Page 352 - Chemical Process Equipment - Selection and Design

11.4. THICKENING AND CLARIFYING
TABLE 11.6. Porosities and Permeabilities of Some Filter the formation and stability of loose cake structures; such behavior
Media normally is not reproducible.

Porosity (%) ANOTHER FORM OF PRESSURE DEPENDENCE
Wedge wire screen 5-10
Perforated sheet 20 Equation (11.24) cannot be entirely valid because it predicts zero
Wire mesh: resistivity at zero pressure, whereas cakes do have structures and
Twill weave 15-25 significant resistivities even at minimal operating pressures.
Square 30-35 Modified Eq. (11.12) is extrapolatable, and Is rewritten hare as
Porous plalstics. metals, cerzrnics 30-50
Crude kieselguhr 50-60
Porous ceramic, special 70 (Y = a0(l + kP)" (11.25)
Membranes, plastic foam 80
Asbestos/ceIlulose sheets 80 with a similar one for porosity
Refined filter aids (diatomaceous earth ex- 80-90
panded lperlite) E = 1 - (1 - ~~)(1+ (11.26)
kP)".
Paper 60-95
Scott plastic foam 97 Some data fitted to these equations by Tiller et al. (1979) are in
Permeability, 10'*Kp llm") (compare Eq. (11.22)) Table 11.8; here the constant k is the same for both a and E,
Filter aids although this is not necessarily generally the case. Unfortunately,
Fine 0.05-0.5 these data show that the parameters are not independent of the
Medium 1-2 pressure range. Apparently the correlation problem has not been
Coarse 4-5 solved. Perhaps it can be concluded that insofar as the existing
Cellulose fibre pulp 1.86 filtration theory is applicable to real filtering behavior, the
Cellulose fibre + 5% asbestos 0.34 approximation of Almy and Lewis may be adequate over the
Filter sheets moderate ranges or pressures that are used commonly, somewhere
Polishing 0.017 between 0.5 and 5 atm.
Fine 0.15
Clarifying 1.13
Sintered metal PRETREATMENT OF SLURRIES
3 pm pore size 0.20 Since the sizes of particles and agglomerates of the slurry are a main
8 pm pore size 1 .o
28 pm pore size 7.5 determinant of a rate of filtration, any methods of influencing these
75 um Dore size 70 sizes are of great practical value. For example, Figures 1.2(b) and
.
,
(c) show CaCO, and TiO, each to be precipitated at two different
(Purchas, 19Sl). values of pH with resultant great differences in resistivity and
porosity. At 10psia, for instance, the resistivities of the two
CaC0,'s are in the ratio of 5, with corresponding differences in rate
of filtration. Pretreatment of a slurry to enhance coagulation and
filtration experiments, as done in Example 11.1, a simpler method is particle growth is an important aspect of filter process design.
'LO measure them in a CP cell as described briefly later in this Another method of long standing for improving filtration behavior
chapter. Equation (11.24) for the effect of pressure was proposed by is the formation of an open cake structure by addition of relatively
Almy and Lewis (1912). For the materials of Figure 1.2(b), for large and rigid particles of a filter aid. The common methods of
instance, it seems to be applicable over at least moderate stretches pretreatment are listed in Table 11.4, and some chemical flocculants
of pressure. Incidentarly, these resistances are not represented well that are of practical value are described in Table 11.5. These effects
by the Kozeny porosity function (1 - E)/E~; for substance 6, the cannot be predicted safely and must be measured.
ratio of resistivities at 100 and 1psia is 22 and the ratio of the
porosity functions is 2.6. The data of Table 11.7 also show a 11.4. THICKENING AND CLARlFYlNG
substantial effect of pressure on resistivity.
Since the drag pressure varies along the cake as a result of When dilute slurries are encountered on a large scale, it is
friction, porosity and resistivity also will vary with position. Figure more economical to concentrate them before filtering. This is
11.5 shows such data at three different overall pressures. The axial accomplished by sedimentation or thickening in tanks for an
profile of the normalized pressure, PLocal/Pface, appears to be a appropriate period. Typical designs of thickeners are sketched in
unique function of fractional distance along the cake, independent Figure 11.6. The slurry is introduced at the top center, dear liquid
of the filtering pressure. The resistivity will vary along the cake just overflows the top edge, whereas the solids settle out and are worked
as the porosity does. As the cake builds up, moreover, the drag graduatly towards the center with slowly rotating rakes towards the
pressure, porosity, and resistivity at a particular distance from the discharge port at the bottom center. The concentrated slurry then is
Filter medium also will vary. Consequently, since the resistivity does suitable for filtration or other further processing. Clarifiers are
not necessarily change linearly with position, any mean value also is similar devices, primarily for recovering dear liquids from dilute
likely to vary as the cake builds up. Thus, in the filtration equation suspensions. Some characteristics of sedimentation equipment are
even a mean value of a has to be expressed as a function of P and given in Table 11.3 and typical applications are listed in Table 11.9
V. The proper mathematical representation of a filtration process is and 14.7. Sedimentation rates often are assisted by addition of
by means of an integro-differential equation with a moving Rocculating agents, some of which are listed in Table 11.5.
boundary (the face of the cake). Such an analysis was made by Specifically, pilot plant testing is advisable when
Wakeman (1978) and a similar one by Tiler, Crump, and Ville
(1979). At present, unfortunately, such a mathematical approach to 1. The expecting filtering area is expected to be substantial,
filtration problems is more of academic than practical value. One of measured in tens of m2.
the factors that is not taken into account is the effect of flow rate on 2. Cake washing is critical.