Page 350 - Chemical Process Equipment - Selection and Design

11.3. RESISTANCE TO FILTRATION 313
EXAMPLE Il.3-(continued) n, 5 68.3APb (8)
The integral at constant pressure is
Comparing (5) and (8), it appears that an rph to meet the
80(t$-/A)' 1- yf/A = 36APbtf.. (3) filtering requirements is 68.3/17.94 = 3.8 times that for washing and
is the controlling speed.
With t$-/A = 0.0854, With a peripheral speed of 60 m/hr
APbtf = 0.04858, 60 = nDn,
= 0.01858/APb = 1/3nf D = 60/nn = 19.1/i.
nf = 17.94ALPb,
The parameters at several pressures are
where nf is the rph speed needed to make the 1 cm thick cake.
From Eq. (2) the washing rate is AP, (bar) 0.2 0.4 0.6 0.8
n (rph) 3.59 7.18 10.76 14.35
368APb = 2.455APb. D (m) 5.3 2.66 1.78 1.33
rw = 1 + 16(9(0.0854)
If the peripheral speed were made 1.22m/min, a drum
Washing time: 1.0 m dia would meet the requirements with AP = 0.8 bar. Another
controllable feature is the extent of immersion which can be made
0.006 0.00244 1 greater or less than 1/3. Sketches of a rotary vacuum iilter are in
t, ~- = -
-
>-
2.4558% APb n,,,' (7) Figure 11.12.

Eq. (11.19) could be written in terms of iL from Eq. (11.17) and reported rather than the resistivity that has been discussed here. It
would then have the same form as Eq. (11.2), but with only Rf as a is defined by the equation
parameter to be found from a single run at constant pressure. In
Example 11.1, the mean resistivity is found from the simpler Q/A = KpAP/yL, (11.21)
equation
where L is the thickness. The relation to the resistivity is
5 = aO(AP)i". (1 1.20)
Rf = L/K,. (1 1.22)
Analysis of the filtration of a compressible material is treated in
Example 11.4. Thus the filtration resistivity of the medium includes its thickness.
Typical measured values of Rf are of the order of l(alOm-'; for
4 1.3. RESISTAINCE TO FlLTRATlON comparison, the fine filter sheet of Table 1.6, assuming it to be
The filtration equation 1 rnm thick, has L/Kp = 0.001/0.15(10-12) = 0.7(1Q1') mpl.

(11.2) CAKE RESISTIVITY
A fundamental relation for the flow resistance of a bed of particles
considers the overall resistance to flow of filtrate to be made up of is due to Kozeny (Ber. Wien. Akad. W5a, 1927, 271-278):
contributions from the filter medium Rf, and from the cake with
specific resistance a.
a = K~;(I - 41~3, (1 1.23)
FILTER MEDIUM K = approximately 5 at Low porosities,
so = specific surface of the particles,
In practice, a measured Rf includes the effects of all factors that are ps = density of the particles,
independent of the amount of the cake; in a plate-and-frame press,
€or instance, piping and entrance and exit losses will be included, E = porosity, volume voids/volume of cake.
although most of the resistance usually is due to the medium itself.
Aging and the resulting increase in resistance is a recognized Because the structure of a cake is highly dependent on operating
behavior, particularly of media made of fibers. Particles are conditions and its history, the Kozeny equation is only of qualitative
gradually occluded in the media so thoroughly that periodic value to filtration theory by giving directional effects.
cleaning cannot restore the original condition. The degree of At increasing pressures, the particles or aggregates may be
penetration of the medium depends on the, porosity, the pore sizes, distorted and brought closer together. The rate of flow also may
particles sizes, and velocity. Normally Rf is found to depend on the affect the structure of a cake: at low rates a loose structure is
operating pressure; or1 plots like those of Example 11.1, the two formed, at higher ones fine particles are dragged into the previously
intercepts may correspond to different values of Rf at the two formed bed. The drag pressure at a point in a cake is the difference
pressures. between the pressure at the filter medium and the pressure loss due
Data for some filter media are shown in Table 11.6. Although to friction up to that point. As the drag pressure at a distance from
these porosities and permeabilities are of unused materials, the the filter cloth increases, even at constant filtering pressure, the
relative values may be useful for comparing behaviors under porosity and resistance adjust themselves continuously. Figure
filtration conditions. Permeability Kp normally is the property 11.4(a) shows such effects of slurry concentration and filtering rates