Incompressible filtration

The bracketed term in Equation (2.32) contains only constants in the case of incompressible filtration, and the medium resistance term includes a contribution to the flow resistance due to the layers of cake deposited prior to increasing the filtration pressure. Some time should be allowed before judging the parallel nature of the lines shown on Figures 2.12, to allow for equilibrium to be established. 

For constant-pressure filtration and washing, such as occur on vacuum filters, the filtration time and washing time can be related through the wash ratio if the wash liquor and filtrate are assumed to have similar physical properties. From the equation for incompressible filtration at constant pressure expressed in terms of a, ecffic resistance ... 

The same moisture content of the produced cake can be obtained in shorter dewatering times if higher pressures are used. If a path of constant dewatering time is taken, moisture content is reduced at higher pressures with a parallel increase in cake production capacity. This is an advantage of pressure filtration of reasonably incompressible soHds like coal and other minerals. 

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. 

Constant-Rate Filtration For substantially incompressible cakes, Eq. (18-51) may be integrated for a constant rate of slurry feed to the filter to give the following equations, in which filter-medium resistance is treated as the equivalent constant-pressure component to be deducted from the rising total pressure drop to... 

For incompressible cake, the pressure distribution and the rate depend on the resistance of the filter medium and the permeability of the cake. Figure L8-150 shows several possible pressure profiles in the cake with increasing filtration rates through the cake. It is assumed that r /i i = 0.8 and /p//i = 0.6. The pressure at / = ri, corresponds to pressure drop across the filter medium Ap, with the ambient pressure taken to be zero. The filtration rate as well as the pressure distribution depend on the medium resistance and that of the cake. High medium resistance or blinding of the medium results in greater penalty on filtration rate. 

This expression shows the relationship between filtration time and filtrate volume. The equation is applicable to both incompressible or compressible calces, because at constant AP the values and x are constant. For constant AP, an increase in the filtrate volume results in a reduction in the filtration rate. If we assume a definite filtering apparatus and set up a constant temperature and filtration pressure, then the values of Rf, r , fi and AP will be constant. We now take note of the well-known filtration constants K and C, which are derived from the above expressions ... 

As follows for the filtration of incompressible sediment (at a constant rate), the pressure increases in a direct proportion to time. However, the above equation... 

Filtration operations are capable of handling suspensions of varying characteristics ranging from granular, incompressible, free-filtering materials to slime-like compositions, as well as finely divided colloidal suspensions in which the cakes are incompressible. These latter materials tend to contaminate or foul the filter medium. The interaction between the particles in suspension and the filter medium determines to a large extent the specific mechanisms responsible for filtration. 

Filter aids as well as flocculants are employed to improve the filtration characteristics of hard-to-filter suspensions. A filter aid is a finely divided solid material, consisting of hard, strong particles that are, en masse, incompressible. The most common filter aids are applied as an admix to the suspension. These include diatomaceous earth, expanded perlite, Solkafloc, fly ash, or carbon. Filter aids build up a porous, permeable, and rigid lattice structure that retains solid particles and allows the liquid to pass through. These materials are applied in small quantities in clarification or in cases where compressible solids have the potential to foul the filter medium. 

Equation 18 defmes a parabolic relationship between filtrate volume and time. The expression is valid for any type of cake (i.e., compressible and incompressible). From a plot of V + C versus (t+Tq), the filtration process may be represented by a parabola with its apex at the origin as illustrated in Figure 5. Moving the axes to distances C and Tq provides the characteristic filtration curve for the system in terms of volume versus time. Because the parabola s apex is not located at the origin of this new system, it is clear why the filtration rate at the beginning of the process will have a finite value, which corresponds to actual practice. 

The ratios in parentheses express the constant volume rate per unit filter area. Hence, Equation 24 is the relationship between time i and pressure drop Ap. For incompressible cakes, rg is constant and independent of pressure. For compressible cakes, the relationship between time and pressure at constant-rate filtration is ... 

The rotary filter breaks down and the operation has to be carried out temporarily in a plate and frame press with frames 0.3 m square. The press takes 120 s to dismantle and 120 s to reassemble, and, in addition, 120 s is required to remove the cake from each frame. If filtration is to be carried out at the same overall rate as before, with an operating pressure difference of 75 kN/m2, what is the minimum number of frames that must be used and what is the thickness of each It may be assumed that the cakes are incompressible and the resistance of the filter media may be neglected. 

A slurry containing 100 kg of whiting/m3 of water, is filtered in a plate and frame press, which takes 900 s to dismantle, clean and re-assemble. If the filter cake is incompressible and has a voidage of 0.4, what is the optimum thickness of cake for a filtration pressure of 1000 kN/m2 The density of the whiting is 3000 kg/m3. If the cake is washed at 500 kN/m2 and the total volume of wash water employed is 25 per cent of that of the filtrate, how is the optimum thickness of cake affected The resistance of the filter medium may be neglected and the viscosity of water is 1 mN s/m2. In an experiment, a pressure of 165 kN/m2 produced a flow of water of 0.02 cm3/s though a centimetre cube of filter cake. 

A sample of the slurry was tested, using a vacuum leaf filter of 0.05 m2 filtering surface and a vacuum equivalent to a pressure difference of 71.3 kN/m2. The volume of filtrate collected in the first 300 s was 250 cm3 and, after a further 300 s, an additional 150 cm3 was collected. It may be assumed that cake is incompressible and the cloth resistance is the same in the leaf as in the filter press. 

Filtration is carried out in a plate and frame filter press, with 20 frames 0.3 m square and 50 mm thick, and the rate of filtration is maintained constant for the first 300 s. During this period, the pressure is raised to 350 kN/m2, and one-quarter of the total filtrate per cycle is obtained. At the end of the constant rate period, filtration is continued at a constant pressure of 350 kN/m2 for a further 1800 s, after which the frames are full. The total volume of filtrate per cycle is 0.7 m3 and dismantling and refitting of the press takes 500 s. It is decided to use a rotary drum filter, 1.5 m long and 2.2 m in diameter, in place of the filter press. Assuming that the resistance of the cloth is the same in the two plants and that the filter cake is incompressible, calculate the speed of rotation of the drum which will result in the same overall rate of filtration as was obtained with the filter press. The filtration in the rotary filter is carried out at a constant pressure difference of 70 kN/m2, and the filter operates with 25 per cent of the drum submerged in the slurry at any instant. 

A rotary drum with a filter area of 3 m3 operates with an internal pressure of 71.3 kN/m2 below atmospheric and with 30 per cent of its surface submerged in the slurry. Calculate the rate of production of filtrate and the thickness of cake when it rotates at 0.0083 Hz, if the filter cake is incompressible and the filter cloth has a resistance equal to that of 1 mm of cake. 

On the assumption that the cake is incompressible and that 5 mm of cake is left behind on the drum, determine the theoretical maximum flowrate of filtrate obtainable. What drum speed will give a filtration rate of 80 per cent of the maximum ... 

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. 

Before this equation can be integrated it is necessary to establish the relation between r and V. If v is the bulk volume of incompressible cake deposited by the passage of unit volume of filtrate, then ... 

It is decided to use a rotary drum filter, 1.5 m long and 2.2 m in diameter, in place of the filter press. Assuming that the resistance of the cloth is the same in the two plants and that the filter cake is incompressible, calculate the speed of rotation of the drum which will result in the same overall rate of filtration as was obtained with the filter press. The filtration in the rotary filter is carried out at a constant pressure difference of 70 kN/m2, and the filter operates with 25 per cent of the drum submerged in the slurry at any instant. 

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