Filtration cake

When the space above the suspension is subjected to a source of compressed gas (e.g., air) or the space under the filter plate is connected to a vacuum source, filtration is accomplished under a constant pressure differential (the pressure in the receivers is constant). In this case, the rate of the process decreases due to an increase in the cake thickness and, consequently, flow resistance. A similar filtration process results from a pressure difference due to the hydrostatic pressure of a suspension layer of constant thickness located over 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 most favorable filtration operation with cake formation is a process whereby no clogging of the filter medium occurs. Such a process is observed at sufficiently high concentrations of solid particles in suspension. From a practical standpoint this concentration may conditionally be assumed to be in excess of 1 % by volume. 

To prevent pore clogging in the filter medium when handling relatively low solids concentrations (e.g., 0.1-1% by volume), general practice is to increase the solids concentration in thickeners before the suspension is fed to the filter. 

Filtration is frequently accompanied by hindered or free gravitational settling of solid particles. The relative directions of action between gravity force and filtrate motion 

Examples of depth filtration are sand and cartridge filtration. Solids are trapped in the interstices of the medium. As solids accumulate, flow approaches zero and the pressure drop across the bed increases. The bed must then be regenerated or the cartridge changed. For this reason, this method is not viable for high solids concentration streams as it becomes cost prohibitive. Cartridge filtration is often used as a secondary filtration in conjunction with a primary, such as the more widely used cake filtration. 

Rates of filtration are dependent upon the driving force of the piece of equipment chosen and the resistance of the cake that is continually forming. Liquid flowing through a cake passes through channels formed by particles of irregular shapes. 

The mathematical descrption of the process starts with the neglect of septum resistance and the use of Darcy s law (Equation 2.3) to relate filtrate flow rate and pressure drop  

Thus Equation (2.7) contains one less variable than Equation (2.3) but one more constant (P). 

Clearly, the volume ratio of cake to filtrate still needs to be calculated befine Equation (2.7) can be evaluated. This is achieved by means of a mass balance on the soUd and liquid entering the filter system. 

Use of Equation (2.8) assumes knowiedge of two constants (exduding densities) shiny concentration by mass fiuction and filter cake concentration by volume firaction. The 

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Filtration. In filtration, suspended solid particles in a liquid or gas are removed by passing the mixture through a porous medium that retains the particles and passes the fluid. The solid can be retained on the surface of the filter medium, which is cake, filtration, or captured within the filter medium, which is depth filtration. The filter medium can be arranged in many ways. 

Fig. 2. Schematic diagram of a surface filter, ie, the cake filtration mechanism.

Deep Bed Filters. Deep bed filtration is fundamentally different from cake filtration both in principle and appHcation. The filter medium (Fig. 4) is a deep bed with pore size much greater than the particles it is meant to remove. No cake should form on the face of the medium. Particles penetrate into the medium where they separate due to gravity settling, diffusion, and inertial forces attachment to the medium is due to molecular and electrostatic forces. Sand is the most common medium and multimedia filters also use garnet and anthracite. The filtration process is cycHc, ie, when the bed is full of sohds and the pressure drop across the bed is excessive, the flow is intermpted and solids are backwashed from the bed, sometimes aided by air scouring or wash jets. 

The trend in the use of deep bed filters in water treatment is to eliminate conventional flocculators and sedimentation tanks, and to employ the filter as a flocculation reactor for direct filtration of low turbidity waters. The constraints of batch operation can be removed by using one of the available continuous filters which provide continuous backwashing of a portion of the medium. Such systems include moving bed filters, radial flow filters, or traveling backwash filters. Further development of continuous deep bed filters is likely. Besides clarification of Hquids, which is the most frequent use, deep bed filters can also be used to concentrate soflds into a much smaller volume of backwash, or even to wash the soflds by using a different Hquid for the backwash. Deep bed filtration has a much more limited use in the chemical industry than cake filtration (see Water, Industrial water treatment Water, Municipal WATERTREATiffiNT Water Water, pollution and Water, reuse). 

Addition of Inert Filter Aids. FUtet aids ate rigid, porous, and highly permeable powders added to feed suspensions to extend the appheabUity of surface filtration. Very dilute or very fine and slimy suspensions ate too difficult to filter by cake filtration due to fast pressure build-up and medium blinding addition of filter aids can alleviate such problems. Filter aids can be used in either or both of two modes of operation, ie, to form a precoat which then acts as a filter medium on a coarse support material called a septum, or to be mixed with the feed suspension as body feed to increase the permeabihty of the resulting cake. 

Electrophoresis and electro osmosis can be used to enhance conventional cake filtration. Electrodes of suitable polarity are placed on either side of the filter medium so that the incoming particles move toward the upstream electrode, away from the medium. As most particles carry negative charge, the electrode upstream of the medium is usuaHy positive. The electric field can cause the suspended particles to form a more open cake or, in the extreme, to prevent cake formation altogether by keeping aH particles away from the medium. 

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. 

This equation is the basis of cake filtration analysis. Feed Hquid flow rate and filtrate volume Dare usually assumed to be related as... 

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 difficulties with approximations used in theoretical derivations and with the experimental techniques have been pointed out (8), and a series of tutorials have been pubHshed in which the deviations from paraboHc behavior are explained and the correct interpretations of cake filtration data, with many numerical examples, are laid down (8,9). 

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. 

Thickening Pressure Filters. The most important disadvantage of conventional cake filtration is the declining rate due to the increased pressure drop caused by the growth of the cake on the filter medium. A high flow rate of Hquid through the medium can be maintained if Httle or no cake is allowed to form on the medium. This leads to thickening of the slurry on the upstream part of the medium filters based on this principle are sometimes called filter thickeners. 

Most authors who have studied the consohdation process of soflds in compression use the basic model of a porous medium having point contacts which yield a general equation of the mass-and-momentum balances. This must be supplemented by a model describing filtration and deformation properties. Probably the best model to date (ca 1996) uses two parameters to define characteristic behavior of suspensions (9). This model can be potentially appHed to sedimentation, thickening, cake filtration, and expression. 

By filtration mechanism. Although the mechanism for separation and accumulation of solids is not clearly understood, hvo models are generally considered and are the basis for the apphcation of theoiy to the filh ation process. When solids are stopped at the surface of a filter medium and pile upon one another to form a cake of increasing thickness, the separation is called cake filtration. When solids are trapped within tne pores or body of the medium, it is termed depth, filter-medium, or clarifying filtration. 

By objective. The process goal of filtration may be diy solids (the cake is the product or value), clarified liquid (the filtrate is the product of value), or both. Good sohds recovery is best obtained by cake filtration, while clarification of the liquid is accomplished by either depth or cake filtration. 

The correlations used are based partly on theoretical consideration and partly on empirical observations. The basic filtration data are correlated by application of the classic cake-filtration equation, aided by various simplifying assumptions which are sufficiently valid for many (but not all) situations. Washing and drying correlations are of a more empirical nature but with strong experimental justification. If steam or thermal diying is being examined, additional correlations are required beyond those summarized below for such applications, it is advisable to consult an eqmpment manufacturer or refer to pubhshed technical papers for guidance. 

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 ... 

Implicit in cake filtration is the removal and handling of solids, since the cake is usually relatively dry and compacted. C es can be sticky and difficult to handle therefore, the ability of a filter to discharge the cake cleanly is an important equipment-selection criterion. 

In practice, cake filtration is used more often than filter-medium filtration. Upon achieving a certain thickness, the cake must be removed from the medium. This can be accomplished by the use of various mechanical devices or by reversing the flow of filtrate back through the medium (hence, the name baclflushing). 

Nonwoven filter media are mostly used for filter medium filtration with pore clogging. Because of the relatively low cost of this medium, it is often replaced after pore clogging. In some cases, nonwoven media are used for cake filtration. In this case, cake removal is so difficult that it must be removed altogether from the filter medium. Nonwoven filter media can be prepared so that pore sizes decrease in the direction from the surface of the filter media contacting suspension to the surface contacting the supporting device. This decreases the hydraulic resistance of... 

This chapter provides a summary of the governing expressions describing conventional pressure-induced filtration and a description of major equipment. Standard filtration practices refers to the most common or classical method of filtration, sometimes referred to as cake filtration. 

Finally, for the case of intermediate filtration, the intensity of increase in total resistance with increasing filtrate volume is less than that occurring in the case of gradual pore blocking, but greater than that occurring with cake filtration. It may be assumed that the intensity of increase in total resistance is directly proportional to this resistance ... 

The expression states that the intensity of increase in total resistance for cake filtration is constant with increasing filtrate volume. Replacing W by dq/dx in Equation 78 and integrating over the limits of 0 to q between 0 and x we obtain ... 

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