Slide 1

Geldart classification

Classification of Powders

Geldart (1973) (Figure 3.3) classified powders into four groups according to their fluidization properties at ambient condition.There are 4 stages of particles: Aerated (A), Bubble (B), Cohesive (C) and Dense (D).

Group B

Bubbling at Umf, thus Umb Umf

Bubbles continue to grow, never achieving a maximum size.

This makes poor fluidization quality associated to large pressure fluctuation.

However, lots of bubbles produced results in less P to generate, thus less entrainment.

Example: construction sand.

Group D

For B and D particles: No inter particle involve.Bed collapses instantly when gas supply interrupted.Short residence time in bed.Example: paddy, beans, soy etc.

Large particles able to produce deep spout bed.Need very large Umf and P to fluidize.It is a costly operation since lots of air is needed for blowing.Quite similar to group B particles, i.e. Umb Umf.Fluidization of group D and larger group B particles: jet circulation/spout bed technique used to get circulation.Example of operation: paddy drying.

Group AFor smaller particles structures where cohesivity becomes significant.Lies between group C and free flowing particles (B).Existence of forces that holds particles together when gas is supplied, bed expands but does not bubble.

Non-bubbling fluidization at beginning of Umf, followed by bubbling fluidization as Uo increases (a.k.a. aeratable state).

Aeratable state = transformation from cohesive to free-flowing particles type.

The freeboard has to be increased to allow for bed expansion.

Danger if the powder is left in a drum high voidage and it could cause blow-up.

Group AUmb > Umf, bubbles are constantly splitting and coalescing, and maximum stale bubble size is achieved.

Take long time to de-aerate after gas supply is cut-off.

Inter particle forces?? yes, but significantly smaller than hydrodynamic forces.

Good quality and smooth fluidization.

Gas bubbles are in limited size, break down at high velocity and it gives good gas/solid contact

Example: Fluid bed catalytic cracking (FCC) catalyst.

Group CVery cohesive particles and do not fluidized at all.Inter particle forces are large compared with the inertial forces on the particles.Structures are so strong: At a given P, not expanding and resist aeration.Upon fluidization, cracks and rat hole form.Slugging blows powder out.Difficult to fluidize: inter particle forces > hydrodynamic forces exerted on the particles by the fluidizing gas.Pressure loss across the bed is always less than apparent weight of the bed cross sectional area due to the particles not fully supported by fluidizing gas.

Group C Pressure loss across the bed is always less than apparent weight of the bed cross sectional area due to the particles not fully supported by fluidizing gas.However, group C fluidization can be improved:Mechanical help: vibration, mixerBinary mixtures: act as flow conditioner

Many industrial processes use fine powders, e.g. pharmaceutical, cosmetics, paint industries, food industries etc.

Thus, many researches going on to improve and predict the behaviour of group C particles.

Example: the application of vibrations to the fluidized bed column.

With the aid of vibration, the bed is found to fluidize well and the pressure drop across the bed is close to the theoretical pressure drop during fluidization.

Theoretically, when vertical vibration is applied to a fluidized bed column, the effect of forces between the bed and the distributor cause the break-up of interparticle forces and this cause the particles to fluidize well.

According to Janssen et al. (1998), at a specific vibration frequency, the ratio between distributors plate and the bed displacement increases with an increase in vibration intensity.

This phenomenon caused the resultant force becomes bigger and hence used to break the interparticle forces between the particles. Hence, these results in better fluidization quality and smaller Umf values obtained compared to fluidization without vibration.Vibration also is predicted to be able to reduce the distance between particles and this reduces the voidage in the bed. This is due to small compaction during negative displacement or due to the downward movement during half cycle of vibration. However, equilibrium created between two mechanisms, i.e. the effect of pressure on the bed during vibration and downward movement which produced the compaction and hence led to a stable fluidization.

BUBBLEThe shape of bubble is a hemispherical capped bubble.

The upper surface of the bubble is approximately spherical, and its radius of curvature is denoted by r.

Since r is not readily determinable, it is usually more convenient to express the bubble size as its volume-equivalent diameter, i.e. the diameter of the sphere whose volume is equal to the bubble.

Bubbling fluidization also known as lean phase.

db+rBubble volume, VbCusp

Condition at where the powder stops behaving like solids but they behave like liquid two phase system.Bubbles are extremely important in supplying circulation as they are major circulating mechanism hence, lead to mixing.As bubbles rise, it grows and expandIf the bed is deep enough and diameter of the column is small,

Then slugging could occurThis means problem because slugging will push the powder up and possibly out of the vessel.

Through bubbles, particles are transported out of the bed.Approximately, when Uo, superficial gas velocity equals to particle terminal velocity, Vt, then carry over/entrainment could occur.

Expansion of non-bubbling bed

Richardson and Zaki (1954) found the function f() which applied to both hindered settling and to non-bubbling fluidization.Thus, in general;Khan and Richardson (1989), suggested the correlation in the equation which permits the determination of the exponent n at intermediate values of Re.

If the packed bed depth (H1) and voidage (1) are known, then if the mass remains constant, the depth at any voidage can be determined:

For the optimization of a fluidization process, is essential for predicting the beds behavior, for both homogeneous and heterogeneous particles. The prediction of the transport disengagement height (TDH) is very important, which directly influences the column's dimensions and the determination of the appropriate placement of a cyclone, the recycling system and the recovery of elutriated materials. Origin of the entrainment of solid particles: Lewis (1962), and Kunii and Levenspiel (1991) observed that the solid particles are released into thefreeboardbecause of bubbles burst up and slugs. Figure 1 shows the three hypotheses explaining this phenomenon. Since the bubbles internal pressure is higher than the bed's surface, they burst when reaching the surface, releasing the particles from their upper surface into thefreeboard.(Figure 1a); Because of the bubbles rapid growth, the solid material present in its lower side (wake) is ejected when it bursts (Fig. 1b); When two bubbles coalesce at the moment its reach the bed's surface, there is an energetic ejection of the particles from the wake of bubble (Figure 1c).

Entrainment and Elutriation of Solids from Fluidized Beds

Figure 1: Mechanism of ejection of solids from a fluidized bed in the freeboard (Kunii and Levenspiel, 1991)ENTRAINMENTEjection of particles from the surface of bubbling bed.Also term as carry over and elutriation.Amongst the factors influencing rate of entrainment are:gas velocityparticle densityparticle sizefines fractionvessel diameter Increasing gas temperature Increasing gas pressure

Ejection of particles from fluidized bed depends on the characteristics of the bed: i.e. bubble size and velocity at surface.

If terminal velocity, Vt > Uo entrainedIf Vt < Uo particle will fall back to the bed.Region above the fluidized bed surface:FreeboardSplash zoneDisengagement zoneDilute-phase transport zone

Transport Disengangement heightIn the study by Wen and Chen (1982), the TDH is considered to be the distance between the end of the fluidized region and the height at which the particles no longer exist. It has also been defined as the region in which the entrainment rate becomes constant (Figure 3).

Figure 3: Entrainment of particles according to Wen and Chen (1982).TDH-GeldartGeldart (1986) defined the TDH as the region where the fluidized solids fall back in the bottom of the bed, and being specific to fine (F) and large (C) particles:(i) TDH (F): is the height at which the solid concentration (especially fines), above the bed surface, reaches a constant or a slight variation.TDH (C): is the height where the large particles (or clusters) are released to the freeboard, and return to the bed.

TDH-Horio et alHorio et al., (1983) have distinguished characteristics of the threefreeboardregions, shown in Figure 5. From it, thesplash'sheight is differentiated from the TDH's: the TDH would be the sum of thesplash'sand the diffusion zone heights.

TDHZenz e Weil (1958), e Fournol et al. (1973) defined the TDH as a height, and above it, the entrainment rate and the particle average diameter become constant.In Figure 2, Zenz and Weil (1958) illustrate the particles movement in the bed. It also shows a theoretical model of particles ejection from the bed surface, and these particles would have the same velocity as the bubble velocity when leaning against the bed surface. With each particle ejected by the gas and affected by the inertia, the gravitational and the entrainment forces. Some particles are continuously carried out; while others only reach a certain height, where they fall back to the bed.

Zenz and Weil (1958) concluded that the increase of entrainment rate is related to the instability of the gas velocity distribution, due increase of bubble frequency. The increase in TDH (F) results from the violent bursting of the large bubbles, which are less frequent in the bed.

Fournol et al., (1973) concluded that the entrainment rate decreases rapidly with the declining of fluidization velocity and with the increasing height above the bed.Baron et al. (1988) e Geldart et al. (1995) established that the gas velocity strongly influences the TDH (F) height.

Sciazko et al. (1988, 1991) based their TDH(C) study on the Pemberton and Davidson's (1984)ghost bubblestheory. The particles movement in a moving state can be described by force balances. The authors proved that excess velocity is the most important parameter for the TDH.

Pinto et al., (1999) analyzed the influence of three factors on the entrainment of particles: fraction of open area in the distributor, solid mass and superficial gas velocity. The material used was sand with mean diameters between 268 and 711mm.Regarding the influence of gas velocity on the homogeneous particles, the authors observed an increase in the TDH(C) only for the low velocities.

Influence of Different Parameters on the TDHSuperficial Gas velocityMore recently, Cipolato et al., (2004) studied in heterogeneous beds of large particles (dp=400mm), the influence of four parameters: fraction of open area in the distributor; solid mass; dispersion index and gas velocity on the entrainment of large particles through a factorial design. For a fraction of open area of 1.4%, and two velocities of 0.46 m/s and 1.60m/s, the TDH(C) is practically equal, leading to the conclusion that the velocity parameter did not affect this parameter.Mass/height of solidHamdullahpur et al., (1986) conducted their experiments in a rectangular fluidized bed of 0.319m 0.176m 4m. The entrainment gas was at atmospheric pressure and room temperature. The material used was sand with mean diameter of 300mm (Geldart's group B). In addition to, the experiments were realized for six different velocities using the LDV(LaserDoppler Velocimeter)system.

The axial velocity and turbulence intensity were measured by the central axis and crossing thefreeboard.The experiments were performed at 5.2 and 12 cm of fixed-bed, by applying velocities between 0.20 and 0.40 m/s. The authors noted that at 0.2 m/s, the gas velocity in the center of the bed increased with the bed height; however, for the other velocities, the intensity was lower. The variation of turbulent magnitude increased 35% with the bed height. This confirms that the freeboard turbulence is induced by the bubbles eruption in the center of the bed, and the level is highly dependent on the bubble size.

Fournol et al., (1973) used FCC with mean diameter of 58 mm as entrained material and gas superficial velocity ranging from 0.11 to 0.22 m/s. The authors concluded that the entrainment rate rapidly decreases with the rise in bed height; moreover, it depends on the reduction in the fluidization velocity.

Pinto et al. (1999) worked experimentaly using homogeneous particles with mean diameter between 268 and 711mm, a solid mass from 1.0 to 3.0 kg, bed height from 0.10 to 0.30, and both of a perforated plate (1.4, 3.4 and 5.9% of free area) and a Tuyere distributor(1.4% of free area). From the results, they observed that the solid mass is the most influential variable to the TDH.

Free board height Wen and Chen (1982) proposed a model that describes the entrainment of solid particles in thefreeboardregion of a fluidized bed. They concluded that the entrainment of the particles rate decreased exponentially with the increasing height of thefreeboard.The elutriation rate of the fine particles was virtually independent of the fluid dynamics of the bed, and both the entrainment and the elutriation rates were affected by the column size. The elutriation rate was especially affected by the column wall; where the solid velocity is low.Pinto et al., (1999) showed that the fraction of open area in the distributor is not relevant to the TDH(C) determination. They used both types of distributor; a perforated plate one with 1.4, 3.4 and 5.9% open area and a Tuyere with 1.4% open area, and the results were substantial for the homogeneous particles averaging from 268 and 711mm.Cipolato et al., (2004) showed that the fraction of open area in the distributor is not relevant to the TDH(C) determination. In this paper, the authors used perforated plate distributor with fraction of open areas of 1.4 and 5.9%, obtaining a significant result for the heterogeneous particles of mean diameter of 4000mm.

Fraction of Open Area in the DistributorColumn diameterZenz and Weil (1958) analyzed the effect of column diameter on the TDH for diameters ranging from 0.051 to 0.61 m. Being noticeable in all cases a decrease in TDH, caused by the walls effect (small diameters) as well as by the poor distribution of the gas phase (large diameters).Empirical CorrelationFournol et al., (1973) describes the TDH (F) - as inversely proportional to the Froude number. Despite this proposition, the authors note that this height is significantly higher than predicted by Zenz and Weil (1958):

Hamdullahpur et al., (1986) proposed an equation that characterizes the TDH(C) as dependent on the bubble diameter:

Baron et al., (1988) suggested a new correlation to estimate the TDH(F), in which the maximum height reached by the largeclustersis directly proportional to the velocity square of the particle (KUb) ejection, which in turn would be the gas velocity:

Sciazko et al., (1988) have shown though, that the ratio between both thesplash-zoneheight and the bed height is strongly influenced by the excess gas velocity (U-Umf). This volumetric fraction would be the critical value of the bubbles fraction, which is related to the difference in the excess gas velocities

Sciazko et al., (1991) determined a new correlation for the TDH(C) depending on the diameter of the bubble on the bed surface:

Pinto et al., (1999) proposed a correlation for the TDH(C) depending on the physical characteristics of both the particles (particle diameter), and the gas (density and viscosity) and the operating conditions (solid mass and gas velocity):

Cipolato et al., (2004 stablished a new correlation for the TDH(C) depending on the solid mass through the statistical analysis, for a first order model with two interactions:

The design of a fluidized bed reactor should be done as to minimize the velocity of the entrainment of particles. Two solutions are usually adjusted: to increase the cross section above the bed surface, and to predict the reactor's gas outlet from a height above the TDH. Devices can be added inside or above the bed to reduce the entrainment, e.g., stirrers, grids, vertical and horizontal baffles and cyclones (Geldart, 1986).The elutriation phenomenon can follow a first order process, i.e., the elutriation velocity of the particle size (dpi) is proportional to the mass fraction (xi) of the particles in the reactor:

Where is the elutriation constant velocity of particles

There are several correlations in terms of proposed in the literature and two of them are summarizing in Table 1:

Entrainment rateThe determination of the entrainment requires knowledge of concentrations of each particle size in the bed. Figure 10 shows a general case and the various possible combinations (Geldart, 1986). For example: Without feed, 100% efficient cyclone; total recycle of product on cyclone; Continuous feed, cyclone's efficiency varies depending on dpi; partial recycle of the fines.No matter the arrangement, the mass balances of each component and global must be reached. As an illustration, it is assumed that RE=RR=0, and F and Q are different from zero. The mass balance of the fraction considering dpigiven by:

The global mass balance given by:

Now:

In addition, in a well-mixed bed: xQi= xBiSubstituting in the mass balance for each particle size and re-arranging:

Figure 9: Balance of the components around a fluidized bed (Geldart, 1986)This equation cannot be directly solved because RT depends on the values from xBifor each fraction. In practice a rapid convergence and an interaction error can be avoided by using RT=0 in the first attempt.If the freeboard height is greater than 2m, and the column's diameter exceeds about 0.2 m, then for the fraction sizes will have Ut/U < 0.5, This simplifies the calculations.

Batch operation For batch operation, the rates of entrainment of each size range, the total entrainment rate and the particle size distribution of bed change with time.Thus, the formula,

where is the mass of solids in size range, i entrained in time increment, t.By assuming that the mass of bed, MBi does not change significantly with time, t thus:

Terminal velocity,VtFor spherical particlesLaminar region (Ret < 0.2) dp < 33 mTurbulent region, (Ret >1000)

dp > 1500 m CD 0.43Transition region, 0.2 < Ret < 1000

or

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Particle size, ((m)

(p - (g (kg/m3)

C

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D