Page 205 - Bird R.B. Transport phenomena

§6.4 Friction Factors for Packed Columns 189
banks, flow near baffles, and near flow around rotating disks. These and many more are
summarized in various reference works. 1 One complex system of considerable interest
in chemical engineering is the packed column, widely used for catalytic reactors and for
separation processes.
There have been two main approaches for developing friction factor expressions for
packed columns. In one method the packed column is visualized as a bundle of tangled
tubes of weird cross section; the theory is then developed by applying the previous re-
sults for single straight tubes to the collection of crooked tubes. In the second method the
packed column is regarded as a collection of submerged objects, and the pressure drop is
obtained by summing up the resistances of the submerged particles. 2 The tube bundle
theories have been somewhat more successful, and we discuss them here. Figure 6.4-1 (я)
depicts a packed column, and Fig. 6.4-1 (b) illustrates the tube bundle model.
A variety of materials may be used for the packing in columns: spheres, cylinders,
Berl saddles, and so on. It is assumed throughout the following discussion that the pack-
ing is statistically uniform, so that there is no "channeling" (in actual practice, channeling
frequently occurs, and then the development given here does not apply). It is further as-
sumed that the diameter of the packing particles is small in comparison to the diameter of
the column in which the packing is contained, and that the column diameter is uniform.
We define the friction factor for the packed column analogously to Eq. 6.1-4:

4
U (6.4-1)
in which L is the length of the packed column, D p is the effective particle diameter (de-
fined presently), and v is the superficial velocity; this is the volume flow rate divided by
0
the empty column cross section, v 0 = zv/pS.
The pressure drop through a representative tube in the tube bundle model is given
by Eq. 6.2-17

(6.4-2)

i *
I

ЦЦ
1

Fig. 6.4-1. (a) A cylindrical tube packed with spheres;
(b) (b) a "tube bundle" model for the packed column in (a).

P. C. Carman, Flow of Gases through Porous Media, Butterworths, London (1956); ]. G. Richardson,
1
Section 16 in Handbook of Fluid Dynamics (V. L. Streeter, ed.), McGraw-Hill, New York (1961); M. Kaviany,
Chapter 21 in The Handbook of Fluid Dynamics (R. W. Johnson, ed.), CRC Press, Boca Raton, Fla. (1998).
W. E. Ranz, Chem. Eng. Prog., 48, 274-253 (1952); H. C. Brinkman, Appl. Sci. Research., Al, 27-34,
2
81-86, 333-346 (1949). Henri Coenraad Brinkman (1908-1961) did research on viscous dissipation
heating, flow in porous media, and plasma physics; he taught at the University of Bandung, Indonesia,
from 1949 to 1954, where he wrote The Application of Spinor Invariants to Atomic Physics.