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3.8 T Fluid–Solid Fluidized Bed Reactors w o-Phase, 207

where d p is the mean siee size of the particles. v
If the bed is deeper than this critical height, slugging will take place for a gas v elocity
higher than the minimum velocity of slugging:

u u 0.16(1.34 D 0.175 Z ) 0.07( ) 2 gD 0.5 (3.491)
sm fm fm
where Z fm is the height of the bed at incipient fluidization. In these equations, SI units
should be used.
Finally, in beds exhibiting low ratios of diameter to height, the bubbles can grow and
become as large as the cross-section. As a result, the bubbles moe through the bed sepa- v
rated by slugs of solids. This phenomenon is called “slugging” and has to be generally
avoided because it can lead to pressure fluctuations and entrainment of solids as well
(McCabe et al. , 1983).

Hydrodynamic modeling of bubbling fluidization (type B fluidization)
The modeling of fluidized beds begins with the analysis of the two most important hydro-
dynamic flow models presented by Davidson (Davidson and Harrison, 1963) and K unii
and Levenspiel (1968).

Two-Phase theory of Davidson According to the two-phase theory, two phases e xist in
the bubbling fluidized bed: (a) the bubbling phase consisting of gas b and (b) the
ubbles,
particulate phase, namely the solids around the bThe particulate phase is alterna- ubbles.
” tively called “the emulsion phase. Bubbles stay in the bubble phase and penetrate only a
small distance into the emulsion phase. This zone of penetration is called “cloud” since it
envelops the rising bubble.
If the gas flow rate is higher than that required 1for the onset of fluidization, the gas will
move through the bed in the form of bubbles. So, in b for a gas v ubbling fluidization, eloc-
elocity
ity aboe the minimum bubbling v the formation of bubbles will lead to a bed
v
,
expansion. In such a case, the condition of the particulate phase is unchanged and thus, the
porosity of the particulate phase is constant after this point. At gas flow rates aboe the v
point of minimum fluidization, the fluidized bed resembles with a boiling liquid—b ubbles
of gas rise rapidly and burst on the surface, and the emulsion phase is thoroughly agitated.
Davidson and Harrison (1963) were the first to state that the fluidized bed had to be treated
as a two-phase system consisting of an emulsion phase and a bubble phase (often called
v
ely).
the dense and lean phases, respectiThis was the basis of the so-called tw o-phase
model (Figure 3.57).
Focusing on the b it should be mentioned that they are not exactly spherical.
ubbles,
They contain very small amounts of solids and hae an approximately hemispherical top v
icant amount ak and a pushed-in bottom. Each bubble of gas has a we that contains a signif
of solids. These characteristics are illustrated in Figure 3.58. Consequently during their ,
journey in the reactor, the bubbles carry an amount of solids. The net flow of the solids in
the emulsion phase must therefore be do The gas within a particular b ubble
wnw
ard.
remains largely within that bubble and only a small part of it penetrates a short distance
into the surrounding emulsion phase, forming the so-called cloud.