What gas velocities are required?
• For particles larger than 100m
– Wen&Yu correlation
• Remf=33.7[(1+3.59*10-5Ar)0.5-1]
– Valid for spheres in the range 0.01< Remf1000
• For particles less than 100 m(xP=particle diameter)
umf 
(  p   f ) 0.934 g 0.934 xP1.8
1110 0.87  g0.066
• For fluidized beds-harmonic mean of mass distribution
used as mean
Bubbles vs. No Bubbles
• umb=superficial velocity at which bubbles
first appear
• umb(Abrahamsen &Fieldart,1980) for
 xP  g0.06 
 2.07Exp(0.716F ) 0.347 
 

• For groups B&D powders, they only bubble,
umf= umb
• For group C, bubbles never form (cohesive
force too high) & channeling occurs
Slugging
• When size of bubbles is greater than 1/3 of diam.
of bed, rise velocity is controlled by equipment
• Slugging leads to large pressure fluctuations &
vibrations
• Don’t want slugging!
• Yagi&Muchi(1952) criteria to avoid slugging
(Hmf:bed height at onset of fluidization, D:diameter
of bed)
 H mf 
1.9


0.3
D
(

x
)


P P
Expansion of a fluidized bed
• For non bubbling, there’s a region where u increases,
particle separation increases but P/H remains
constant
• u is related to uT –single particle terminal velocity in
general u= uTn, =voidage of the bed
  P x P uT 
u= uT4.65
  0.3
Re P  
  
ReP > 500
u= uT2.4
• Between - Khan & Richardson, 1989
0.27 

4.8  n
x
0.57
 0.043Ar 1  2.4  
n  2.4
 D  

More Bed Stuff
Expansion for bubbling beds
• Simple theory-any gas excess of that needed for fluidization
could form bubbles (not perfect since for low cohesive
powders, much increase in gas velocity can occur before
bubbling & increase leads to lower density,bigger bed
volume)
• Relationship between gas as bubbles & gas doing
fluidization depends on type of powder
Entrainment
• Removal of particles from bed by fluidizing gas
• Rate of entrainment & size distribution of entrained particles
will depend on particle size & density, gas density &
viscosity, gas velocity & fluctuations, gas flow regime, radial
position, vessel diameter
Entrainment
All particles are carried up & particle
flux+suspension concentration are
constant with height
Disengagement zone-upward flux and
suspension concentration of fine
particles decreases with increasing
height
Coarse particles fall back down
Applications for fluidized beds
• Drying – minerals, sand, polymers, pharmaceuticals, fertilizers
• Mixing – all kinds of materials
• Granulation – process of making particles
cluster by adding a binder
• Coating
• Heating/cooling – provides uniform temperature and good heat transport
Issues to consider
• Gas distribution
screen
• Erosion – solid, hard particles may cause wear in bed
• Loss of fines- reduces quality of fluidization lowers g
as-solid contact area, reduces catalytic activity
• Cyclones – can be used to separate entrained fines for
recycle
Feeding the bed
• May need to feed fluidized bed
• Important for drying, granulation,
recycle of fines
• Methods of solids feeding
– Screw conveyors
– Pneumatic conveying