Compressible Cake

The constant given the value 5 in equation 1 depends on particle size, shape, and porosity it can be assumed to be 5 for low porosities. Although equation 1 has been found to work reasonably well for incompressible cakes over narrow porosity ranges, its importance is limited in cake filtration because it cannot be used for most practical, compressible cakes. It can, however, be used to demonstrate the high sensitivity of the pressure drop to the cake porosity and to the specific surface of the soHds. 

The most important feature of the pressure filters which use hydrauHc pressure to drive the process is that they can generate a pressure drop across the medium of more than 1 x 10 Pa which is the theoretical limit of vacuum filters. While the use of a high pressure drop is often advantageous, lea ding to higher outputs, drier cakes, or greater clarity of the overflow, this is not necessarily the case. Eor compressible cakes, an increase in pressure drop leads to a decrease in permeabiUty of the cake and hence to a lower filtration rate relative to a given pressure drop. 

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... 

At n = 1 N-s/m, hj, = 1 m and u = 1 m/s, the value r = AP. Thus, the specific cake resistance equals the pressure difference required by the liquid phase (with a viscosity of 1 N-s/m ) to be filtered at a rate u = 1 m/s for a cake 1 m thick. This hypothetical pressure difference is, however, beyond a practical range. For highly compressible cakes, the value ro reaches 10 m or more. Assuming V = 0 (at the start of filtration) where there is no cake over the filter plate, the equation becomes ... 

For incompressible cakes, eoefficient r is constant and independent of pressure. For compressible cakes (s 0) r may be estimated from the expression r = aAP. Substituting for r into the above relation, we obtain ... 

When the cake structure is composed of particles that are readily deformed or become rearranged under pressure, the resulting cake is characterized as being compressible. Those that are not readily deformed are referred to as sem-compressible, and those that deform only slightly are considered incompressible. Porosity (defined as the ratio of pore volume to the volume of cake) does not decrease with increasing pressure drop. The porosity of a compressible cake decreases under pressure, and its hydraulic resistance to the flow of the liquid phase increases with an increase in the pressure differential across the filter media. 

Figure 3. Frictional drag on particles in compressible cakes.

Equation 13 is the relationship between filtration time and filtrate volume. The expression is applicable to either incompressible or compressible cakes, since at constant Ap, r and Xq are constant. If we assume a definite filtering apparatus and set up a constant temperature and filtration pressure, then the values of Rf, rQ, n and Ap will be constant. 

Bierck, B. R., Wells, S. A., and Dick, R. I. (1988) "Compressible Cake Filtration Monitoring Cake Formations Using X-Rays from a Synchrotron Source," Water Pollution Control Federation Journal, Vol. 60, No. 5, 645-650... 

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... 

Wells, S. A. and Plaskett, J. H. (1992) "Modeling Compressible Cake Filtration with Uncertainty," in Advances in Filtration and Separation Technology Separation Problems and the Environment, Volume 5, ed. by B. Scheiner, American Filtration Society, pp. 351-354... 

Wells, S. A. and Dick, R. I. (1993) "Permeability, Solid and Liquid Velocity, and Effective Stress Variations in Compressible Cake Filtration," Proceedings, American Filtration Society Conference on System Approach to Separation and Filtration Process Equipment, Chicago, Illinois, May 3-6, pp. 9-12... 

R.G. Holdich, 1994, Simulation of Compressible Cake Filtration, Filtration and Separation, 31, pp 825-829... 

Ruech, Wolfgang An experimental and theoretical study of. .. An experimental and theoretical study of compressible cake filtration. Verfasser Ruech. .. http //www.tugraz.at/forschung/diplomarbeiten/1996/17-37.html [More Results From www.tugraz.at]... 

Staff profile page - the Engineering Faculty at Loughborough. .. Broad Interests and Expertise. Compressible cake filtration Selection, scale-up and process simulation of solid/liquid separation equipment Washing and. .. http //WWW. Iboro. ac. uk/departments/eng/research/staff/html/tarleton. html [More Results From www.lboro.ac.uk]... 

DJ Mullan - Extended Abstract. .. Internal Cylindrical Compressible Cake Filtration Model. To date no one has developed a model which. .. http //www.und.ac.za/und/prg/posters/daveabs.html [More Results From www.und.ac.za]... 

APS Table of Contents Vol. 12. .. On Parameters Affecting Flow Behavior During Compressible Cake Filtration in the Centrifugal Field.. .. http //WWW. afssociety.org/publications/Contents/vol 12.shtml [More Results From www.afssociety.org]... 

Also from (7.3.1.1), rm is the filter media resistance and a is the average specific cake resistance. If the filter cake is incompressible, a is constant for compressible cake a is defined as ... 

Having a differential pressure in the above filtration process, and reducing the pressure drop from 10 to 5 psi, increases the filter area by 19%. The main reasons why an increase in the pressure drop results in less filter area are the compressed cake and the porosity of the filter cake. 

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. 

The equations that apply for a compressible cake are as follows. 

Filter cakes may be divided into two classes—incompressible cakes and compressible cakes. In the case of an incompressible cake, the resistance to flow of a given volume of cake is not appreciably affected either by the pressure difference across the cake or by the rate of deposition of material. On the other hand, with a compressible cake, increase of the pressure difference or of the rate of flow causes the formation of a denser cake with a higher resistance. For incompressible cakes e in equation 7.1 may be taken as constant and the quantity e3/[5(l — e)2S2] is then a property of the particles forming the cake and should be constant for a given material. 

In a compressible cake, the volume v of cake deposited per unit area as a result of the flow of unit volume of filtrate will not be constant, but will vary during the filtration cycle. If the particles themselves are not compressible, however, the volume of particles (vr) will be almost independent of the conditions under which the cake is formed assuming a dilute feed suspension. Any small variations in v arise because the volume of filtrate retained in the cake is a function of its voidage, although the effect will be very small,... 

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