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Filtration of Electrified Solid Particles Oswaldo B. Duarte Fo.,† Wiclef D. Marra Jr.,† George C. Kachan,‡ and Jose´ R. Coury*,† DEQ/UFSCar, C. P. 676, 13565-905 Sa˜ o Carlos (SP), Brazil, and DEQ/EPUSP, 05508-900 Sa˜ o Paulo (SP), Brazil
The filtration of electrified solid particles in a fixed bed of sand was carried out. The particles were electrified by impacting them against an obstacle. This was done in a controlled way, so that several levels of charging could be attained. The collection of the charged particles took place in a cylindrical filter 0.15 m in diameter and three bed heights (0.01, 0.02, and 0.04 m) tall. Phosphatic concentrate particles with a mean diameter of 5.2 µm were utilized as the test powder. The results have shown that the presence of electrostatic charges can alter significantly the filtering behavior of the granular bed. The measured penetration of particles through the bed in the initial stages of the filtration was compared to the theoretical prediction, and the discrepancies suggest that the effect of electrostatic charges is stronger in the larger particles (>3 µm). As filtration progresses, the effect of charges is strongly felt, as the increase in the pressure drop caused by the deposited particles becomes less pronounced with increasing particle charge. In some cases, an increase in the penetration of particles is observed. The relation between particle charge and filtering behavior was not linear: the bed penetration increased, passed through a maximum, and then decreased with increasing particle charge, and the pressure drop behaved accordingly. The measurement of charge distribution between the particles revealed the presence of both positively and negatively charged particles, with the predominance of the former, which resulted in a positive mean charge for the aerosol. This distribution was affected by the level of charging and seems to be responsible for the nonlinear behavior of the filter. Introduction The sophistication in the industrial production and the accompanying increase in the air quality standards worldwide have lead to the need for gas-cleaning equipment for specific purposes. This is the case, for instance, of the removal of fine solid particles (diameters below 10 µm) from gas streams at high temperatures, for which no standard equipment accomplishes the necessary performance. Recent studies1,2 confirm ceramic and granular filters (fixed or moving beds) as the more promising alternatives for this use. The quantitative and qualitative knowledge of the phenomena involved, including the filtration mechanisms, is therefore of prime importance for the technological development of viable filters. Several studies on the effect of electrostatic charges on filter performance have been carried out in the past decades that include filtration on fiber, fabric, or granular filters, removing droplets or solid particles from gas streams, with or without the presence of an external electric field.3-9 In most cases, the particles have been electrified by corona charging and an external field was applied. Under suitable conditions, an increase in particle collection efficiency with particle charge is always reported. Also, a sensible decrease in the resistance to fluid flow through the deposited layer with the aid of an external electric field has been achieved, and an extensive review has been published.10 The specific case of filtration of solid particles electrified by impact, collected in electrically neutral beds * Corresponding author. E-mail:
[email protected]. † DEQ/UFSCar. ‡ DEQ/EPUSP.
(image-dipole collection mechanism), although likely to occur in practice, has received little attention. Coury11 and Coury et al.12 have reported an increase in the initial collection efficiency of triboelectrified fly ash when compared to the same particles uncharged. Also, a decisive role of particle charge on the deposited layer of powder was noticed: early cake formation and stronger adhesion for the charged particles. In these studies, the tribocharge was acquired by the particles in the dispersion process11 or by impact against the conducting duct12 and could not be varied. Improved performance of a fabric filter attributable to electrical charge added to the particles by corona charging is reviewed by Donovan.10 For this work, a device for tribocharging the particles by impact was devised, so that the effect of different levels of charging of the same powder on its collection by a granular bed could be detected. It gives sequence to research on the characterization of a granular bed filter,13-17 operating on the removal of solid particles from air streams. Here, a neutral filter response to the presence of different levels of electrostatic charge on challenging solid particles, electrified by impact, is analyzed. The tests are performed at ambient temperature. Filtration in Granular Beds and Electrostatic Effects Collection Mechanisms. The theory of filtration of solid particles normally considers the removal of the particles from the gas stream occurring by the action of some mechanisms. Each mechanism would add to the total collection efficiency of the filter, E, which, in the
10.1021/ie0002430 CCC: $19.00 © 2000 American Chemical Society Published on Web 10/02/2000
Ind. Eng. Chem. Res., Vol. 39, No. 10, 2000 3885
case of a fixed bed of height H composed of collectors of diameter dC, can be expressed as
[
E ) 1 - P ) 1 - exp
]
-K1H(1 - )ηT dC
KBTFS 3πµdp
(2)
where KB is the Boltzmann’s constant, T is the absolute temperature, µ is the gas viscosity, and FS is the Cunningham slip factor. The nature of the phenomenon suggests that it becomes significant for very small particles. Since this is a region of good adhesion between particle and collector, the process can be seen as analogous to molecular diffusion from a gas to an absorbing solid, so that it is possible to apply correlations for conventional mass transfer, utilizing δ instead of molecular diffusivity. This analogy led to a number of correlations for the diffusional efficiency of an individual collector with the same general form, that can be written as -2/3
ηD ) f() Pe
U0dC δ
(4)
where U0 is the gas superficial velocity. A correlation derived by Pendse and Tien19 and described by Tien20 has been widely used and will be adopted here. It has the following form:
ηD ) 4(1 - )2/3AS1/3 Pe-2/3
(5)
AS )
2 - 3(1 - )1/3 + 3(1 - )5/3 - 2(1 - )2
ηG ) (1 - )-2/3vtU0-1
(8)
where
vt )
dp2gFp 18µU0
(9)
The parameter K1 is given by eq 7. (c) Inertial and Direct Interception. The inertial mechanism results from the particle inertia: as the aerosol approaches the collector, the gas streamlines bend to contour the obstacle, while the particles, depending on their mass and velocity, tend to impact against it. It is therefore a dominating mechanism at high gas velocities and large particle sizes. Dimensional analysis of the equation of motion indicates that particle inertia is a function of the Stokes number, given by
St )
FSU0dp2 Fp 9µdC
(10)
where Fp is the particle density. Direct interception results from the relative size between particle and collector in the filter. A particle that follows the gas streamlines is captured when it passes at a distance shorter than its radius from the collector surface. Therefore, it is a function of
NR )
dp dC
(11)
As this mechanism is also relevant at large particle sizes, Jung et al.21 derived a correlation for the combined effect of direct interception and inertia, that has the following form:
ηI,DI ) 0.2589Steff1.3437NR0.23
(12)
valid for Steff < 1.2 and 1.5 × 10-4 < NR < 4.5 × 10-2. Steff is the effective Stokes number, given by
Steff ) 0.5St[AS + 1.14Re0.5-1.5]
(13)
Here, the parameter K1 in eq 1 is given by
where AS is the Happel parameter, given by
2[1 - (1 - )5/3]
(7)
(b) Gravitational Mechanism. Gravity acts in the particle collection by altering its trajectory and favoring or worsening contact with the collector, depending on the flow direction (favoring when in downflow). It is predominant for low gas velocities and for particles with high terminal velocity, vt. Tien20 suggests for the collection efficiency due to a gravitational mechanism, in downflow, the following expression:
(3)
where Pe, the Pe`clet number, is given by
Pe )
K1 ) 1.5(1 - )-2/3
(1)
where P is the penetration of particles through the bed, is the bed porosity, ηT is the total collection efficiency of an individual collector, and K1 is a parameter that depends on the adopted definition of individual collector efficiency η. The total collector efficiency is the overall contribution of the efficiencies due to a number of collection mechanisms, which ideally represent the physical principles that promote the contact between the particle and the collector. The collection mechanisms that are considered to be responsible for most of the particle collection in applications of practical importance are those of either mechanical or electrophoretic nature.18 A brief description of them follows. Mechanical Mechanisms.. (a) Diffusional Mechanism. The diffusional mechanism results from the chaotic movement (Brownian) that small particles are subjected to in a gas as a result of molecular impacts. It is assumed that the particle diffusivity δ due to Brownian motion can be estimated from the StokesEinstein equation, which, for a particle of diameter dp, can be expressed as
δ)
calculating the total efficiency E from eq 1, K1 is given by
(6)
This expression is valid for Re < 30, where Re is the collector Reynolds number ()FU0dC/µ). In this case, for
K1 )
[
6 (1 - )2/3
]
1/3
(14)
Electrophoretic Mechanisms. Electrophoretic collection results from the presence of electrostatic charges on the particles or collectors or both. These charges are
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either generated by phenomena inherent in the process (e.g. triboelectrification) or deliberately introduced (by corona charging, for example). The attraction between particle and collector occurs by several mechanisms, first identified by Ranz and Wong:22 (i) attraction between a charged particle and an oppositely charged collector (Coulombic attraction); (ii) attraction between a charged particle and an image dipole in a collector; (iii) attraction between a charged collector and an image dipole in a particle; (iv) space charge repulsion, that is, repulsion of a charged particle by a neighboring particle with similar charge; (v) attraction between a charged particle and a grounded collector carrying an opposite charge induced by surrounding particles. Mechanisms iv and v only become significant for very high particle concentrations, being negligible in most practical cases. Kraemer and Johnstone23 derived characteristic dimensionless groups for each of these mechanisms. For mechanism ii, the relevant one in the present study, the image-dipole parameter KM was defined as
KM )
γCFSQ2 3π20dpdC2 µU0
(15)
where Q is the particle charge, 0 is the permittivity of free space, and γC is the collector polarization coefficient, given by
γC ) (C - f)/(C + 2f)
(16)
where C and f are the collector and fluid dielectric constants, respectively. A relation between KM and collection efficiency for individual collectors was theoretically derived by Nielsen and Hill,24 for the case of inertialess particles of negligible size (dp , dC) collected by isolated spheres. Numerical solutions for potential and Stokes flow were indicated, and the results were presented as a family of curves. For the interval 0.003 < KM 0.1) verified a decreasing filter efficiency with increasing St, contrary to the predictions based on the collection mechanisms.21,27,28 This decrease was attributed to particle bouncing, and a correction factor, γ, for the individual collector efficiency to account for this effect was proposed, so that
ηC ) γηΤ
(20)
where ηC is the corrected efficiency. The value of γ was a function of St and was unity for St < 0.01 and decreased with St for St > 0.01. A recent work by Cavenati and Coury29 verified that the data could be better correlated in terms of Steff, given by eq 13, and of the bed aspect ratio (H/D), where H and D are the filter thickness and diameter, respectively. They proposed a correction for particle bouncing in the form
γ ) 0.284(H/D)-0.22781Steff-2.12482
(21)
valid for Steff > 0.684 and 0.06 < H/D < 0.3 (b) Effect of Particle Loading. The second and third assumptions imply that the previously collected particles play no role in the collection of the subsequent ones. The effect of the deposit on the filter performance is therefore not accounted for, and the predictions are restricted to the initial stages of the filtration process. Although a number of studies can be found on the prediction of the effect of the collected particles on filter performance (see recent reviews by Tien20,30), no reliable correlation is yet available. Particle deposition can either occur within the bed (deep filtration) or as an independent layer in the filter entrance (cake filtration), and the mode of deposition cannot be predicted beforehand. For the case of deep bed filtration in fiber filters, Zhao et al.31 present a simple form of estimating filter efficiency and pressure drop with particle loading. Later, Tardos32 extended the study to granular filters. They assume that the particles deposit uniformly over the collectors, causing an increase in their size, which does not vary with bed depth. For a bed composed of spherical collectors of density FC with total mass MC, loaded with a mass MTR of particles, a dust loading factor Kd is defined and has the following form:
Kd ) (1 + MCFC/MTRFp)1/3
(22)
where MC ) FCAH(1 - ) and A is the filter area. Note that eq 22 assumes that the deposit has no porosity.
Ind. Eng. Chem. Res., Vol. 39, No. 10, 2000 3887 Table 1. Properties of the Materials Utilized in This Work material
property
sand bed
dc ) 180 µm ) 0.401 c ) 6.0
dust
dp ) 5.2 µm Fp ) 2730 kg/m3 size distribution diameter (µm) mass % 0.5-1.0 1.69 1.0-2.0 6.59 2.0-3.0 7.68 3.0-4.0 13.7 4.0-5.0 13.1 5.0-6.0 12.6 6.0-7.0 9.28 7.0-8.0 7.53 8.0-9.0 4.75 9.0-10.0 4.18 >10.0 18.86
Under these conditions, it can be shown that the loaded bed porosity ′ is related to the clean bed porosity by
(1 - ′) ) Kd3(1 - )
(23)
Likewise, the collector diameters are related by
dC′ ) KddC
(24)
It is suggested that the collection efficiency and pressure drop of the loaded filter could be calculated utilizing the same correlations derived for the clean filter, by replacing ′ by and dC′ by dC. The clean bed pressure drop can be estimated by the well-known Ergun correlation:33,34
(1 - )2µU0 (1 - )FU02 ∆P ) 180 + 1.80 H 3d 2 3d C
(25)
C
The electrified dust was then directed to the granular filter, which was built inside a Faraday cage (see Figure 3). The granular bed consisted of a layer of ordinary sand, previously washed. The global charge in the particles could be measured by an electrometer (Keithley 6024) connected between the cage and the ground. The pressure drop across the bed was monitored with a micromanometer (Furness FC060). The collection efficiency was measured utilizing an optical particle counter (Climet 208-HT), which counted the particles before and after the filter in six ranges, from 0.3 to 10 µm. Each counting was made twice, and their arithmetic average was utilized in the calculations. The filtration tests have been performed for three bed heights (0.01, 0.02, and 0.04 m), three gas superficial velocities (0.07, 0.11, and 0.15 m/s), and four levels of particle charging (ranging from 0 to 0.061 C/kg). Charge Distribution Rig. The charge measurements carried out in the Faraday cage could only provide the global charge carried by all the particles. Nevertheless, the charging process by triboelectrification and impact normally produces a charge distribution ranging from positive to negative.35 Due to experimental limitations, the measurement of the particle charge distribution was not possible. Therefore, the experimental rig shown in Figure 4 was built with the intention of extracting some qualitative information of the charge distribution. It consisted of two parallel plates of copper through which the dust-laden gas was driven. A highvoltage supply, Spellman 20 kV, was connected to them, in such a way that one of the plates was negative and the other connected to the ground. This caused migration of the particles toward the plates and the deposition of a fraction of them. For the tests, the particles were dispersed and charged under the same conditions as for the filtration procedure described above, but with the parallel plate device replacing the filter. After some time of operation, the plates were removed and the particles in each plate wiped out and weighed. Also, the particles not collected by either plate were collected in a filter situated downstream and weighed.
Experimental Section Test Powder and Filter Bed. The powder utilized in this work consisted of a fine fraction of a phosphatic concentrate, with a Stokes mass mean diameter of 5.2 µm, measured in a Sedigraph 5000D, and a density of 2730 kg/m3, measured in a Micromeritics Accupic helium pycnometer. The granular filter consisted of ordinary washed sand screened between 149 and 210 µm mesh sieves and it formed a bed with a porosity of 0.401, measured by image analysis. Table 1 lists the physical properties of these materials. Filtration Rig. A schematic view of the experimental apparatus utilized in this work is illustrated in Figure 1. A particle-free air stream, kept dry by passing through a silica gel column, was fed to the rig and used to disperse the powder (T. S. I. Fluidized Bed Aerosol Generator). The loaded stream was then directed to the particle charger, shown in Figure 2. The particles were charged by impact as the aerosol was forced to flow through the small duct and directed against the grounded disk of copper. The impact conditions could be varied by changing the distance between the exit of the duct and the surface of the disk and also by changing the dilution air flow rate.
Results Initial Efficiency. A typical set of data of the bed efficiency as a function of particle diameter in the first minutes of the filtration tests is shown in Figure 5. These data refer to H ) 0.01 m, with U0 ) 0.07 m/s in Figure 5a, U0 ) 0.11 m/s in Figure 5b, and U0 ) 0.15 m/s in Figure 5c. It was assumed that, under these conditions, the filter could be taken as clean and the theoretical development of the individual collector efficiency would apply. Thus, in the same figures, a plot of the theoretical predictions for the efficiencies at different levels of charging is presented. This theoretical curve was calculated from eq 1, utilizing ηC calculated by eq 20, instead of ηT, to account for particle bouncing. The individual collector efficiency ηT was estimated from eqs 5, 8, 12, and 17. The calculation of ηE is shown in detail in the Appendix. The general trend of the experimental results is somewhat distinct of the theoretical prediction. The agreement with prediction is fairly reasonable for particles above 1 µm. In this region, the theoretical prediction was able to identify the effect of electrostatics both in the increase of bed efficiency (for sizes between 1.0 and 2.5 µm) and in the decrease in particle bouncing
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Figure 1. Scheme of the experimental apparatus.
Figure 2. Charging device.
(for sizes above 3 µm). On the other hand, there is no correspondence between experimental and theoretical data in the submicron size range: the low efficiencies measured are closer to the theoretical curves for noncharged particles, as if the charges had no effect. Not even the increase due to the diffusional mechanism could be observed. Part of these discrepancies may be due to the experimental technique adopted. The particle counter utilized measured optical diameters when, strictly, Stokes diameters should be used. Also, the counting of particles in the lower size ranges is more sensitive to noises and is less reliable. As for the theoretical prediction, a number of assumptions have been made for estimating ηE (see Appendix), once the amount of electrostatic charge per particle size was not known. Filtration Results. (i) Fractional Penetration. Figure 6a illustrates the measured initial fractional penetration of particles 0.75 µm in diameter through a bed 0.02 m deep, as a function of electrostatic charge per unit mass, for the three superficial velocities studied: the penetration increases, passes through a maximum, and decreases again with increasing particle charge. The same trend has remained for the whole filtration period, as can be seen in Figure 6b, which shows the penetration after 50 min. Figures 6c and d show the behavior for particles of 2.0 µm under the same experimental conditions. The oscillating behavior of the
penetration, as for U0 ) 0.15 m/s, was noticed in a number of tests. It can be noticed that the superficial gas velocity has no clear effect on penetration, under the conditions studied. Figure 7a shows the measured initial fractional penetration of particles 0.75 µm in diameter through a bed as a function of charge per unit mass, having bed depth as a parameter, for a gas superficial velocity of 0.07 m/s. Figure 7b refers to the penetration after 50 min. Figures 7c and d are relative to particles 2.0 µm in diameter under the same experimental conditions. The expected decrease in penetration with increasing bed depth can be seen. The general trend is similar to that of Figure 6. Note again the oscillating behavior of the penetration for H ) 0.04 m. (ii) Global Penetration and Pressure Drop. Parts a and b of Figure 8 show the global penetration (percent of total mass leaving the filter) and the increase in bed pressure drop, respectively, as a function of mass of particles retained in the filter, for a bed 0.02 m deep and gas superficial velocity, U0, of 0.11 m/s. As expected, the global penetration decreases with increasing filtration time (expressed here as amount of dust collected by the filter, to allow for direct comparison between tests performed with different dust penetrations). The influence of particle charge in the global penetration reflects the behavior depicted in Figures 6 and 7, for fractional penetration.
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Figure 3. Faraday cage.
Figure 5. Initial efficiency as a function of particle size for H ) 0.01 m with (a) U0 ) 0.07 m/s; (b) U0 ) 0.11 m/s; and (c) U0 ) 0.15 m/s. The points refer to experimental measurements while the continuous lines refer to predictions from eqs 1, 5, 8, 12, 17, and 20.
Figure 4. Parallel plates utilized for the charge distribution measurements.
As for the increase of pressure drop across the bed, it increases with filtration time and shows a very good
correspondence with the respective curve of global penetration (higher penetrations corresponding to smaller increases in bed pressure drops). It is worth stressing that these two measurements are independent of each other, which corroborates the observed effect of particle charge. The same trend was noticed in all tests, as the one for U0 ) 0.07 m/s, illustrated in Figure 9. The effect of the electrostatic charges is considerable: the differences in pressure drop between tests reached almost 1 order of magnitude, as can be seen in Figure 8a: the final pressure drop increase for the uncharged dust was nearly 1400 Pa, compared to
