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3.6 T o-Phase Fix ed Beds w 157

for low Eo , up to 0.01, is equal to 0.11 m 3 /m 3 . The following equation holds for spherical
particles:
0.11 (3.335)
h e,s
1 Eo
where the static holdup h e,s is based on the total volume of the bed. For aqueous solutions
at ambient temperature and particle sizes between 0.2 and 3.5 mm, the follo wing equation
v can be deried from the abo e equations: v

h 0.0453 d 0.053 (3.336)
e,s p
where d p is in m, while h e,s is based on the total volume of the bed. For zeolite-packed beds
and particle sizes of 1.2–1.3 mm, this equation results in a static holdup equal to 18.4%,
very close to the one found for the zeolites holdup equation (3.332).

g ations Bed voidae consider

The above analysis on liquid holdup determination for different particle sizes (eq. (3.333))
and as will be analyzed, the procedure of scaleup (Chapter 6) is based on the grounds that
the bed voidage is approximately the same for different beds of the same material.
However, bed voidage depends on d / D (Dixon, 1988). It can be proed that for v d / D
p
p
values lower than 0.1, the bed v it is oidage can be considered practically constant. Indeed,
common practice to use ratios of d / D lower than 0.1, and therefore, the bed voidage can
p
be actually considered the same for common fed beds. For instance, a bed consisting of ix
particles with 2 mm diameter should hae a diameter greater that 2 cm, which leads to a
v
d / D ratio with a value of 0.1 maximum. Consequently the bed voidage is critical only in ,
p
laboratory experiments. In Figure 3.39, Dixon’ s correlations are presented for spheres and
cylinders, in the case of d / D 0.4 (Dixon, 1988). For c ylinders, d p is equal to the diam-
p
eter of a sphere of equal v olume.
It is obvious that for d / D 0.1, the differences of bed voidage are small, whereas for
p
d / D 0.1, the bed v gularly shaped or irre fected by the diameter ratio. F oidage is greatly af
p
v
particles, measurements should be conducted in order to ealuate bed voidage and its
dependence on d / D . For example, for irregularly shaped particles of zeolite (clinoptilo-
p
lite), the bed voidage was measured to be in the range 0.48–0.51 for d / D between 0.019
p
,
and 0.074 (Inglezakis, 2002). Finally as the pressure drop is very sensitie to the bed v
voidage, the ratio d / D has a great effect on the pressure drop across the bed in the case of
p
d / D 0.1 (Afandizadeh and F 2001; Fumen , y oumen y et al ., 1996). Again, this happens
p
because for d / D 0.1, the bed voidage changes considerably (Figure 3.39).
p
Loading of particles in fixed beds
A major problem associated with loading methods could be the inconsistency in bed struc-
ture, i.e. mean and local voidage properties, from fill to f aking into consideration the ill. T
fact that pressure drop is greatly influenced by the bed voidage and that pressure drop is
critical for gas-phase systems, the loading of particles is of great importance, especially in
gas-phase reactors (Afandizadeh and F, 2001). y oumen