Fluidised pressure drop

However, on die basis of the relation between pressure drop and die minimum fluidisation velocity of particles, the point of transition between a packed bed and a fluidised bed has been correlated by Ergun41 using (17.7.2.3). This is obtained by summing the pressure drop terms for laminar and turbulent flow regions. 

As noted in Section 6.1.3 of Volume 2, the Carman-Kozeny equation applies only to conditions of laminar flow and hence to low values of the Reynolds number for flow in the bed. In practice, this restricts its application to fine particles. Approaches based on both the Carman-Kozeny and the Ergun equations are very sensitive to the value of the voidage and it seems likely that both equations overpredict the pressure drop for fluidised systems. 

Figure 6.2. Pressure drop over fixed and fluidised beds... 

The theoretical value of the minimum fluidising velocity may be calculated from the equations given in Chapter 4 for the relation between pressure drop and velocity in a fixed packed bed, with the pressure drop through the bed put equal to the apparent weight of particles per unit area, and the porosity set at the maximum value that can be attained in the fixed bed. 

In a fluidised bed, the total frictional force on the particles must equal the effective weight of the bed. Thus, in a bed of unit cross-sectional area, depth l, and porosity e, the additional pressure drop across the bed attributable to the layout weight of the particles is given by ... 

There is evidence in the work reported in Chapter 5 on sedimentation 5) to suggest that where the particles are free to adjust their orientations with respect to one another and to the fluid, as in sedimentation and fluidisation, the equations for pressure drop in fixed beds overestimate the values where the particles can choose their orientation. A value of 3.36 rather than 5 for the Carman-Kozeny constant is in closer accord with experimental data. The coefficient in equation 6.3 then takes on the higher value of 0.0089. The experimental evidence is limited to a few measurements however and equation 6.3, with its possible inaccuracies, is used here. 

It is probable that the Ergun equation, like the Carman-Kozeny equation, also overpredicts pressure drop for fluidised systems, although no experimental evidence is available on the basis of which the values of the coefficients may be amended. 

In general, the behaviour of gas-fluidised systems is considerably more complex than that of liquid-fluidised systems which exhibit a gradual transition from fixed bed to fluidised bed followed by particle transport, without a series of transition regions, and with bed expansion and pressure drop conforming reasonably closely to values calculated for ideal... 

When deep beds of solids are fluidised by a gas, the use of a tapered bed can counterbalance the effects of gas expansion. For example, the pressure drop over a 5 m deep bed of solids of density 4000 kg/m3 is about 105 N/m2. Thus, with atmospheric pressure at the outlet, the volumetric flowrate will double from the bottom to the top of an isothermal cylindrical bed. If the area at the outlet is twice that at the base, the velocity will be maintained approximately constant throughout. 

Magnetic particles may form much more stable beds when subjected to a magnetic field. Saxena and Shrivastava(51) have examined the complex behaviour of spherical steel particles of a range of sizes when subjected to fields of different strengths, considering in particular the bed pressure drop, the quality of fluidisation and the structure of the surface of the bed. 

In fluidisation with a liquid, a bed of particles of mixed sizes will become sharply stratified with the small particles on top and the large ones at the bottom. The pressure drop is that which would be expected for each of the layers in series. If the size range is small however, no appreciable segregation will occur. 

The pressure drop over a spouted bed is normally lower than that for a fluidised bed, because part of the weight of the solids is supported by the frictional force between the... 

As the velocity of the fluidising fluid (gas or liquid) is increased through a bed of solid particles, there comes a point where the drag force exerted by the fluid on the particles, which is proportional to the global pressure drop across the bed, is balanced by the buoyant weight of the suspension. At this point, the particles are lifted by the fluid, the separation between them increases and the bed becomes fluidised. Thus ... 

An important property of fluidised beds follows immediately from this simple relation as the bed expands, the product (1-e) L, which represents the total volume of particles per unit cross section, remains unchanged. As the fluid flux is increased, L increases and (1 — s) decreases so as to maintain their product at a constant value. As a consequence, the pressure drop through the fluidised bed remains constant for further increases in fluid velocity, as shown in Figure 9. 

The pressure drop and bed expansion profiles shown in Figure 9 represent the different stages from fixed to bubbling fluidisation for a typical gas-solid system of fine particles. Knowing the bed height, the average bed voidage can be obtained ... 

Thonglimp s equation estimates the minimum particle fluidisation velocity and the particle entrained height and Ergun s law approximates the pressure drop across the filter. Darcy s law predicts the gas flowrate distribution through out the filter. 

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