Resistance cake filtration

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. 

Conventional filtration theory has been challenged a two-phase theory has been appHed to filtration and used to explain the deviations from paraboHc behavior in the initial stages of the filtration process (10). This new theory incorporates the medium as an integral part of the process and shows that the interaction of the cake particles with the medium controls filterabiHty. It defines a cake-septum permeabiHty which then appears in the slope of the conventional plots instead of the cake resistance. This theory, which merely represents a new way of interpreting test data rather than a new method of siting or scaling filters, is not yet accepted by the engineering community. 

Benefits of Prethickening. The feed soHds concentration has a profound effect on the performance of any cake filtration equipment. It affects the capacity and the cake resistance, as weU as the penetration of the soHds into the cloth which influences filtrate clarity and medium resistance. Thicker feeds lead to improved performance of most filters through higher capacity and lower 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... 

Filtration. In many mineral processing operations, filtration follows thickening and it is used primarily to produce a soHd product that is very low in moisture. Filtration equipment can be either continuous or batch type and either constant pressure (vacuum) or constant rate. In the constant pressure type, filtration rate decreases gradually as the cake builds up, whereas in the constant rate type the pressure is increased gradually to maintain a certain filtration rate as the cake resistance builds. The size of the device is specified by the required filter surface area. 

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 ... 

Parameter x can be expressed in terms of the ratio of the mass of solid particles settled on the filter plate to the filtrate volume, x, and, instead of r , a specific mass cake resistance, r , is used. That is, r, is the resistance to the flow presented by a uniformly distributed cake in the amount of 1 kg/m. Replacing units of volume by mass, the term r x into the above expression changes to r x,j,. Neglecting the filter plate resistance (i.e., R, = 0), then ... 

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 ... 

Constants C and K can be determined from several measurements of filtrate volumes taken at different time intervals. There are some doubts as to the actual constancy of C and K during constant pressure filtration. Constants C and K depend on r (specific volumetric cake resistance), which, in turn, depends on the pressure drop across the cake. This AP causes some changes in the cake, especially during the initial stages of filtration. When the cake is very thin, the main portion of the total pressure drop is exerted on the filter medium. As the cake becomes thicker, the pressure drop through the cake increases rapidly but then levels off to a constant value. Isobaric filtration shows insignificant deviation from the expressions developed. For approximate calculations, it is possible to neglect the resistance of the filter plate, provided the cake is not too thin. Then the filter plate resistance, Rf, is equal to zero, C = 0, and r = 0. Hence, a simplified equation is = Kr. 

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... 

For a cycle consisting of filtration and washing stages, and accounting for the filter plate resistance, the cake resistance corresponding to a maximum filter capacity is given by ... 

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 ... 

The structure of the cake formed and, consequently, its resistance to liquid flow depends on the properties of the solid particles and the liquid phase suspension, as well as on the conditions of filtration. Cake structure is first established by hydrodynamic factors (cake porosity, mean particle size, size distribution, and particle specific surface area and sphericity). It is also strongly influenced by some factors that can conditionally be denoted as physicochemical. These factors are ... 

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. 

If the suspension is fed to the filter with a reciprocating pump at constant capacity, filtration is performed under constant flowrate. In this case, the pressure differential increases due to an increase in the cake resistance. If the suspension is fed by a centrifugal pump, its capacity decreases with an increase in cake resistance, and filtration is performed at variable pressure differentials and flowrates. 

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. 

Filter cake resistance (Rq) is the resistance to filtrate flow per unit area of filtration. R increases with increasing cake thickness during filtration. At any instant, Rc depends on the mass of solids deposited on the filter plate as a result of the passage of V (m ) filtrate. Rf may be assumed a constant. To determine the relationship between volume and residence time t. Equation 5 must be integrated, which means that Rc must be expressed in terms of V. 

The numerator of Equation 79 characterizes the cake resistance. The denominator contains information on the driving force of the operation. Constant K (sec/m ) characterizes tile intensity at which the filtration rate decreases as a function of increasing filtrate volume. 

Determine the filtration constants a and b, where a is the constant characterizing cake resistance related to 1 of filter area in sec/m, and b characterizes the resistance of the filter medium related to 1 m of filter area in sec./m. ... 

Assume laminar flow of filtrate of liquid through the filter cake. Rate of filtration is usually measured as the rate at which liquid filtrate is collected. The filtration rate depends on the area of the filter cloth, the viscosity of the liquid, the pressure drop across the filter and filter cake resistance. At any instant during filtration, the rate of filtration is given by the equation ... 

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. 

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). 

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... 

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