanlan, M.; Melsen, A.; Mathur, K. 8. Can. J . Chem. Eng. 1078, 56, 298. Briggs. D. “Electrostatics 1979”, Inst. Phys. Conf. Ser. 1970, 48, 201-213.
453
Chavarle. C.; (;race, J. R. Chem. Eng. Scl. 1978, 37,741. Cheng, L.; Soo, S. L. J . Appl. Phys. 1970, 47. 585. Clborowski, J.; Zakowski, L. Int. Chem. Eng. I. 1977, 77, 529. Cotbell, 0. A.; Reed, C.; Rose-Innes, A. C. “Electrostatics 1979
