Page 342 - Chemical Process Equipment - Selection and Design

306 SOLID-LIQUID SEPARATION
TABLE 11.2. Equipment Selection on the Basis of Rate of The resistance R is made up of those of the filter cloth Rf and that
Cake Buildup of the cake R, which may be assumed proportional to the weight of
the cake. Accordingly,
Rate of
Process Type Cake Buildup Suitable Equipment
(11.2)
Rapid 0.1-10 cm/sec gravity pans; horizontal belt or
filtering top feed drum; continuous E= specific resistance of the cake (m/kg),
pusher type centrifuge
Medium 0.1-10 cm/min vacuum drum or disk or pan or c = wt of solids/volume of liquid (kg/m’),
filtering belt; peeler type centrifuge p = viscosity (N sec/m2)
Slow 0.1-10 cm/hr pressure filters; disc and tubular P = pressure difference (N/m2)
filtering centrifuges; sedimenting
centrifuges A = filtering surface (m’)
Clarification negligible cartridges; precoat drums; filter v = volume of filtrate (m’)
cake aid systems; sand deep bed Q = rate of filtrate accumulation (m’/sec).
filters
(Tiller and Crump, 1977; Flood, Parker, and Rennie, 1966). Rf and E are constants of the equipment and slurry and must be
evaluated from experimental data. The simplest data to analyze are
those obtained from constant pressure or constant rate tests for
which the equations will be developed. At constant pressure Eq.
(11.2) is integrated as
pure water to displace the residual filtrate. Qualitative cost
comparisons also are shown in this table. Similar comparisons of
[YC
filtering and sedimentation types of centrifuges are in Table 11.19. = RfV + - V2 (11.3)
Final selection of filtering equipment is inadvisable without P 2A
some testing in the laboratory and pilot plant. A few details of such
work are mentioned later in this chapter. Figure 11.2 is an outline and is recast into linear form as
of a procedure for the selection of filter types on the basis of
appropriate test work. Vendors need a certain amount of in- (11.4)
formation before they can specify and price equipment; typical
inquiry forms are in Appendix C. Briefly, the desirable information
includes the following. The constants Rf and E are derivable from the intercept and slope
of the plot of t/V against V. Example 11.1 does this. If the constant
1. Flowsketch of the process of which the filtration is a part, with pressure period sets in when t = to and V = V,, Eq. (11.4) becomes
the expected qualities and quantities of the filtrate and cake.
2. Properties of the feed: amounts, size distribution, densities and (11.5)
chemical analyses.
3. Laboratory observations of sedimentation and leaf filtering rates.
4. Pretreatment options that may be used. A plot of the left hand side against V + V, should be linear
5. Washing and blowing requirements. At constant rate of filtration, Eq. (11.2) can be written
6. Materials of construction.
e=-= AAP (11.6)
V
A major aspect of an SLS process may be conditioning of the t p(Rf + acV/A)
slurry to improve its filterability. Table 11.4 summarizes common
pretreatment techniques, and Table 11.5 lists a number of and rearranged into the linear form
flocculants and their applications. Some discussion of pretreatment
is in Section 11.3. _-_=_ ’Rf+7V. (11.7)
PEC
Q -V/t A A
11.2. THEORY OF FILTRATION
The constants again are found from the intercept and slope of the
Filterability of slurries depends so markedly on small and linear plot of AP/Q against V.
unidentified dserences in conditions of formation and aging that no After the constants have been determined, Eq. (11.7) can be
correlations of this behavior have been made. In fact, the situation employed to predict filtration performance under a variety of
is so discouraging that some practitioners have dismissed existing constant rate conditions. For instance, the slurry may be charged
filtration theory as virtually worthless for representing filtration with a centrifugal pump with a known characteristic curve of output
behavior. Qualitatively, however, simple filtration theory is pressure against flow rate. Such curves often may be represented by
directionally valid for modest scale-up and it may provide a parabolic relations, as in Example 11.2, where the data are fitted by
structure on which more complete theory and data can be an equation of the form
assembled in the future.
As filtration proceeds, a porous cake of solid particles is built P =U - Q(b + cQ). (11.8)
up on a porous medium, usually a supported cloth. Because of the
fineness of the pores the flow of liquid is laminar so it is represented The time required for a specified amount of filtrate is found by
by the equation integration of

e=-=- AAP t = [ dVlQ. (11.9)
dV
dt pR ’ (11.1)