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3.8 T Fluid–Solid Fluidized Bed Reactors w o-Phase, 215

unii–Le
v
either a plug-flow route, as assumed in Kenspiel model, or they are considered
to be in a perfect mixing state, which means that the whole emulsion phase, and conse-
quently the gas itself, is completely mixed throughout the reactor as assumed in the tw , o-
phase model.
For example, in circulating fluidized beds, for a gi en superf icial gas v elocity and solid v
mass velocity, se w that the solids are distributed in two regions in the ves- eral studies sho v
sel–a constant solid fraction in the lower dense region of a certain height, and a solid frac-
tion that falls exponentially with height in an upper lean region of a certain height (K unii
and Levenspiel, 2000).
Consider a first-order reaction in a fluidized bed, where we hae plug-flow for the gas v
through the bed, while the distribution of solids across the cross-section of the bed is uni-
form. In general, the solution of this model, under the additional assumption of uniform
, solids distribution throughout the reactor is

C in
ln ( , fk Z u k S , , ) m i (3.511)
,
f
s
C
out
where S is a parameter involving the solids fraction. For simplicity, consider this parame-
i
ter to be the solid fraction itself ( ). If this parameter is not constant, it introduces an inte-
S
gral in the model:
Z f
∫ h ()d z (3.512)
S
S
o
Gas mixing in bbling fluidization ub In bubbling fluidization, the mixing of gases as
they trael vertically through the bed is complete. In contrast, mixing in the radial direc-
v
tion is extremely poor and effective distributors have to be used, especially if two gases are
to be mixed. In bubbling beds, for velocities less than 5 –11 times that of u fm , the gases
will moe upward in both the emulsion and the bubble phases. On the other hand, for
v
velocities higher than about 5 to 11 times that of u fm , the mo ement of the emulsion phase v
downward will carry the contained gas doard as well. The backmixing of gases
wnw
increases up to a point as u / u fm is increased. After this point, the circulating or f ast re gime
s
appears and the backmixing decreases with increasing v elocities.
It should be noted that since the solid phase is not stationary in a fluidized bed,
the moement of the solid phase can also be described by a Peclet numberThus, there
.
v
are two Peclet numbers in fluidized beds for axial and radial mixing, i.e. one for the
,
fluid side and one for the solid one. Ho only the fluid-side Peclet numbers are
er
v
we
presented here.
Fluid mixing in particulate fluidization alues of In particulate fluidization, the v Pe p are
much higher than the corresponding ones for packed beds (2 –10 times) for the same value
of Re p , coering the range 0.004 –0.06 for 0.4 < Re p < 100, and thus axial dispersion is
v
more intense (Gunn, 1968).