Effect of Pressure on Cake Filtration

The probable success of correlation of cake resistivity in terms of all the factors that have been mentioned has not been great enough to have induced any serious attempts of this nature, but the effect of pressure has been explored. Although the a s can be deduced from filtration experiments, as done in Example 11.1, a simpler method is to measure them in a CP cell as described briefly later in this chapter. Equation (11.24) for the effect of pressure was proposed by Almy and Lewis (1912). Eor the materials of Figure 11.4(b), for instance, it seems to be applicable over at least moderate stretches of pressure. Incidentally, these resistances are not represented well by the Kozeny porosity function (1 — s)/s for substance 6, the ratio of resistivities at 100 and 1 psia is 22 and the ratio of the porosity functions is 2.6. The data of Table 11.7 also show a substantial effect of pressure on resistivity. 

The effect of pressure shown earlier is modified in most industrial flltrations in which cake compressibility usually lies between 0.1 and 0.8. Furthermore, the resistance of the filter reduces the effects of the respective variables. It has been found, however, that an increase in pressure causes a nearly proportionate increase in the flow rate in the filtration of granular or crystalline solids. Flocculent or slimy precipitates, on the other hand, have their filtration rates increased only slightly by an increase in pressure. Some materials have a critical pressure above which a further increase results in an actual decrease in flow rate. 

Whilst cake cracking and drop-off are piinc al sources of differences in the yield of actual plant, conq)ared with laboratory-scale tests, other considerations include (1) equality of the pressure differential available for cake formation and (2) equivalence of media condition and resistance. The latter will depend on the age of the medium and the effectiveness of cloth wadung operations. Filtration equipment is generally poorly instrumented. The location of the AP measuring device and the pressure (vacuum) losses present between the measurement and point of filtration will vary ftom station to station. 

Equation (1), known as the two-resistance filtration model, is a simple expression for describing the filtration of incompressible cakes, the specific cake resistance, a, can be regarded as a constant. In the case of compressible cakes, the effect of variation in cake porosity on spedfic cake resistance must be considered (Tiller and Shirato, 1964). Filtration tests should be performed under diflerent pressure drops to establish an empirical relation between the specific cake resistance, a, and the pressure drop across the filter cake, APe (McCabe et al., 1993) ... 

The primary factor in the design of filters is the cake resistance or cake permeability. Because the value of the cake resistance can be determined only on the basis of experimental data, laboratory or pilot-plant tests are almost always necessary to supply the information needed for a filter design. After the basic constants for the filter cake have been determined experimentally, the theoretical concepts of filtration can be used to establish the effects of changes in operating variables such as filtering area, slurry concentration, or pressure-difference driving force. 

The experiments consisted of three parts. In the first part, the characterization of minerals was explained by using x-ray diffractometer and electron microscope studies. Also, it was performed electrokinetic s studies of suspension. The effect of particle shape and size on the vacuum and pressure filtration of minerals has been investigated in the second part of the study. At the last part, the comparison of the particle shape and size effect on shear strength of the mineral filter cakes was performed. 

The oscillated backflushing mechanism accounts for the effect of the pressure waveform on TMP. When the minimum pressure of the pulsatile pressure waveform results in a negative TMP, a reverse permeate flow may occur that acts as a backwash flow that drives particles deposited on or near the membrane surface back to the bulk flow. In this way, concentration polarization and cake formation caused by the filtration operation could be limited, depending on the properties of the particles and the magnitude of the reverse pressure. 

Expression Mechanical ejqiression applies pressure directly on filter cakes rather than relying on flow frictions generated by hydraulic pressure drop to deliquor the cake. The effects of stress distribution in a compactible filter cake by these two different mechanisms are shown in Fig. 18-185. The stress distribution of an expression is more uniform than that of a pressure filtration, leading to a more uniform filter cake. Expression is therefore a better choice for deliquoring of compactible filter cakes. 

When DE is used as an admix to produce a less resistant cake, selection of the type and amounts of filter aids depends on laboratory tests with a constant pressure filter cell. A graph illustrating the effect of filter aid addition on the average flow rate is shown in Figure 22.15 (Tiller 1978). Overdose of Alter aid resulted in a decrease of filtrate rate. 

Cake filtration could be used for some of these materials, but a cake of l-/rm particles would have a high resistance to flow, and the filtration rate would be very low. Ultrafiltration (UF) covers a wider size range, from 1-pm particles down to molecules about 10 /rm in size (Af= 300). The term hyperfiltration is sometimes used for separation of small molecules or ions, but reverse osmosis is a more descriptive term, because the osmotic pressure has a major effect on the flux. Furthermore, the separation in reverse osmosis occurs by a solution-diffusion mechanism in the dense polymer rather than by a screening action at the membrane surface (see Chap. 26). 

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