Filtration specific resistance

The concept of the specific resistance used in equation 4 is based on the assumptions that flow is one-dimensional, growth of cake is unrestricted, only soHd and Hquid phases are present, the feed is sufficiently dilute such that the soHds are freely suspended, the filtrate is free of soHds, pressure losses in feed and filtrate piping are negligible, and flow is laminar. Laminar flow is a vaHd assumption in most cake formation operations of practical interest. 

The specific resistance coefficient for the dust layer Ko was originally denned by Williams et al. [Heat. Piping Air Cond., 12, 259 (1940)], who proposed estimating values of the coefficient by use of the Kozeny-Carman equation [Carman, Trans. Inst. Chem. Fng. (London), 15, 150 (1937)]. In practice, K and Ko are measured directly in filtration experiments. The K and Ko values can be corrected for temperature by multiplying by the ratio of the gas viscosity at the desired condition to the gas viscosity at the original experimental conditions. Values of Ko determined for certain dfists by Williams et al. (op. cit.) are presented in Table 17-5. 

It is known that the specific resistance for centrifuge cake, especially for compressible cake, is greater than that of the pressure or vacuum filter. Therefore, the specific resistance has to be measured from centrifuge tests for different cake thicknesses so as to scale up accurately for centrifuge performance. It cannot be extrapolated from pressure and vacuum filtration data. For cake thickness that is much smaller compared to the basket radius, Eq. (18-116 7) can be approximated by... 

Filter aids are evaluated in terms of the rate of filtration and clarity of filtrate. Finely dispersed filter aids are capable of producing clear filtrate however, they contribute significantly to the specific resistance of the medium. As such, applications must be made in small doses. Filter aids comprised of coarse particles contribute considerably less specific resistance consequently, a high filtration rate can be achieved with their use. Their disadvantage is that a muddy filtrate is produced. 

The ability of an admix to be retained on the filter medium depends on both the suspension s concentration and the filtration rate during this initial precoat stage. The same relationships for porosity and the specific resistance of the cake as functions of suspension concentration and filtration rate apply equally to filter aid applications. 

Wells, S. A. (1990) "Determination of Sludge Properties for Modeling Compressible Cake Filtration from Specific Resistance Tests," Proceedings A.S.C.E. National Environmental Engineering Conference, Washington, D.C., 125-131... 

Size a Nutsch filter for processing a suspension containing 15 % solids. The desired cake wetness is 45 % and the filter capacity for the filtrate should be 5 mVhr. The allowable pressure drop is 500 mm Hg. The cake specific resistance is r = 9 X 1011 m and the filter plate resistance is Rf = 2 x 10 ... 

Measurements of filtration rates should be repeated at different pressures or different vacuum levels. This gives information on the influence of pressure on the specific cake resistance. The specific resistance of cakes that are difficult to filter is often pressure-dependent. Thus, use of excessive pressure can result in blocking of the cake, causing filtration to stop. In the case of compressible cakes, information is needed over the whole range of pressures being considered for industrial filters since extrapolation of compressibility beyond the experimentally covered region is always risky. The larger the scale of an experimental filter, the less risky predictions based on the experimental data. 

If the volume of filtrate is measured as a function of time, under constant pressure, then a plot of t/V against V should give a straight line, the slope of which can be used to calculate the specific resistance. 

Experiments to determine specific resistance, based on Equation 7, have usually been carried out by some form of vacuum filtration. These methods are time-consuming and subject to error. More rapid techniques such as the measurement of capillary suction time (CST) can be used (8), although these do not give absolute values of specific resistance. Nevertheless, the CST method is very useful for rapidly obtaining comparative data on the flocculation of fairly concentrated suspensions by polymers (9). In the present work, specific resistance has been determined by an automated technique, which will be described below. 

The method described here provides a convenient means of determining the specific filtration resistance of fairly dilute suspensions. Results for clay suspensions flocculated by cationic polymers show that the specific resistance gives a sensitive indication of flocculation and is a useful guide in the selection of optimum flocculant concentrations. In a series of trials not reported here, it has been shown that the specific resistance results are very well matched by re-filtration rate data, as expected. The results also agree well with other, unrelated techniques. For more concentrated suspensions, some discrepancies have been found between permeability methods and other measures of flocculation (4). 

It is desired to increase the rate of filtration by raising the speed of rotation of the drum. If the thinnest cake that can be removed from the drum has a thickness of 5 mm, what is the maximum rate of filtration which can be achieved and what speed of rotation of the drum is required The voidage of the cake = 0.4, the specific resistance of cake = 2 x 1012 m-2 the density of solids = 2000 kg/m3, the density of filtrate = 1000 kg/m3, the viscosity of filtrate = 10-3 N s/m2 and the slurry concentration = 20 per cent by mass solids. 

Equation 7.2 is the basic filtration equation and r is termed the specific resistance which is seen to depend on e and S. For incompressible cakes, r is taken as constant, although it depends on rate of deposition, the nature of the particles, and on the forces between the particles, r has the dimensions of L-2 and the units m-2 in the SI system. 

Thus there is a linear relation between (t — h)/ V — V ) and V — Vx, as shown in Figure 7.2, and the slope is proportional to the specific resistance, as in the case of the flow of the filtrate through the filter cake alone given by equation 7.14, although the fine does not now go through the origin. 

The blocking of the pores of the filter medium by particles is a complex phenomenon, partly because of the complicated nature of the surface structure of the usual types of filter media, and partly because the lines of movement of the particles are not well defined. At the start of filtration, the manner in which the cake forms will lie between two extremes — the penetration of the pores by particles and the shielding of the entry to the pores by the particles forming bridges. Heertjes(11) considered a number of idealised cases in which suspensions of specified pore size distributions were filtered on a cloth with a regular pore distribution. First, it was assumed that an individual particle was capable on its own of blocking a single pore, then, as filtration proceeded, successive pores would be blocked, so that the apparent value of the specific resistance of the filter cake would depend on the amount of solids deposited. 

Whilst it may be possible to predict qualitatively the effect of the physical properties of the fluid and the solid on the filtration characteristics of a suspension, it is necessary in all cases to carry out a test on a sample before the large-scale plant can be designed. A simple vacuum filter with a filter area of 0.0065 m2 is used to obtain laboratory data, as illustrated in Figure 7.5. The information on filtration rates and specific resistance obtained in this way can be directly applied to industrial filters provided due account is taken of the compressibility of the filter cake. It cannot be stressed too... 

If the resistance of the filter medium is neglected, t = BiV2 and the time during which filtration is carried out is exactly equal to the time the press is out of service. In practice, in order to obtain the maximum overall rate of filtration, the filtration time must always be somewhat greater in order to allow for the resistance of the cloth, represented by the term B2V. In general, the lower the specific resistance of the cake, the greater will be the economic thickness of the frame. 

The substitution of a more logical approach to filtration of slurries yielding compressible cakes and redefinition of the specific resistance (Chapter 7). 

Ng HY and Hermanowicz SW. Specific resistance to filtration of biomass from membrane bioreactor reactor and activated sludge Effects of exocellular polymeric substances and dispersed microorganisms. Water Environ Res. 2005 77 187-192. 

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