Solids transport, separation and classification

POWDER TECHNOLOGY ELSEVIER

Powder Technology 88 (1996) 323-333

Solids transport, separation and classification Stuart B. Savage a, Robert Pfeffer b, Zhong M. Zhao b a Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, Que. H3A 2K6, Canada b Department of Chemical Engineering, Chemistry and Environmental Science, New Jersey Institute of Technology, Newark, NJ 07102, USA Received 6 January 1995; revised 3 May 1995; accepted 19 February 1996

Abstract We have attempted to summarize and consolidate the topics treated in the papers presented in the sessions on Solids Transport, Separation and Classification at the First International Particle Technology Forum, held at the AIChE Summer National Meeting in Denver, CO, August 17-19, 1994. Keywords: Solids transport; Pneumatic conveying; Granular flow; Vibration segregation; Separation processes; Hydrocyclones; Filters; Electrostatic precipitators; Particle classification; Mixing; Drying

1. Introduction

2.1. Pneumatic transport

In the following, we give a short summary of each of the papers presented in the sessions on Solids Transport, Separation and Classification at the First International Particle Technology Forum, held in Denver, CO, August 17-19, 1994. Some attempt is made to consolidate logically the material and point out the interrelations that exist. While authors sometimes may not agree, we regard oral and poster presentations to be of equal importance, only differing in their format. Hence, in this summary we have categorized and grouped all papers according to their subject area and not distinguished them as to their mode of presentation. The papers may conveniently be divided into the groups and subgroups as listed in Table 1. A detailed discussion of some of the highlights and key points in these papers is now presented. Naturally, because of space limitations, not all of the important results presented by the original authors could be included.

Two important parameters characterizing pneumatic transport of solid particles in horizontal pipelines are saltation and pick-up velocities. The former is defined as the minimum gas velocity at which the particles start to drop out of suspension and settle on the bottom of the pipe whereas the latter is defined as the gas velocity required to resuspend the particles initially at rest on the bottom of a horizontal pipe. Their relationship is qualitatively described by Klinzing and Cabre-

2. Solids transport The first group of the papers is concerned with solids transport which is widely used in many process industries, such as food, petroleum, power generation, mining and chemical industries. These papers can be further divided into two subgroups, pneumatic transport and granular flow. 0032-5910/96/$15.00 © 1996 Elsevier Science S.A. All rights reserved PIIS0032-5910(96)03137-3

jos [1]. The particles initially at rest form a layer or deposit on the bottom of the pipe with zero particle velocity. As shown in Fig. 1, when the particle Reynolds number is increased slowly, that is, by increasing the mean gas velocity, a point is reached where particles on the top of the layer reorientate and move no more than a few diameters without being entrained by the gas stream. As the mean gas velocity continues to be increased the rest state becomes unstable and individual particles start being picked up and separated from the surface of the layer (pick -up of single particles). If the mean gas velocity is increased further, a point is reached where lots of particles separate from the surface and erosion of the layer of particles take place. This pick-up phenomenon occurs when the particle Reynolds number reaches a critical value, Rep.cnt. After the particles are entrained and blown forward they are transported as an homogeneous gas-solid suspension flowing with a given particle velocity. Further increase in mean gas velocity will increase the particle velocity and the particle Froude number.

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S.B. Savage et al. / Powder Technology 88 (1996) 323-333

Table 1 Division of papers into subgroups 1. Solids transport Pneumatic transport

Granular flows

2. Separation and classification processes Liquid-solid separation

Gas-solid separation

Particle classification

3. Mixing and drying Mixing

Drying

Pick-up and saltation mechanisms Pneumatic conveying of solids High density pneumatic transport Low velocity gas-solids flow Gas-particle flow in vertical tubes Gas-solids flow in an inclined pipeline Rotating drum simulations Rotating drum experiments Dryer structural optimization Vibration induced segregation Vibration induced convection Pseudo-acoustic waves

Klinzing and Cabrejos [ 1] Molerus [2] Hong and Tomita [3] Barton and Mason [4] Dasgupta et al. [ 5 ] Marjanovi6 and Mason [ 6] Walton [7] Boateng and Barr [81 Abrah/to et al. [9] Rosato et al. [ 10] Rosato and Lan [ 11 ] Astarita et aL [ 12]

Inclined particle settling Hydrocyclones Magnetic spiral separator Counterflow centrifuge Multiwir packings High temperature pulse jet cleaning filter New design equations for ESPs Separation process for fly-ash Vibration classification Centrifugal air classification Porous plate classifier

Ward and Poh [ 13] ; Gecol and Davis [ 14] Ortega-Rivas and Svarosky [ 15 ] Borsch and Sch0nert [ 16] Priesemann and SchOnert [ 17] Fischer and Leschonski [ 18 ] Berbner and LOftier [ 19] Zhao and Pfeffer [20] Mori et al. [21] Khoory and Mahgerefleh [ 22 ] Ortega-Rivas and Svarovsky [23] ; Galk et al. [24] Wu et al. [25 ]

Comparisons and general considerations Variance reduction ratio Vertical mixer tubes Static mixer dryer Filter-dryers

Taylor [26] ; Sommer [27] Weinek0tter and Reh [28] Gyenis and N6meth [29] Alonso et al. [30] Perlmutter [31 ]

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across the pipe) is slowly decreased, a change in the flow patterns is observed. Below the critical particle Reynolds number, instabilities due to low mean gas velocity affect the

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behavior of the particles being transported in suspension in the pipe and several flow regimes may develop before saltation actually occurs, for example, stratified flow, pulsating flow, and moving dunes. If the mean gas velocity is decreased further, a point is reached where the particles drop out of the suspension and deposit on the bottom of the pipe. This condition, called saltation, always occurs below the critical Reynolds number for pick-up. Two different phenomena take place at this point: some of the particles remain at rest on the bottom of the pipe forming dunes while others continue to flow, sliding and bouncing over these settled dunes, causing particle entrainment until an equilibrium condition is achieved where particles are transported on top of a settled layer. Therefore the mean gas velocity increases due to the free cross-section area reduction, and a steady transport is reestablished on top of the settled layer. The particle Reynolds number at this dense phase transport condition is about 20% below the critical value, corroborating that the presence of solids in the stream 40O0

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causes the deposit to be removed easily. The following flow patterns of the gas-solid flow may be observed at mean gas velocities below saltation velocity: blowing dunes, settled dunes, and settled layer. As the mean gas velocity continues to be decreased, no gas-solids flow is possible any more and the particles just continue to accumulate in the pipe with the risk of a blockage. For horizontal conveying of polystyrene particles (dp= 2.3 mm) in a pipe of i.d. = 4 cm, a phase diagram shown in Fig. 2, which reflects quantitatively these flow phenomena for polystyrene powder, has been given in the invited paper by Molerus [2]. At high gas velocities fully suspended flow prevails. At low velocities a segregation of the suspended particles occurs and the state of strand type conveying is achieved. The transition from fully suspended conveying to strand type conveying is gradual. At low mass flow rates and further reduction in gas velocity, the strand is stationary and the pressure drop increases in a sudden jump. Between fully suspension type conveying and strand type conveying, there is a small velocity range in which dunes are conveyed. At high solid mass flow rates a direct transition from strand type conveying to plug flow occurs for solids of large particle sizes and, in the case of fine-grained solids, blockage of the system develops. Due to several reasons (low energy consumption, high mass flow ratio and low particle and pipe attrition), the unstable plug flow type of pneumatic conveying is of interest in industrial practice. However, the risk of blocking of the pipe can be ignored only for rather large particles with uniform shape and smooth surfaces. Therefore, this operational regime requires additional measures, as described by Molerus [ 2 ], including adding axial vibration where the time interval between each vibration cycle is chosen so as to propel the solid moving forward in the pipe. A theoretical analysis has been made by Hong and Tomita [ 3] for high density pneumatic transport which is defined as non-suspension and non-plug transport in horizontal pipes and compared to four other models by different authors. As shown in Fig. 3, in contrast with the predictions of pressure drop by the other four models, which predict that the pressure drop decreases monotonically with increasing gas velocity,

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326

S.B. Savage et al. /Powder Technology 88 (1996) 323-333

the model by Hong and Tomita predicts a minimum which was also shown by Molerus [2] and is confirmed by experimental phase diagrams. Around the minimum, there is a relatively constant section which shows the pressure drop changes little with changing gas velocity. This means that safe operating points chosen near the minimum may be possible. Their results also show that under high density transport, the larger the pipe diameter or the smaller the solids mass ftowrate, the less the difference between the five models. Hong and Tomita's model can also be used to calculate the height of the sliding bed in the stratified flow regime which increases with increasing solids flow rate and decreasing pipe diameter. The transport of a bulk solids material in a low velocity non-suspension mode of flow has many benefits in the operation of pneumatic conveying systems. Unfortunately, many bulk solids materials cannot be transported in a non-suspension mode of flow. This has lead to the development of a number of special systems specifically devised to overcome this limitation. The paper by Barton and Mason [4] presents an investigation into the use of air bypass pipelines as a means of transporting materials, that would otherwise require high velocity, in a non-suspension mode of flow. The experimental data show that these systems can successfully achieve this objective. In vertically upward conveying, at constant solid mass flow rate, the pressure drop due to solids transportation increases with decreasing superficial gas velocity [2]. When a low solids mass flow rate is conveyed, on decreasing the gas velocity to below a critical value, the pressure drop increases sharply. At low pressure drop, the solid is conveyed in the form of strands and clusters whereas, at high pressure drop, the solid is transported as a migrating fluidized bed. A sudden increase in pressure drop produces an equally sudden change in the flow pattern. However, ifa larger solids mass flow rate is pneumatically conveyed, the pressure drop increases continuously, not suddenly, with decreasing gas velocity. This means that the flow pattern changes continuously, too. At high gas velocities, the solids are conveyed in the form of strands and clusters, and by decreasing the gas velocity, a gradual change of flow pattern towards fluidized bed conveying takes place. A theoretical state diagram has been derived which reflects this flow phenomena. The effect of relative motion between gas and particles in the context of riser flows, both at the level of the time-averaged and fluctuating flow, is studied by Dasgupta et al. [5]. Instead of solving the equations of motion for two phases in terms of the velocities of individual phases, equations for the suspension and slip are constructed based on mass weighted and slip velocities. The results indicate that the slight time lag in the fluctuating motion of gas and particles do not provide an important physical mechanism for dissipating turbulent energy in riser flows. A method for the comparative analysis of the influence of pipeline inclination on the energy loss in a pneumatic conveying system has been presented by Marjanovi6 and Mason

[6]. The method is based on the assessment of the angle at which a solid particle moves in a pipeline and impacts on the pipe wall. Their results show that the larger the impact angle, the sooner the particle impacts the wall and the greater the energy loss. The impact model predicts that the flow in an inclined pipeline requires a higher total energy than the flow in a vertical pipeline with an identical length if the inclined angle of the pipeline is greater about 14-21 °, depending on the ratio of gravity to drag forces acting on the particle. The total energy required shows a maximum and the angle at which that maximum occurs also depends on the ratio of gravity to drag forces. 2.2. Granular flows

This group of papers is concerned primarily with the mechanics of dry granular materials and, except for the paper by Astarita et al. [ 12], with situations in which the interstitial gas effects are negligible. The invited lecture by Walton [7] deals with granular flows in rotating drums, a configuration that has numerous industrial applications such as horizontal axis drum mixers, rotary grain dryers, ore reduction, etc. The flow patterns developed in the granular material contained in the rotating drum are complex; the flows can be unsteady and the granular flow regimes range from the slow quasi-static mode to the more vigorous grain inertia type that can occur in the avalanching free surface layer. Walton [7] has.paid particular attention to modelling the particle interactions and energy dissipation accurately. Hysteresis is incorporated in the force displacement model to account for energy dissipation during particle interactions. Normal contacts are modelled by using a spring constant K1 during loading and a stiffer spring constant K2 during unloading, thereby accounting for plastic deformations and giving rise to an effective coefficient of restitution e = (K1/K2) ~/2 The tangential forces are modelled in an analogous way with a tangential force displacement relation for the initial part of the loading. However, there is a Coulomb-like dry friction limit to the tangential forces given by the product the friction coefficient/z and the normal contact force. Walton considered both spherical particles as well as more irregular shapes by combining different numbers of spherical particles into clusters that move as a single unit. As might be expected the particle clusters give rise to a larger static angle of repose ~brthan the material consisting of uniform spherical particles. Simulations of particle motions in a rotating drum were performed for different rotation rates. At slow rotations slumping and avalanching flows were observed. With different sized particles, size segregation occurred quite rapidly in the radial direction. The dynamic angle of repose was determined; for spherical particles it increased from 13° to 31 ° as the surface friction coefficient increased from 0.02 to 1.0. At very high rotation rates the particles were centrifuged and rotated as a rigid annular bed along with the outer rotating wall. As rotation rate was decreased, there was some sliding

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down the rising inner bed surface. For even slower speeds, particles rained down from the surface of the upper half of the rotating bed. Walton determined empirical relationships to delineate the boundaries between the different modes of flow. Boateng and Barr [ 8 ] described experiments performed in a large rotating drum of 1 m outside diameter. They used three types of particles: spherical polyethylene pellets (4,=22°-24°), ellipsoidal rice grains (4,=30°-32°), and irregular limestone particles (4,= 35°-40°). Particle surface velocities and granular temperature (proportional to the mean square of the particle velocity fluctuations) were measured across the free surface by means of fibre optic probes. As shown in Fig. 4, the distributions of particle velocities and granular temperatures across the inclined free surface of granular material were roughly similar, being zero at the two extreme ends and having one or more peaks over the surface, higher granular temperatures being associated with larger surface velocities. The authors characterized the multiple peaked flows as resulting from instabilities. It would be useful to have further information on temporal variations of freesurface depth profiles, and distributions of the thickness of the rapidly flowing surface layers, in order to better understand and interpret the experimental measurements. Abrah~o et al. [9] presented a structural analysis of a rotating dryer for small farm producers with the aim of optimizing the design for cost. They used the ANSYS-5.0 finite element software package to achieve a design weight reduction of 47%. The paper is a useful contribution, but its focus falls somewhat outside that of the rest of the papers in the sessions which deal with particulate flows. The two papers by Rosato et al. [ 10] and Rosato and Lan [ 11] deal with granular materials subjected to vibrations. The first is an experimental study of size segregation, or more specifically the vertical upward transport of a large sphere (diameter D) immersed in a bed of smaller uniform acrylic spheres (diameter d = 3.18 ram). The spherical particles were placed in a cylindrical container which was vibrated with a sinusoidal vertical motion at different amplitudes a and (radian) frequencies w. Making the inner walls of the container rough apparently stimulates a convective motion in the

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bulk of bed spheres in which the particles move upward along the vertical centerline and downward next to the cylindrical container walls. The time Tfor the large sphere to rise through a vertical distance H was measured as a function of a and o9. As shown in Fig. 5, the authors were able to correlate data on rise time T (or perhaps more appropriately the dimensionless rise time T(g/d) ~/2 for D/d = 6 and for various values of a and co ( w = 27rf) as a function of the parameter F = aoo2/g, where g is the gravitational acceleration. Further experiments showed that the rise time was almost independent of the diameter ratio D/d (for D/d of 3, 6 and 10) and surprisingly that heavier large spheres of nearly the same diameter rose faster than lighter ones. These data, after verification by further experiments, currently underway will provide a challenge for those doing computer modelling of these phenomena. The second paper of Rosato and Lan [ 11 ] concerns computer simulations of the convection patterns induced in granular material contained in a rectangular box that is subjected to vertical sinusoidal vibrations. The simulations are based upon modifications of the granular flow computer code developed by Walton and co-workers using inelastic, frictional, I0 ~

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328

S.B. Savage et al. /Powder Technology 88 (1996) 323-333

soft particles. Studies were performed to examine the effects of box width to particle diameter ratio W/d, wall roughness, vibration amplitude a and radian frequency to. For small amplitude a with W/d = 6, no convection was evident; but, for a > 0.3d with rough vertical side walls, particles move downward at the side walls and upward in the center of the box, with two recirculating convection cells developing next to both side walls. When the walls are made smooth the direction of the recirculation cells reverses, with particles moving down at the center of the box and upward next to the vertical side walls. For wide boxes, W/d= 100, noticeable recirculation cells develop next to the side walls. In the middle region of the box, the pattern is less clear over the long term, but in the short term, there appear to be a number of convection cells that evolve and disappear. The paper of Astarita et al. [ 12] makes use of the analogy between gases at the molecular level and granular flows in which the particles are in a highly agitated state, that is, the analogy between the kinetic temperature associated with the square of the velocity fluctuations of the gas molecules and the pseudo or so-called granular temperature. When the granular material is in a highly agitated or fluidized state, we can think of pseudo-acoustic waves associated with the propagation of infinitesimal disturbances of solids volume fraction. Such an analysis presumably applies to relatively dilute systems in which long term contacts (that give rise to quasistatic Coulomb-like stresses) are absent. The one-dimensional conservation of mass, linear momentum and energy equations for granular flows are compared with the corresponding ones for ideal compressible gases. The presence of an additional term in the conservation of energy equation, the difference between the mechanical energy input and the dissipation of pseudo-energy associated with the particle velocity fluctuations, affects the formation and development of pseudo-shocks in granular flows. The detailed solution to this problem is underway. Knowledge of the behavior of pseudoacoustic waves would contribute to a better understanding of vibration induced fluidization and convection.

3. Separation and classification processes The second group of papers deals with particle separation and classification. These papers can be further split into three subgroups, liquid-solid separation, gas-solid separation and particle classification.

3.1. Liquid-solid separation The two papers by Ward and Poh [13] and Gecol and Davis [ 14] are concerned with flow in inclined parallel walled settlers. These devices work more rapidly than conventional settlers because of the increased surface area and the decreased settling distance. Ward and Poh [13] performed experiments to study the effects of inclined settler aspect ratio (height to channel spacing, which was varied

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between O(1) and O(100)), solids concentration (varied between 0 and 30%), and inclination angle (0 to 90°). The aim was to verify the theoretical analyses of Acrivos and Herbolzheimer and Nakamura and Kuroda. A cin6 camera was used to measure the temporal development of the clear liquid layer formed along the length of the separator. Experimental results compared reasonably well with those predicted theoretically and it was concluded that the analyses provide satisfactory guidelines for design purposes. Gecol and Davis [ 14] consider the more general problem of classification of particle of different sizes and densities at concentrations such that hindered settling effects are significant. The analysis of Davis, Herboltzheimer and Acrivos for classification of dilute suspensions was extended to higher concentrations by accounting for hindered settling effects. Experiments were performed with mixtures of 267/xm spherical glass particles and 83/xm acrylic beads in a Newtonian liquid (Union Carbide UCON 50 HB-280X). As shown in Fig. 6, the inclined settler was operated in a continuous mode in which the feed suspension was introduced near the bottom of the vessel, the underflow containing the coarser, faster settling particles was also removed at the bottom and some of the fine, slower settling particles were removed as overflow. After a steady state was developed, samples taken from the overflow line and feed reservoir were analyzed. Plots of the experimental fractional recovery of acrylic beads in the overflow as a function of dimensionless overflow rate agreed well with theoretical predictions. It was noted that the efficiency of classification by inclined settling increased with increasing concentration. The scale-up of conical hydrocyclones at high feed concentrations such that the slurry behavior is non-Newtonian was investigated by Ortega-Rivas and Svarovsky [15]. Selection and operation of hydrocyclones is based on relationships between pressure drop and flow rate, and the relationship between separation efficiency and flow rate. Relevant dimensionless groups for hydrocyclones were enumerated and discussed. These are the Euler number, a Stokes number associated with the size of the particles likely to be

S.B. Savage et al. / P o w d e r Technology 88 (1996) 323-333

separated, an appropriate Reynolds number for non-Newtonian behavior, the ratio of underflow (that leaves through the apex of the cone) to throughput, and the feed concentration. Experiments were performed with suspensions of dolomitic limestone, with feed concentrations ranging from 5 to 25 vol.%. By using a multiple regression analysis the authors obtained correlations relating these dimensionless groups appropriate for high feed concentrations. The correlations can be used for performance prediction as well as for the design and selection of small diameter hydrocyclones. Sch6nert and his co-workers designed and tested mechanical classifiers for the separation of very fine particles from water slurries. Botsch and Sch6nert [ 16] described a laboratory scale high intensity magnetic separator which can operate in a continuous mode. It is in the form of a cylindrical chamber which surrounds a rotating spiral, the upper part of which is brass and the lower part is pure iron. The upper part of the chamber is of reduced diameter to form a worm conveyer directed toward the overflow outlet. The slurry is introduced in the middle of the separation zone and the chamber is placed in a horizontal magnetic field. Magnetic material is transported upward and nonmagnetic particles flow with the water to the underflow outlet. Good performance was obtained with water slurries of siderite and quartz, and of hematite and quartz having 1% volumetric solids content. Priesemann and Sch6nert [ 17] present the results of tests with a counterflow centrifuge designed to perform classification for slurries of fine particles having volumetric concentrations of between 5 and 30%. They achieved excellent results without any bypass at cut sizes between 2 and 5 ~m and reasonable classifications down to 0.8/zm.

3.2. Gas-solid separation Due to recent laws enacted dealing with the protection of the environment (for example, the United States Clean Air Act Amendments of 1990), a great deal of research to improve dust control has been done. This topic is addressed by the papers in this subgroup. To separate effectively fine particles in the size range below 1 /xm, the existing devices have to be improved or to be operated under changed conditions. Separators used today in industrial applications differ not only in their performance but also in their investment and operating costs. Centrifugal separators, such as cyclones, are economical in principle but their performance is usually limited to fairly coarse particles. Fibrous filters, such as baghouses, can obtain high grade efficiencies, even in the submicron range, but the investment and operating costs are high in most cases. Recently, a new separator, named multiwir, was developed by Fischer and Leschonski [ 18 ]. As shown in Fig. 7, the new separator consists of a structured packing which subdivides the incoming gas into a great number of narrow streams which cross each other. As a result of a transfer of momentum between these gas streams, they keep rotating. Due to the centrifugal forces, originating from the rotation, the particles

329

Fig. 7. MultiwirPacking. entrained in the gas streams are separated and deposited on the wall of the packing. The influence of particle size and gas velocity on the grade efficiency and total efficiency for the multiwir packings with a channel height of 15 mm and an inclination angle of 90 ° was examined by Fischer and Leschonski. At any given gas velocity, the grade efficiency increases with increasing particle size since larger particles have larger inertia. The results are also very impressive for fine particles. Multiwir separates 1 /zm particles at efficiencies as high as 54-75% whereas conventional dust collectors based on gravity, inertial or centrifugal forces generally show less than 10% efficiency for such fine particles! Their results also shows that there exists an optimum velocity of about 9.3 m/s, below which both the grade and total efficiencies increase with increasing gas velocities and after which the efficiencies decrease with increasing gas velocity, due to particle bouncing and particle reentrainment. Beside its simple design and low capital and operating costs, multiwir has very high grade efficiencies for fine particles which can be even higher by combining packings with narrow channels and by electrically charging the particles before entering the packings. If the particles deposited on the wall can be continuously removed without producing a secondary pollution problem, multiwir appears to be an excellent new dust collector. The separation of particles directly from high temperature gas streams is becoming increasingly important in many industrial processes. This topic is addressed by Stefan and L6ffler [ 19]. In their experiments, the hot exhaust gas produced by a natural gas burner is mixed with dust from a continuous dust feeder and enters the filter housing within which a filter element is hung. The pulse jet regeneration of this rigid ceramic surface filter was investigated under the influence of high temperatures 600 and 850 °C for three different dusts (quartz, brown coal and hard coal fly ashes). If the influence of the temperature dependent gas viscosity upon the pressure drop at the filter is eliminated, an improved dedusting of the filter element is achieved at higher temperatures for all three dusts investigated. This can be explained

330

S.B. Savage et al. / Powder Technology 88 (1996) 323-333

by a higher maximum pressure built up inside the filter element during the pulse jet regeneration. Increased maximum pressures prevail during the dedusting causing stronger separating forces and improved jetting of the filter cake. Their results demonstrated that a prolongation of the valve opening time, an increase of the pressures in the jet gas reservoir and the filtration of thicker dust layers also improve the regeneration of the filter element. Electrostatic precipitators (ESPs) are widely used in many industries as efficient dust collectors. However, it is necessary to be able to design ESPs for different applications. The Deutsch-Anderson equation has been used as the basis for the engineering design of ESPs. However, in this equation the so-called effective migration velocity of particles is an empirical parameter. This quantity is taken to represent the collection behavior of an entire dust of a certain kind and under a certain set of operating conditions. It is determined by back calculation using the Deutsch-Anderson equation from experimental data (mostly proprietary) and therefore really is a measure of the performance of the ESPs. Thus, in actual use, the Deutsch-Anderson formula is a purely empirical tool. By integrating the Deutsch equation representing the grade efficiency using a normal particle size distribution, a theoretical design equation was developed by Zhao and Pfeffer [ 20]. Using an order of magnitude analysis, the 30- principle of statistics and typical operating conditions of ESPs in industry, the theoretical model was further simplified for convenient use in engineering design. The simplified model explicitly shows the influence of particle mass median diameter and electrical strengths for particle charging and collection. Comparing the simplified model with the Deutsch-Anderson equation, one can obtain the expression for the effective migration velocity which clearly shows that the effective migration velocity is directly proportional to the particle mass median diameter, and to the electrical strengths for particle charging and collection. This equation also demonstrates that the effective migration velocity is independent of the gas stream flow rate and the collecting surface area, which is in agreement with the fact that the previous empirical Veffdata are given without specification of the conditions of gas flow rate and collecting surface. Coal fly ash discharged from pulverized coal-fired power stations has been utilized in cement mixtures (fly ash cement). However, the unburned carbon in the fly ash spoils the quality of the fly ash cement. In order to be able to utilize fly ash of higher carbon content, a new two stage separation process of the unburned carbon from the fly ash has been developed by Mori et al. [21 ]. In the first stage, the fly ash is classified into a carbon rich coarser fraction and into a finer fraction by a fluidized bed or by an air separator. The finer fraction of the fly ash is fed into the second stage which consists of a horizontal vibrofluidized bed as shown in Fig. 8. Since the finer fly ash is a typical group C powder, it could not be uniformly fluidized at low gas velocity in a conventional ftuidized bed. In the vibrofluidized bed the lower den-

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I

I Fig. 8. Second vibrofluidized bed.

sity unburned carbon rises to the bed surface and is removed by suction nozzles. A bench scale continuously operating vibrating fluidized bed system was built and the measured data confirmed that the carbon content of the produced fly ash is less than 5% and the total yield of the produced fly ash is higher than 60% of the raw fly ash.

3.3. Particle classification The main object of classification of powders is to define the behavior of the powders into definite specific regimes of class patterns. There are three main types of classification of powders relating to their handling properties. They refer to handling and storage of deaerated powders; handling of aerated powders, such as fluidized beds; and handling of suspension of powders, such as pneumatic conveying of powders or separation of particles from gases. For aerated powders, such as in fluidized beds, particle density and size are the two most important parameters governing the behavior of powders as was originally shown by Geldart. A vibrating reed technology for the classification of powders in the aerated state was developed by Khoory and Mahgerefteh [22]. This technology is based on relating the amplitude of transverse vibration of a reed at resonance to the average particle size. The device used for vibrating classification basically consists of a centrally driven reed made of spring steel which is secured at both ends within a steel cylindrical chamber. The test powder with a constant mass is placed in a glass container mounted at the center of the reed. A cover is used to prevent the escape of powder during vibration. The system is sinusoidally vibrated using an electromagnet. The frequency and amplitude of the transverse

S.B. Savage et al./Powder Technology 88 (1996) 323-333

vibration of the reed are measured by monitoring the induced voltage signal from an optical detector consisting of an infrared emitter and receiver placed at either side of the reed. During the test, the samples of powder have been previously classified by sieving and the drive voltage applied to the electromagnet is maintained at a constant voltage throughout. The amplitude of transverse vibration of the reed is monitored using a Keithley multimeter. The powder groups classified by the device closely correlate with those shown on Geldart's classification chart which plots the density difference between the powder and the fluidizing medium against mean particle size so that powders fall into four groups, referred to as Groups A, B, C and D. Powders corresponding to group C (fine particles