Page 145 - Chemical Process Equipment - Selection and Design

6.9. GRANULAR AND PACKED BEDS 117
Direct application of these equations in Example 6.14 is not Leva et al. (1951). Differences in voidage are pronounced as Figure
successful, bul. if E, is taken as the reciprocal of the given 6.8(c) shows.
expression, a plausible result is obtained. A long-established correlation of the friction factor is that of
Ergun (Chew. Eng. Prog. 48, 89-94, 1952). The average deviation
e GRANULRR AND PACKED BEDS from his line is said to be f20%. The friction factor is
Flow through granular and packed beds occurs in reactors with solid
catalysts, adsorbers, ion exchangers, filters, and mass transfer (6.108)
equipment. The particles may be more or less rounded or may be
shaped into rings. saddles, or other structures that provide a = 150/Re, + 1.75 (6.109)
desirable ratio of surface and void volume. with
Natural porous media may be consolidated (solids with holes in (6.110)
them), or they may consist of unconsolidated, discrete particles. ReP = D,G/p(l - E).
Passages through the beds may be characterized by the properties of
porosity, permeability, tortuosity, and connectivity. The flow of 5~10~
underground water and the production of natural gas and crude oil,
for example, are affected by these characteristics. The theory and
properties of such structures is described, for instance, in the book
of Dullien (Porous iMedia, Fluid Transport and Pore Structure, io4
Academic, New 'fork, 1979). A few examples of porosity and
permeability are in Table 6.9. Permeability is the proportionality
constant k in the flow equation u = (k/p) dP/dL.
Although consolidated porous media are of importance in
chemical engineering, only unconsolidated porous media are LQ
incorporated in process equipment, SO that further attention will be lo3
restricted to them.
Granular beds may consist of mixtures of particles of several
sizes. In flow problems, the mean surface diameter is the 0 PRESENT WORK
appropriate mean, given in terms of the weight fraction distribution, A WENTZ THODOS'~)
xi, by IO2
2 5
(6.106)
When a particle is not spherical, its characteristic diameter is taken
as that of a sphere with the same volume, so that

0, = (~V,/Z)''~. (6.107)
SINGLE PHASE FLUIDS
Extensive meiasurements of flow in and other properties of beds of
particles of various shapes, sizes and compositions are reported by

TABLE 6.9. Porosity and Permeability of Several
IUnconsolidated and Consolidated Porous Media

Porosity Permeability
Mediia 1%) (em2)
~ - ~ - ~
Bed saddles 68-83 1.3 X 10-3-3.9 X
Wire crimps 68-76 3.8~ 10-~-1.0 x 10-~
Black slate powder 57-66 4.9 x IO-'~-I.Z x IO-'
Silica powder 37-49 1.3 X 10-'0-5.1 X IO-''
Sand (loose beds) 37-50 2.0~ 10-7-1.8x
Soil 43-54 2.9X 10-'-1.4~ IO-'
Sandstone (oil sand1 8-38 5.0 X 10-'2-3.0 X IO-'
Limestone, dolomite 4-10 2.0 x 10-"-4.5 x lo-''
Brick 12-34 4.8 x 10-~'-2.2 x IO-' Ratio of porticle to tube diameter ~ !E
Concrete 2-7 1 .O x 1 0C9-2.3 x Dt
Leather 56-59 9.5~10-~~-1.2~10-~ (bi
Cork board - 3.3 x 10-'-1.5 x IO-'
Hair felt - 8.3 x 10-'-1.2 x Figure 6.8. Friction factors and void fractions in flow of single phase
Fiberglass 88-93 2.4~ 10-7-5.1 x fluids in granular beds. (a) Correlation of the friction factor,
Cigarette filters 17-49 1.1 x Re = DpG/(l - c)p and f, = [g,D,~~/pu~(l- E)](AP/L =
Agar-agar - 2.0 x 10-10-4.4 x IO-' 150/Re + 4.2/(Re)'" [Safo et al., J. Chem. Eng. Jpn. 6, 147-152
(l973)l. (b) Void fraction in granular beds as a function of the ratio
(A.E. Scheidegger, Physics of Now through Porous Media, of particle and tube diameters [Leva, Weintraub, Grurnmer,
University of Toronto Press, Toronto, Canada, 1974). Pollchik, and Storch, U.S. Bur. Mines Bull. 504 (1951)l.