Voidage, bed

Fig. 3. Zenz plot. Correlation of bed voidage, S, the volume fraction of the fluidized bed that is occupied by gas, for values of S from 1.0 to 0.5, and dimensionless velocity and particle properties, where p — p )/(3 PgU ). The horizontal lines represent the different values of e = 0.5...

Eor turbulent and fast-fluidized beds, bubbles are not present as distinct entities. The following expression for bed voidage, bed occupied by gas, where U is in m/s, has been suggested (17) ... 

The heat-transfer coefficient depends on particle size distribution, bed voidage, tube size, etc. Thus a universal correlation to predict heat-transfer coefficients is not available. However, the correlation of Andeen and Ghcksman (22) is adequate for approximate predictions ... 

Our knowledge of the pellet size and shape and the bed voidage are thus suffieient to eharaeterize the bed resistanee. For the partieular ease investigated here, the resistanee ean be represented as ... 

In general bed voidage is dependent on the paeking eharaeteristies of the material (a funetion of the orientation of the partieles in the bed), whieh is both partiele size and shape dependent. Unfortunately, at present it is only possible to prediet bed porosity for eertain distributions of regular partieles. Porosity ean be related to erystallizer solids hold-up empirieally, however, by an expression of the form... 

Fluidised beds have been used previously for the industrial-scale recovery of the antibiotics streptomycin and novobiocin.30 However, more recently, considerable interest has been shown in the use of fluidised beds for the direct extraction of proteins from whole fermentation broths.31 In a packed bed, the adsorbent particles are packed within the contactor. The voidage, that is, the inter-particle space, is minimal and thus feedstock clarification is mandatory to avoid clogging of the bed. In a fluidised/expanded bed, the adsorbent bed is allowed to expand by irrigation with feedstock. Bed voidage is increased, allowing the passage of particulates in the feed. The diameters of the adsorbent beads are exaggerated for illustrative clarity. 

The voidage (e) of abed of particles is the fraction of the bed volume occupied by the interstitial space between the particles. Its value depends upon the geometrical configuration of the beads, the pattern in which they are arranged within bed, the size distribution of the particles and the ratio of mean particle and contactor diameter. The bed voidage can be calculated using the following equation ... 

The relation between superficial velocity (U) and bed voidage (e) in a fluidised bed can be described by the classical correlation first postulated by Richardson and Zaki 49... 

A sensitivity analysis showed that the calculated value of pressure gradient was very sensitive to the value of the coefficient of friction pF. but was relatively insensitive to the slip velocity uB and to the bed voidage. 

Before the bed can become fluidized, however, the particles must dislodge from their packed state, which expands the bed. Thus, the porosity (s) in Eqs (14-5) and (14-9) is not the initial packed bed porosity but the expanded bed porosity at the point of minimum fluidization ( ml ), i.e., the minimum bed voidage in the bed just prior to fluidization. Actually, the values of C and C2 in Eq. (14-8) that give the best results for fluidized beds of uniform spherical particles have been found from empirical observations to be ... 

Subzwari et al. (1978) also reported that bed voidage and bed expansion increased with pressure for FCC catalyst (a Group A material). However, Knowlton (1977) reported little change in either bed density or bed expansion at with increasing pressure over the range of 1 to 70 atmospheres for large, -2000/+74 micron material. 

The fluidized-bed voidage at minimum bubbling conditions (emb) also has been shown to increase with increasing temperature (Fig. 7) and increasing pressure (Fig. 8). 

The bed voidage, s, is the ratio of the interpartide void space to the total volume V ... 

Calculate the pressure drop (-AP/kPa) for flow of fluid through a fluidized bed of solid particles based on the following data the difference in density between solid particles and fluid is 2500 kg m-3 at mf conditions, the bed voidage (em/) is 0.4, and the bed depth (Lm ) is 1.2 m. State any assumptions) made. 

The relation between bed voidage e and fluid velocity uc for particulate fluidisation of uniform particles which are small compared with the diameter of the containing vessel is given by ... 

Obtain a relationship for the ratio of the terminal falling velocity of a particle to the minimum fluidising velocity for a bed of similar particles. It may be assumed that Stokes Law and the Carman-Kozeny equation are applicable. What is the value of the ratio if the bed voidage at the minimum fluidising velocity is 0.4 ... 

It may be assumed that the terminal falling velocities of both particles may be calculated from Stokes law and that the relationship between the fluidisation velocity u and the bed voidage e is given by ... 

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