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150 3. Heterogeneous Processes and Reactor Analysis

ion-exchange systems, such as zeolites and similar particles of irregular shape (Inglezakis
et al ., 2001; Specchia and Baldi, 1977; Colombo and Baldi, 1976). For this kind of mate-
rials, which are common in w the follo w aste ater treatment applications, wing equation can
be used (Inglezakis et al ., 2001):
Pe p LRe p k
(3.313)
where L is 0.523 for upflow and 0.050 for do , w wnflo k is equal to –0.645 for upflow and
0.475 for doThis correlation has been deried for 0.6 w wnflo v Re p 8.5 where Re p is
.
based on superficial velocity (Figure 3.35). In all equations, the Re ynolds number is based
on superficial v, unless otherwise specif elocity ied.
gular
Generally, for spherical and other irre-shaped particles (intalox saddles, rasching
rings, berl saddles), the particle Peclet number is found to be between 0.3 and 0.8
for Reynolds number between 0.01 and 150 (Ebach and White, 1958). For a wide range
of values of the Reynolds number the Chung equation can be used (Chung and
,
Wen, 1968):
1 0.48
Pe (0.2 0.011 Re )
p p
(3.314)
This correlation has been deried using glass beads, aluminum beads, and steel beads.
v
Furthermore, according to Chung and W the particle Peclet number is between
en (1968),
0.06 and 0.3, shofor 0.01 wing no particular trend, Re p whereas it steadily increases 10,
for Re p 10.

1
Kubo
Chung
0.9
Inglezakis (up)
Inglezakis (down)
0.8
Bennet
0.7
0.6
Average value
0.5
p
Pe
0.4
0.3

0.2
0.1
0
0.1 1 10 100
Re p

Figure 3.35 Axial dispersion in liquid–solid fixed beds (for 0.45 and Sc 1000). A v alue erage v
v v enspiel (1972). is estimated by data gien by Le