Porosity filter cakes

Eylander (16) modified Barkman and Davidson s (2) equation for internal formation plugging and introduced the filter cake porosity parameter (0.2). His equation is based on internal filter cake formation that grows towards the wellbore. 

Flocculants and surfactants (qv) are used frequently as filter aids, particularly when slimes are present or when the particles to be filtered are very fine and difficult to filter. Low molecular weight polymers are more commonly used. These form small, dense floes which provide higher cake porosity. 

Diatomaceous Silica Filter aids of diatomaceous silica have a dry bulk density of 128 to 320 kg/m (8 to 20 Ib/fU), contain paiiicies mostly smaller than 50 [Lm, and produce a cake with porosity in the range of 0.9 (volume of voids/total filter-cake volume). The high porosity (compared with a porosity of 0.38 for randomly packed uniform spheres and 0.2 to 0.3 for a typical filter cake) is indicative of its filter-aid ability Different methods of processing the crude diatomite result in a series of filter aids having a wide range of permeability. 

Filter aids may be applied in one of two ways. The first method involves the use of a precoat filter aid, which can be applied as a thin layer over the filter before the suspension is pumped to the apparatus. A precoat prevents fine suspension particles from becoming so entangled in the filter medium that its resistance becomes exces-sive. In addition it facilitates the removal of filter cake at the end of the filtration cycle. The second application method involves incorporation of a certain amount of the material with the suspension before introducing it to the filter. The addition of filter aids increases the porosity of the sludge, decreases its compressibility, and reduces the resistance of the cake. In some cases the filter aid displays an adsorption action, which results in particle separation of sizes down to 0.1 /i. The adsorption ability of certain filter aids, such as bleached earth and activated charcoals, is manifest by a decoloring of the suspension s liquid phase. This practice is widely used for treating fats and oils. The properties of these additives are determined by the characteristics... 

The characteristics of the pump relate the applied pressure on the cake to the flowrate at the exit face of the filter medium. The cake resistance determines the pressure drop. During filtration, liquid flows through the porous filter cake in the direction of decreasing hydraulic pressure gradient. The porosity (e) is at a minimum at the point of contact between the cake and filter plate (i.e., where x = 0) and at a maximum at the cake surface (x = L) where sludge enters. A schematic definition of this system is illustrated in Figure 2. 

Sometimes filtration can be improved by using filteraids. These filteraids, which are based on diatomaceous earth, improve the porosity of a resulting filter cake leading to a faster flow rate. Before filtration a thin layer is used as a precoat of tire filter (normally standard filters). After that a mix is made with the harvest broth and filtration is started. 

In general, fungal mycelia are filtered relatively easily, because mycelia filter cake has sufficiently large porosity. Yeast and bacteiia are much more difficult to handle because of thefr small size. Alternative filtration methods, which eliminate the filter cake, are becoming more acceptable for bacterial and yeast separation. Micro-filtration is achieved by developing large cross-flow fluid velocities across the filter surface while the velocity vector normal to the surface is relatively small. Build up of filter cake and problems of high cake resistance are therefore prevented. Micro-filtration is not discussed in this section. 

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. 

The washing of filter cake is carried out to remove liquid impurities from valuable solid product or to increase recovery of valuable filtrates from the cake. Wakeman (1990) has shown that the axial dispersion flow model, as developed in Sec. 4.3.6, provides a fundamental description of cake washing. It takes into account such situations as non-uniformities in the liquid flow pattern, non-uniform porosity distributions, the initial spread of washing liquid onto the topmost surface of the filter cake and the desorption of solute from the solid surfaces. 

Program FILTWASH models the dimensionless filtration wash curves for the above case of a filter cake with constant porosity, axial dispersion in the liquid flow and desorption of solute from the solid particles of the filter bed (Boyd, 1993). 

Distance measured from filter cloth Dimensionless distance Cake porosity... 

In compressible filter cakes, the porosity varies from a minimum next to the filter septum to a maximum at the cake surface. How could you include such a variation within the context of a simulation program Remember that as the porosity changes, the local fluid velocity will also change as a result of... 

Filter aids can be added to the slurry to reduce the filter cake resistance. These are materials that have high porosity. Their application is normally restricted to cases where the filtrate is valuable and the solid cake is a waste. In cases where the solid is valuable, the filter aid should... 

Heertjes(11) has studied the effect of pressure on the porosity of a filter cake and suggested that, as the pressure is increased above atmospheric, the porosity decreases in proportion to some power of the excess pressure. 

By the use of this technique, a much higher rate of filtration can be achieved than is possible in a filter operated in a conventional manner. In addition, the resulting cake usually has a lower porosity because the blades effectively break down the bridges or arches which give rise to a structure in the filter cake, and the final cake is significantly drier as a result. 

Figure 11.4. Data of compressibilities and porosities of filter cakes, (a) Parameters of the correlation a = a0(hP)n for resistivity of CaSi03 filter cakes at two rates and two concentrations (Rushton and Katsoulas, 1984). (b) Resistivity as a function of pressure measured in a compressibility-permeability (CP) cell [Grace, Chem. Eng. Prog. 49, 303, 367, 427 (1953)]. (c) Porosity as a function of pressure for the same six materials (Grace, loc. tit.).

TABLE 11.8. Parameters of Equations for Resistivity a and Porosity e of Some Filter Cakes... 

Centrifugation is one of the most widely employed types of filtration, notable for operational speed (assuming the solid packs well on the filter cloth, or sintered metal bowl, and the porosity of the solid cake is maintained to allow thorough washing) and for producing a relatively dry cake—it is not uncommon for a centrifuged filter cake to be dried out to a solvent content of approximately 20%. Sometimes... 

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