Velocity and Voidage

3 Packed Beds, Granual Media Flow, Voidage. - 8.3.1 Velocity and 

Voidage. Single- and two-phase flows in fixed-bed reactors were visualized by three-dimensional NMR imaging and MRI velocimetry. The fluid velocity vector is determined at a pore-scale resolution of 156 pm. Characteristics of 

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Many attempts have been made to obtain general expressions for pressure drop and mean velocity for flow through packings in terms of voidage and specific surface, as these quantities are often known or can be measured. Alternatively, measurements of the pressure drop, velocity, and voidage provide a convenient way of measuring the surface area of some particulate materials, as described later. 

For relatively coarse particles, the rates of fall of the interface between (a) and (b) and between (b) and (c) can be calculated approximately if the relation between sedimentation velocity and voidage, or concentration, is given by equation 5.76. Richardson and Shabi 65) have shown that, in a suspension of particles of mixed sizes, it is the total concentration which controls the sedimentation rate of each species. 

For the fluidized bed process the bed expansion as a consequence of an increase in linear flow rate has to be considered. In a simplified picture diffusive transport takes place in a boundary layer around the matrix particle which is frequently renewed, this frequency being dependent on velocity and voidage, as long as convective effects, e.g. the movement of particles are neglected. Rowe [74] has included these considerations into his correlation for kf in fluidized beds, which is applicable for a wide range of Reynolds numbers, including the laminar flow regime where fluidized bed adsorption of proteins takes place (Eq. 19). The exponent m is set to 1 for a liquid fluidized bed, a represents the proportionality factor in the correlation for packed beds (Eq. 18) and is assumed as 1.45. 

Equation (37) describes the relationship between fluidising velocity and voidage as a function of the particle terminal fall velocity and of a parameter n which depends on the particle Reynolds number according to the following relations 10... 

A more rigorous analysis of the problem has recently been made by Lefroy and Davidson (L2). This analysis takes into account the vertical gas velocity and voidage profiles in the spout, as well as the effect of particle cross-flow from the annulus. Disregarding the radial variations across any horizontal section of the spout, the following equation can be written for continuity of gas flow and solids flow, respectively ... 

What appears to be the best correlation of choking velocities is due to Yang [AIChE J- 21, 1013-1015 (1975)], supplemented by Punwani et al. and Yang (cited by Teo and Leung, 1984, pp. 520-521). The choking velocity and voidage e are found by simultaneous solution of the equations... 

Hills, J.H. (1974), Radial non-uniformity of velocity and voidage in a bubble column, Trans. IChemE, 52, 1-9. 

Hills, J. H., (1974) Radial Non-Uniformity of Velocity and Voidage in a Bubble Column, Trans. Inst. Chem. Engrs. 52,1-9. 

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...

Ishii and Murakami (1991) evaluated the CFB scaling relationships of Horio et al. (1989) using two cold CFB models. Solids flux, pressure drop, and optical probe measurements were used to measure a large number of hydrodynamic parameters to serve as the basis for the comparison. Fair to good similarity was obtained between the beds. Dependent hydrodynamic parameters such as the pressure drop and pressure fluctuation characteristics, cluster length and voidage, and the core diameter were compared between the two beds. The gas-to-solid density ratio was not varied between the beds. As seen in Table 7, the dimensionless solids flux decreased as the superficial velocity was increased because the solids flux was held constant. 

Equation (64) predicts correctly the increase in solid entrainment into thejet with increases in jet velocity and the decrease with increases in solid loading in a two-phase jet. Since neither the voidage nor the particle velocity inside thejet were measured, direct verification of Eq. (64) was not performed. 

It may be assumed that the drag force F of the fluid on the particles under the free falling conditions is given by Stokes law and that the relation between the fluidisation velocity uc and voidage, e, for particles of terminal velocity, u0, is given by ... 

If flow conditions within the bed are streamline, the relation between fluid velocity uc, pressure drop (—A P) and voidage e is given, for a fixed bed of spherical particles of diameter d, by the Carman-Kozeny equation (4.12a) which takes the form ... 

Figure 6.5. Relation between fluid velocity (uc) and voidage (e) for the fluidisation of 6.4 mm steel spheres...

Thus, the bubbling region, which is an important feature of beds operating at gas velocities in excess of the minimum fluidising velocity, is usually characterised by two phases — a continuous emulsion phase with a voidage approximately equal to that of a bed at its minimum fluidising velocity, and a discontinous or bubble phase that accounts for most of the excess flow of gas. This is sometimes referred to as the two-phase theory of fluidisation. 

From Figure 6.4 it is seen that for emf = 0.40, <0/um/ is about 78 at low values of the Galileo number and about 9 for high values. In the first case, the drag on the particle is directly proportional to velocity and in the latter case proportional to the square of the velocity. Thus the force on a particle in a fluidised bed of voidage 0.4 is about 80 times that on an isolated particle for the same velocity. 

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