Cake filterability, specific

Slurry characteristics determine whether a clarifying or a cake filter is appropriate and if the latter, they determine the rate of formation anci nature of the cake. They affect the choice of driving force and cycle as well as specific design of machine. 

In the brewing process diatomite is used as precoat and body aid on candle filters and horizontal leaf filters. Hermia Brocheton [1993] give a conparison of these methods and cite typical precoat dosage as 1.5 kg/rn and body feed dosage as 1 kg/rn with a cake average specific resistance of lO m/kg. Other aspects of diatomite filtration are discussed comprehensively in a historical review by Cummins [1973]. 

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 specific cake resistance is the most troublesome parameter ideally constant, its value is needed to calculate the resistance to flow when the amount of cake deposited on the filter is known. In practice, it depends on the approach velocity of the suspension, the degree of flow consoHdation that the cake undergoes with time, the feed soHds concentration, and, most importantly, the appHed pressure drop Ap. This changes due to the compressibiHty of most cakes in practice. often decreases with the velocity and the feed concentration. It may sometimes go through a maximum when it is plotted against soHds concentration. The strongest effect on is due to pressure, conventionally expressed as ... 

An additional benefit of prethickening is reduction in cake resistance. If the feed concentration is low, there is a general tendency of particles to pack together more tightly, thus leading to higher specific resistances. If, however, many particles approach the filter medium at the same time, they may bridge over the pores this reduces penetration into the cloth or the cake underneath and more permeable cakes are thus formed. 

An example of the concentration effect on the specific cake resistance is available (12) that reports results of some experiments with a laboratory horizontal vacuum belt filter. In spite of operational difficulties in keeping conditions constant, the effect of feed concentration on specific cake resistance is so strong that it swamps all other effects. 

Enclosed agitated filters are useful when volatile solvents are in use or when the solvent gives off toxic vapor or fume. Another significant advantage is that their operation does not require any manual labor. Control can be manual or automatic, usually by timers or by specific measurements of the product. Most filters are made of mild steel, with the exposed surfaces protected by lead, tile, mbber lining, or by coating or spraying with other substances as necessary. Filtration areas up to 10 m are available and the maximum cake thickness is 1 m. Apphcations are mainly in the chemical industry for the recovery of solvents. 

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 ... 

All filters require a filter medium to retain solids, whether the filter is for cake filtration or for filter-medium or depth filtration. Specification of a medium is based on retention of some minimum parficle size at good removal efficiency and on acceptable hfe of the medium in the environment of the filter. The selection of the type of filter medium is often the most important decision in success of the operation. For cake filtration, medium selection involves an optimization of the following factors ... 

Filter aids should have low bulk density to minimize settling and aid good distribution on a filter-medium surface that may not be horizontal. They should also be porous and capable of forming a porous cake to minimize flow resistance, and they must be chemically inert to the filtrate. These characteristics are all found in the two most popular commercial filter aids diatomaceous silica (also called diatomite, or diatomaceous earth), which is an almost pure silica prepared from deposits of diatom skeletons and expanded perhte, particles of puffed lava that are principally aluminum alkali siheate. Cellulosic fibers (ground wood pulp) are sometimes used when siliceous materials cannot be used but are much more compressible. The use of other less effective aids (e.g., carbon and gypsum) may be justified in special cases. Sometimes a combination or carbon and diatomaceous silica permits adsorption in addition to filter-aid performance. Various other materials, such as salt, fine sand, starch, and precipitated calcium carbonate, are employed in specific industries where they represent either waste material or inexpensive alternatives to conventional filter aids. 

It is known that the specific resistance for centrifuge cake, especially for compressible cake, is greater than that of the pressure or vacuum filter. Therefore, the specific resistance has to be measured from centrifuge tests for different cake thicknesses so as to scale up accurately for centrifuge performance. It cannot be extrapolated from pressure and vacuum filtration data. For cake thickness that is much smaller compared to the basket radius, Eq. (18-116 7) can be approximated by... 

Specific cake resistance (porosity) Viscosity Homogeneity of cake as deposited on the filter medium... 

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. 

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 ... 

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. 

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