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218 3. Heterogeneous Processes and Reactor Analysis

C out

C p C bub, out

Particulate Phase Bubble Phase
C = C p C = C bub
(-r) = f (C p )

C o C o
U fm × A (U s – U fm ) × A

Gas flow
U s × A

Figure 3.62 Two-phase model.

The model equations are the following:
For the bubble phase (gas phase),

C d b
f bub s u L be C ( b C ) b,vs r ( ) 0 (3.516)
p
bub b
z d
where:
L the mass transfer coef ubble and emulsion phase f icient between the b
be
(m 3 gas interchange v olume/m 3 of reactor) (1/s)
the volume fraction of the bubble occupied by solids
b
(– r ) the reaction rate in bubbles per unit volume of solids, based on the
b,vs
reactant
f the fraction of the gas flow carried by the bubble phase:
bub
u u
f bub s fm (3.517)
u
s
The material balance is expressed per unit volume of reactor .
For the particulate phase (dense phase),

Z f
(
(1 f ) Q C C ) AL C be∫ (C z AZ )d (1 )r ( ) 0 (3.518)
bub G o p b p f bub eS p,vs
0