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3.9 P article Analysis 227

olume,
a bub the interfacial area of the bubble phase per reactor v m 2 bub-
bles/m 3 reactor, estimated by (Kelkar and Ng, 2002)
6
a bub (3.549)
bub
d bub
and
6
o
a bub (3.550)
d bub
On the basis of these relationships, Kelkar and Ng (2002) presented the following rela-
tionships for k :
m
Bubbling bed model

Mass transfer between bubble and cloud:

g
3 D 12 1 4
g
k bc u fm 0.975 14 (3.551)
4 d
bub
where the unit of k is in m/s.
bc
Mass transfer between cloud and emulsion:
 4 fm Du g bub  12
k ce   d bub   (3.552)

where the unit of k bc is in m/s.
Two-phase model
Mass transfer between bubble and emulsion:

Du
u  4 fm g bub  12
k fm   (3.553)
be d
3  bub 
where the unit of k is in m/s.
be

3.9 PARTICLE ANALYSIS

In this section, v The analysis co v ers arious issues concerning solid particles are presented.
the most important particle properties (surface area, particle shape and size distrib ution,
mechanical strength, and density) as well as the beha vior of a single particle in suspension
(terminal velocity) and of a number of particles in fluidization state. Finally the dif , fusion
of molecules in a porous particle (dificients) is also discussed. fusion coef f
This “particle analysis” is of paramount importance when dealing with heterogeneous
operations like adsorption, ion e and catalysis. xchange,