Figure 10: Particle distribution image and rotated plot
of particle density vs height showing the zones in the freeboard
of a fluidized bed.
- Freeboard: the entire region between the bed surface and
the gas outlet.
- Splash zone: the region just above the bed surface,
in which coarse particles fall back down.
- Disengagement zone: the region above the splash zone,
in which both the upward flux and the suspension concentration
of fine particles decreases with increasing height.
- Dilute-phase transport zone: region above the disengagement zone,
in which all particles are carried upwards; particle flux
and suspension concentration are constant with height.
Note that, although in general fine particles will be entrained
and leave the system and coarse particles will remain,
in practice fine particles may stay in the system at velocities
several times their terminal velocity and coarse particles may be entrained.
The height from the bed surface to the top of the disengagement zone
is known as the transport disengagement height (TDH).
Above TDH the entrainment flux and concentration of particles is constant.
Thus, from the design point of view, in order to gain maximum benefit
from the effect of gravity in the freeboard, the gas exit
should be placed above the TDH. Many empirical correlations
for TDH are available in the literature (e.g. Zenz, 1983, Horio 1980).
We will use that of Horio, which is presented in Equation 37.
(dBvs = equivalent volume diameter of a bubble at the surface).
The empirical estimation of entrainment rates from
fluidized beds is based on the following rather intuitive equation:
where elutriation rate constant (the entrainment flux
at height h above the bed surface for the solids of size xi,
when
mBi = 1.0).
MB = total mass of solids in the bed
A = area of bed surface
mBi = fraction of the bed mass with size xi at time t.
For continuous operation, mBi and MB are constant and so:
and total rate of entrainment,
The solids loading of particles of size xi
in the off-gases is
i = Ri / (U A)
and the total solids loading leaving the freeboard is
T = 
i.
For batch operation, the rates of entrainment of each size range,
the total entrainment rate and the particle size distribution
of the bed change with time. The problem can best be solved by writing
Equation Eq.38 in finite increment form:
where 
(mBi MB)
is the mass of solids in size range i entrained in time
increment t.
Then total mass entrained in time
(for k size ranges) and mass of solids remaining in the bed at time
(where subscript t refers to the value at time t.) Bed composition at time
Solution to a batch entrainment problem is by sequential application
of Equations 41 to 44 for the required time period.
The elutriation rate constant K*ih cannot be predicted from first principles
and so it is necessary to rely on the available correlations which differ
significantly in their predictions. Correlations are usually in terms
of the carryover rate above TDH, . Two of the more reliable correlations are given below:
For particles > 100 
m and U > 1.2 m/s Geldart et al. (1979) give
For particles < 100 m and U < 1.2 m/s Zenz and Weil (1958) give
