Bubble voidage

The bubble voidage in the draft tube, ebr, was calculated on the basis of the velocity of a rising gas slug relative to its surrounding solids. The total gas superficial velocity in the draft tube, lJjn can be derived to be... 

Gibilaro, L.G., Di Felice, R. and Foscolo, P.U. (1988). On the minimum bubbling voidage and the Geldart classification for gas-fluidized beds. Powder Technol., 56, 21. 

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 effect of local enthalpy at CHF is due primarily to the wall voidage, which impairs the critical flux, and secondarily to the bulk voidage, which affects the flow pattern. The coupled effects of local subcooling and flow velocity in a subcooled bubbly flow were first reported by Griff el and Bonilla (1965), neglecting the pressure effect ... 

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 voidage inside the bubble street, can be calculated as follows... 

We next consider the volume fractions of the various regions in the fluidized bed. The volume fraction of bubbles, fb, m3 bubbles (m3 bed)-1, can be assessed from the point of view of either voidage or velocity. In terms of voidage, if we assume the void fraction... 

For cracker catalyst (d = 55 (im, density = 950 kg/m3) fluidised by air, values of umb/umf of up to 2.8 have been found by Davies and Richardson(45). During the course of this work it was found that there is a minimum size of bubble which is stable. Small bubbles injected into a non-bubbling bed tend to become assimilated in the dense phase, whilst, on the other hand, larger bubbles tend to grow at the expense of the gas flow in the dense phase. If a bubble larger than the critical size is injected into an expanded bed, the bed will initially expand by an amount equal to the volume of the injected bubble. When, however, the bubble breaks the surface, the bed will fall back below the level existing before injection and will therefore have acquired a reduced voidage. 

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. 

Pavlov s equation (3.475) is used for voidage determination at minimum bubbling conditions (for it, = bm), and since dp < 0.5 mm, the Broadhurst-Becker equation (3.466) is used for lm. For a wide range of particle sizes, the values of efm and ebm are close to each other, within a ratio between 0.95 and 1.1 for all particle densities. Values of bm/efm ratio... 

Hie Foscolo-Gibilaro equation indicates multiple solutions for st. However, two solutions at maximum are to be expected in the operating range between 0.4 and 1. The second solution exists because bubbling beds are known to revert to particulate behavior at high voidages (Foscolo and Gibilaro, 1984). 

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