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3.8 T Fluid–Solid Fluidized Bed Reactors w o-Phase, 221

C Aout

Bubble phase cloud and wake Emulsion
δ β + c αδ 1– δ– β c
Z f

u bub
K bc K ce

C Ao u s
Figure 3.64 Levenspiel model (simplified Kunii–Levenspiel model).

Material balances can be written over a differential section of the bed (d z ) for a reactant,
in each of the three-phases (bubble, cloud, and emulsion). the equations of the model Then,
ws: are as follo
For the bubble phase (gas phase),

d C 2 b d C b
D L,b 2 u bub K bc ( C b C c ) b r ( ) 0 (3.528)
b
b,vs
d z d z
where K bc is the mass transfer coeficient between the bubble and cloud phase in (m f 3 gas
interchange v olume/m 3 of bubble) (1/s).
For the cloud phase (cloud and w e), ak

 C d 
u c   c   c z d K bc C ( b C c ) ce C K ( c C e ) c r ( c,vs ) 0 (3.529)

where K ce is the mass transfer coefficient between the cloud and the emulsion phase in (m 3
olume/m gas interchange v 3 of bubble) (1/s).
For the emulsion phase (dense phase),
 1 C d 
r (
u e     z d e K ce C ( c C e ) e,v s ) 0 (3.530)
e
where u c and u respecti e . ely v are the velocities of the gas in the cloud and emulsion phases,
The material balance is expressed per unit volume of bubble phase.