Filtration specific cake resistance

The scale-up of conventional cake filtration uses the basic filtration equation (eq. 4). Solutions of this equation exist for any kind of operation, eg, constant pressure, constant rate, variable pressure—variable rate operations (2). The problems encountered with scale-up in cake filtration are in estabHshing the effective values of the medium resistance and the specific cake resistance. 

The benefits of prethickening can be summarized as an increase in dry cake production, reduction in specific cake resistance, clearer filtrate, and less cloth blinding. 

If ah of the nonfiltration operations are grouped together into a downtime, assumed to be fixed and known, an optimum filtration time in relation to p can be derived by optimizing the average dry cake production obtained from the cycle. Eor constant pressure filtration and where the medium resistance R and the specific cake resistance are constant, the fohowing equation appHes ... 

When the medium resistance R is smah compared with the specific cake resistance (, the second term in the above equation becomes negligible and the optimum filtration time becomes equal to downtime p. For any other case, p is always greater than p. It fohows, therefore, that the filtration time... 

It is both convenient and reasonable in continuous filtration, except for precoat filters, to assume that the resistance of the filter cloth plus filtrate drainage is neghgible compared to the resistance of the filter cake and to assume that both pressure drop and specific cake resistance remain constant throughout the filter cycle. Equation (18-51), integrated under these conditions, may then be manipulated to give the following relationships ... 

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 ... 

This expression can be represented graphically in dimensionless form to simplify its use. It is generally expressed as the so-called filtration number , defined as follows E, = /iR, / 2APT3 jr x . The filtration number, E, is dimensionless and varies from zero at Rf = 0 to a large value when there is an increase in the viscosity of the sludge and Rf or a decrease in pressure drop, auxiliary time, specific cake resistance and the ratio of cake volume to filtrate volume. It may be assumed in practice that F(, = 0 to 10. If washing and drying times are constant and independent of filtration time, they may be added directly to the auxiliary time. In... 

To apply these equations, let s consider the following example. Determine a constant rate of filtration and the time of operation corresponding to the maximum capacity of a batch filter having the following conditions maximum permissible pressure difference AP = 9x10 N/m sludge viscosity /r = 10 N-s/m filter plate resistance Rf = 56x 10 ° m specific cake resistance r = 3 X 10 m ° x = 0.333 auxiliary time = 600 s maximum permissible cake thickness h = 0.025 m. The solution is as follows ... 

A further recommendation, depending on the application, is not to increase the pressure difference for the purpose of increasing the filtration rate. The cake may, for example, be highly compressible thus, increased pressure would result in significant increases in the specific cake resistance. We may generalize the selection process to the extent of applying three rules to all filtration problems ... 

Comparative calculations of specific capacities of different filters or their specific filter areas should be made as part of the evaluation. Such calculations may be performed on the basis of experimental data obtained without using basic filtration equations. In designing a new filtration unit after equipment selection, calculations should be made to determine the specific capacity or specific filtration area. Basic filtration equations may be used for this purpose, with preliminary experimental constants evaluated. These constants contain information on the specific cake resistance and the resistance of the filter medium. 

Both permeability, K, and specific cake resistance, a, depend on the particle shape and size distribution. However, this relationship has not been recognized conclusively. Therefore, information on the crystal shape and size distribution, which can be obtained from experiments on crystallization, cannot be easily translated into the language of filtration characteristics. 

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. 

In conclusion, the following experiments on filtration-washing-deliquoring should be performed to produce data (viscosity of liquids, effective solid concentration, specific cake resistance, cake compressibility, etc.) that are necessary to evaluate times of individual steps of filtration at an industrial scale, i.e. to obtain the proper basis for scale-up of filtration processes measure the filtrate volume versus time make marks on your vacuum flask and take down the time when the filtrate level reaches the mark => no more experiments are needed for preliminary evaluations of filtration properties of slurries initially fines pass the filter medium => recirculate them to the slurry,... 

The overriding factor will be the filtration characteristics of the slurry whether it is fast filtering (low specific cake resistance) or slow filtering (high specific cake resistance). The filtration characteristics can be determined by laboratory or pilot plant tests. A guide to filter selection by the slurry characteristics is given in Table 10.3 which is based on a similar selection chart given by Porter et al. (1971). 

Figure 14.4 Specific cake resistance of several microorganisms measured by dead-end filtration.

Calculate the volume of filtrate versus time relationship, when the specific cake resistance of baker s yeast a and the resistance of the filtering medium are 7 X lO m kg and 3.5 X 10 ° m", respectively. How long does it take... 

In dead-end filtration, a cake forms on the surface of the pad as the filtration proceeds. The cake permeability is the most important physical property of a porous medium and the hydraulic properties of the flow and the specific cake resistance are described by Darcy s Law ... 

Filtration tests with a given sluny have indicated that the specific cake resistance a is 157 h2/lb. The fluid viscosity is 2.5 lb/(hXft), and 3 lb of dry cake is formed per cubic foot of filtrate. The cake may be assumed to be noncompressible, and the resistance of the filter medium may be neglected. If the unit is operated at a constant pressure drop of 5 psi, what is the total filtering area required to deliver 30 ft3 of filtrate in j h ... 

The specific cake resistance and the specific air-suction cake resistance can be assumed to be independent of pressure drop, drum speed, temperature, fraction of drum submerged, fraction of drum available for suction, and slurry concentration. However, to eliminate possible errors due to this assumption, a lab test should be run at conditions approximating the planned design. The results of these tests can be used as a basis for the design (i.e., cake and filtrate compositions and densities can be assumed to be the same for the design as those found in the lab). 

Specific cake resistance—A measure for the resistance of a cake to filtration. 

Measured pressure build up versus accumulated amount of fly ash is shown in Fig. 5 a). Calculated fly ash accumulation is based on averaged dust load measured gravimetiically during die respective filtration cycle. Observed pressure loss is close to ideal behavior for surface filtration (i.e. inconqiressible cake formation and constant dust concentration). Calculated specific cake resistance is shown in Fig. 5 b). 

Fig. 6 shows the variation in and residual pressure drop during six hours of operation. K is calculated from Eq. 4. Calculated mean specific cake resistance equals 6.5-10 [s ], with a standard deviation of approx. 15%. is defined as the velocity across the exposed filter surface (vy 2 U,). Observed fluctuations in pressure build-up did not result in any increase in the residual pressure drop. The residual pressure drop could be maintained at a constant level. The average filtration efficiency was 0.9983. Filter regeneration was conducted with off-line pulsing (P,a = 2barg and total sand spill of 10 kg). 

It is evident that attention paid in the laboratory to the factors affecting particle size distribution will save on capital investments made for separation equipment and downstream process equipment. Specific cake resistance (a) can be determined in the laboratory over the life of a batch, to evaluate if time in the vessel and surrounding piping system is degrading the product s particle size to the point it impedes filtration, washing and subsequent drying. 

As the cake thickness of a product varies, filtration rates and capacity will also change. Equation 4 shows that rates increase as the cake (W/A)mass decreases thus, thin cakes yield higher filtration rates. This is particularly the case with amorphous materials or materials with high specific cake resistance. As a increases, maximizing dV/dO requires W/A to decrease. 

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