Maximum spoutable depth

The two derivations quoted above rely on the boundary condition that the gas flow through the annulus near the top of the bed is sufficient to fluidize the solids, and they therefore are valid only for beds of maximum spoutable depth. The derived values of APa/APmf thus represent the upper limit which would be approached with increasing bed depth for a pven system. This is borne out by the experimental results plotted in Fig. 11, which cover different materials as well as column geometries. The maximum APa/APmf ratios attained are seen to be in remarkably good agreement with the predicted values of 0.64-0.75. 

Semiempirical expressions for Tfm have been developed by Lefroy and Davidson from their theoretical analysis discussed in Section IV,B and V,A. From measurements of spout diameter made in beds of kale seeds, polyethylene, and peas at maximum spoutable depths, they determined the value of the left-hand side of their force-balance equation q. (66) ] and found it to be about 0.36 in all cases. Therefore... 

Because of the limitation that the diameter of the spouting orifice must be smaller than about 30 particle diameters and the observation that the maximum spoutable depth is proportional to the cube root of the particle size spouting in small particle systems can only be achieved in columns a few centimetres diameter with low bed depths. Clearly these are of no commercial interest. 

Spouting cannot be maintained once the bed height exceeds a certain level, coim monly known as maximum spoutable bed depth, Hm. At Hm, the spout starts to collapse and the bed starts to change from a spouted bed to a fluidized bed. As indicated in Eq. (9.67), the minimum spouting velocity increases with an increase in the bed height. Consequently, (7msp achieves its maximum at Hm. The maximum value of the minimum spouting velocity can be related to the minimum fluidization velocity by... 

For a given solid material, column diameter, and fluid inlet diameter, a maximum spoutable bed depth exists beyond which the spouting action degenerates into poor-quality fluidization. 

Mamuro and Hattori further suggest that for depths below the maximum spoutable, where the value of C7 at z = /f (i.e., U ) does not reach Umt, the above equation should be modified to the form... 

The first part of this section briefly summarizes the main findings concerning the effect of the various factors on spouting stability, while the second part deals with methods proposed for calculating the maximum spoutable bed depth. 

The maximum spoutable bed depth was found to decrease with increasing particle size by Malek and Lu (M3), who experimented with four different sizes of wheat (1.2-3.7 mm) in a 6-in. column. On the other hand, Reddy et al. (Rl), who worked with mixed-size materials (alimdum, glass spheres, and polystyrene), also in a 6-in. column, reported that Hm first increases with particle size and then decreases, a peak value being attained at a mean particle size of 1.0-1.5 mm. The observed variation of Hm, correlated by Reddy et al. with mean particle size, is likely to be also influenced by size distribution, which cannot be fully characterized by any particular mean diameter. Nevertheless, the existence of a peak Hm with respect to particle size alone is theoretically predictable from a comparison of the effect of particle size on the gas velocities required for spouting and for fluidizing a given material (Rl). From Eq. (3), the effect of particle size and bed depth on spouting velocity, with all other variables held constant, is as follows ... 

As previously mentioned, the vertical pressure gradient in a spouting bed increases from zero at the base to a maximum near the top of the bed. A total spouting pressure drop APgg at the maximum spoutable bed depth can be estimated by the following relation ... 

At a depth just above the maximum spoutable, a spouted bed changes into a fluidized state. Therefore, if the minimum fluidization velocity for a solid material is known, its maximum spoutable bed depth in a given column can be estimated by substituting for u s ir> the minimum spouting velocity equation. A general expression for the maximum spoutable bed depth is given as follows ... 

APsb Total spouting pressure drop at maximum spoutable bed depth (M/ LP)... 

The maximum value of the minimum spouting velocity, occurs when the bed height is at the maximum spoutable bed depth or... 

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