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3.5 Agitated Slurry Reactors 135

Note that the relationship between the sexpressions is the same as in the slurry eral rate e v
bubble column reactors (Section 3.4.4).

3.5.2 Hydraulics

The special characteristic of three-phase systems is the demand for simultaneous and ef f i-
cient gas dispersion and solid suspensions.
Down-pumping axial flow impellers are more appropriate for most particle-suspension
operations (Perry and Green, 1984). Typical dimensional ratios are D T /D a 2–3.3, and
Z /D a T 0.25–0.5. The power can be calculated as in the case of liquid agitation (see eq.
(3.107)) (Perry and Green, 1984).
It is well known that the critical impeller speed for solid suspensions is higher in
the presence of a gas, depending mainly on the superficial gas velocity (Re atkar w et al .,
1991). This is because of a decrease in the impeller power draw due to the formation of
xample,
ventilated cavities behind the impeller blades on gassing. For e for Rushton tur-
bines, D T / D a 2–3.3:
N jsg N js Q 0.85 gv (3.255)

where N jsg is the critical impeller speed for solid suspensions under gassing conditions, and
Q gv is the gassing rate in volume of gas per volume of liquid per minute (vvm). This cor-
relation holds for vessels up to 1.8 m diameter 20% solids, and 3.5 vvm. Under similar
,
conditions and for other typical impellers (45° pitched blade impellers and hydrofoils), the
N jsg / N js ratio is between 1 and 2 (0.25 Q gv 3.5 vvm).
Another important function of the impeller in three-phase systems is to generate f inely
dispersed and homogeneously distributed bubbles throughout the vessel. At the same time,
the turbulent velocities should be suficiently high to preent coalescence of gas b f v ubbles.
The most important variable concerning gas dispersion is the gas holdup in the v essel.
Apart from the critical impeller speed for solid suspension and ef icient gas dispersion, f
flooding is also a very important phenomenon in three-phase systems. Flooding may tak e
place at low impeller speed or high gassing rate. Under these conditions, the gas is dis-
persed just around the central shaft of the tank, whereas the solids are settled at the bot-
tom. Flooding characteristics are not affected by particles. Furthermore, high-viscosity
liquids are able to handle more gas before flooding than lo w-viscosity liquids.
v
Birch and Ahmed (1997) hae shown that the location of the sparger has an important
role in the flooding characteristics of impellers, and thus on eficient solids suspension. f
The energy of dissipation per unit mass of liquid in a liquid–solid agitated vessel is related
to the power consumption per unit volume of liquid ( P ) as follows (Kato s et al ., 2001):
P P
s (3.256)
o
M
L L
where M L is the mass of liquid and in cm 2 /s 3 ( er where er g/g s, g g cm 2 /s ). In case 2
o
of gas injection in the liquid, the energy of dissipation per unit mass of liquid in a fully