Page 871 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

826 Appendix E: Porous Media Hydraulics

to ‘‘tailwater.’’ Piezometers are placed at positions A, B, C, D. ment, involving a considerable effort, constitutes available
For the flow condition, the headloss, Dh ¼ 4 units. Therefore, data for a full-scale filter. Even for pilot scale, the data
the hydraulic gradient, dh=dz ¼ Dh=Dz ¼ 4=18 ¼ 0.22 units provided by Chang et al. (1999) constitute available data.
of head=unit of length. In addition to measuring hydraulic Porosity data by Hsu (1994) were obtained for different
gradient, the flow, Q, must be measured, and the cross-section media as follows:
area must be measured (v ¼ Q=A). Also the water temperature
must be measured so that the fluid properties, r w and m
may be calculated. From these data, k is calculated by Material d 10 (mm) UC Porosity
Equation E.5.
Coarse garnet 3.00 1.22 0.31
The column may be oriented vertically or horizontally and
Anthracite 1.08 1.48 0.34
for most situations Dh can be based on only the headwater and Garnet 8–12 1.43 1.60 0.33
tailwater elevation difference (rather than a series of piezo- Garnet 30–40 0.37 1.41 0.33
meters), which assumes a uniform hydraulic gradient. In some Fine garnet 0.11 3.44 0.36
cases if a mat has developed on the surface of the bed, the Dowex 50 resin 0.53 1.31 0.37
piezometers give a more accurate hydraulic gradient. A cau-
tion is to remove the air from the column by using a slow
displacement by air-free water rising from the bottom. The The measurements by Hsu were by salt displacement. The
size of the column may be whatever is convenient but a size columns were used for dispersion tests and had been tapped
10–15 cm (4–6 in.) diameter and perhaps 61 cm (24 in.) long lightly to consolidate the media (i.e., to minimize arching). As
would be sufficient to provide a ‘‘packing’’ that is statistically seen, the data are on the low side of other measurements, such
representative and to minimize wall effects. In addition, sev- as by Chang et al. (1999) and by Boulding (1995).
eral tests, perhaps 10–12, should be conducted such that As a matter of interest, the minimum possible porosity of a
enough k values are obtained for calculating the statistics of porous media of uniform spheres with rhombohedral packing
the variation, e.g., average k and the standard deviation of the is 0.259 (Scheidegger, 1960, p. 19; Muskat, 1946, p. 12). The
measurements. Repacking between tests would be preferred maximum possible porosity for ‘‘face.centered’’ or cubic
as opposed to a repetition with the same packing. As men- packing of spheres is 0.4764 (Muskat, 1946, p. 12). Muskat
tioned by Chang et al. (1999) the porosity of the media will (1946, p. 13) states that the most stable array of spheres is
affect the results of the test. For a given media, the porosity rhombohedral since it has sufficient points of contact to pro-
may vary, as indicated in Figure E.2, depending upon the rate vide support from any direction, while cubic is stable only to
of backwash termination or the amount of tapping on the side forces normal to the cell faces. He states further (p. 13) that:
of the column. Thus, a technique is involved in packing the
media. Porosity should be measured also to provide a more ...in natural assemblages, even when agitated to induce close
complete picture. packing, one should anticipate groups of spheres packed in
orderly arrays separated by boundaries in which no orderly
arrays are present and where the porosity is even higher than
E.4.2 POROSITY
that of cubic packing. Such zones can be maintained because
Porosity is defined as the ratio of the volume of voids to the of the ‘‘bridging’’ of groups of particles under pressures less
bulk volume. As shown by Chang et al. (1999) in Figure E.2, than the crushing strength of the particles. . . . Moreover, it is
found experimentally that assemblages of spheres, or even
porosity for a given media has a significant effect on its
sand particles, will have porosities averaging about 40 percent
intrinsic permeability. The porosity values, from Figure E.2
in spite of careful efforts to induce closer packing, and even
for media in pilot filters, show groupings as follows:
though the predominant array in the assemblage is rhombohe-
dral with a porosity of only 26 percent. Theoretically, the
actual size of the spheres has no influence on the porosity,
Media UC Porosity Range
but in the assemblages of natural materials this does not
Potter’s beads 1.00 0.35–0.40 prove true.
Sand 1.23–1.31 0.35–0.44
Anthracite 1.24–1.33 0.46–0.58
Material Porosity
Coarse sand 0.39–0.41
Trussell et al. (1999) estimated the porosity for a full-scale Medium sand 0.41–0.48
anthracite filter as P 0.48, slightly less than the porosities Fine sand 0.44–0.49
measured for pilot scale filters of anthracite. The full-scale Fine sandy loam 0.50–0.54
filter was located at the Aqueduct Filtration Plant at Sylmar,
California, operated by the Los Angeles Department of Water
2
and Power. The design capacity was 33.0 h=h (13.5 gpm=ft ) Boulding (1995, p. 856) gave porosity ranges for different
and the bed was mono-media of anthracite, 1.8 m (6.0 ft) media: fine gravel, 0.20–0.40; coarse sand, 0.25–0.45;
deep, with d 10 ¼ 1.5 mm, UC ¼ 1.33. This single measure- medium sand, 0.25–0.45; fine sand, 0.25–0.55; dune sand,