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226 3. Heterogeneous Processes and Reactor Analysis

Bubble–particulate phase mass transfer (bubbling fluidization)
v
unii–Le
enspiel,
Following the bubbling bed model of K the mass transfer coeficient of f
enspiel,
gas between the bubble and the cloud is (Le 1972; F 1999) , ogler
v

12 1 4
u D g g
K 4.5 fm 5.85 (3.544)
bc 54
d d
bub bub
where the units of K bc is (m 3 olume/m gas interchange v 3 bubble)(1/s) and D g is the dif fu-
f
sion coeficient of the solute in the gas phase. Here, CGS units are used. A typical v alue
of K bc is 2 s 1 .
f The mass transfer coeficient of gas between the cloud and the emulsion is
 Du  12
K ce 6.78  fm g bub 3  (3.545)

d
bub 
where the units of K ce is (m 3 gas interchange v olume/m 3 bubble)(1/s). CGS units are also
used in this relation. A typical value of K ce is 1 s 1 . Here, both mass transfer coef icients f
are based on bubble vAnother useful expression in reactor modeling is that of a
olume.
mass transfer coeficient based on reactor v olume: f
L bub (3.546)
K
where:
bub the volume fraction of the bubble phase, m 3 bubbles/m 3 reactor
L the mass-transfer coeficient based on the reactor v (m f olume, 3 gas inter-
olume/m change v 3 of reactor) (1/s)
K the mass-transfer coeficient based on the bubble v (m f olume, 3 gas inter-
olume/m change v 3 of bubble) (1/s)
f
Mass transfer coeficients are also expressed in m/s. These units are related to the other
ws (K ones as folloelkar and Ng, 2002):
L
k L k (3.547)
m m bub

bub
and
K o
k
k K (3.548)
m o m bub
a bub
where:
icient,
f
k the mass transfer coef m/s or in the equialent unit of (m v 3 gas
m
interchange v olume/m 2 of bubble interfacial area) (1/s)
L the mass transfer coef (m icient, f 3 gas interchange v olume/m 3
of reactor) (1/s)
a o the interfacial area of the bubble phase per bubble v olume
bub
(m 2 bubble/m 3 bubble)