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3.6 T o-Phase Fix w ed Beds 149

examined with respect to its flow patterns, as a v for e irrespecti essel, xample, e of the spe- v
cific chemical reaction or physical phenomenon that will take place in it. In the present book,
the several methods used for RTD studies as well as the mathematical background will not
be presented. This information can be found elsewhere (Levenspiel, 1962). Instead, se v eral
correlations will be presented to assess the behavior of fixed beds.

Axial mixing Packed bed is an array of voids into which fluid flows at relati ely v
.
high velocityAcceleration occurs in the ports created by particle–particle intersections,
and deceleration upon entering the voids. The net result of this situation is axial
mixing. In the ideal case, this mixing is perfect and the bed may be viewed as a series of
perfectly mixed vessels (voids) interconnected by ports consisting of closely pack ed
regions. Plug flow is the situation where axial mixing between the seeral cross-sections v
of the bed is minimal, whereas radial mixing in each section is maximal.
w Re f Axial and radial dispersion coeficients are equal at loynolds numbers because the
dispersion is due to the molecular diffusion and the axial and radial structures of the bed
,
er
v
are similar (Gunn, 1968). Ho at high Reynolds numbers, the con e dispersion v ecti v
we
dominates and the values are different because the axial dispersion is primarily caused by
differences in the fluid velocity in the flow channels, whereas the radial dispersion is pri-
marily caused by deviations in the flow path caused by the particles.
Ideal flow is studied and represented using the classic dispersion or dispersed plug-flow
v
model of Leenspiel (1962). Recall the material balance of a fed-bed reactor with per- ix
fect radial mixing (eq. (3.285)):
2 C C C
D u ( R ) (3.311)
L 2 s
z z t
C 2
w In the case of ideal plug flo D L 0, while in ideal mix w ed flo 0. Thus, in ideal,

2
z
mixed, or plug flo the first term is zero. , w
The main parameter in this model characterizing the quality of the flow is the axial dis-
persion coefficient. The term “axial” is used to distinguish mixing in the direction of flo w
from mixing in the radial direction. Then, based on this parameter, the particle Peclet num-
ber is introduced:
ud p
Pe
p (3.312)
D L
where
d p the particle diameter
D L the axial dispersion coef icient f
u the interstitial fluid v . elocity
Multiplying this number with the term Z / d , where Z is the f we obtain the ix ed-bed length,
p
.
vessel Peclet numberA high vessel Peclet number means better flow quality thus closer ,
wif this number is higher than about 100, to ideal flo. Typically, the flow is considered to
be ideal (plug flo w).
Liquid–solid fixed beds: In the related literature, there are correlations for the e aluation v
of the particle Peclet number ( Pe p ) for materials that are frequently used in adsorption and