Pressure-Drop Filtration

How many square feet of filter surface (21.1°C) are needed to yield 200.5 ft of filtrate in 1 hr Additional data Slurry is 3.0 lb of solid/ft filtrate, pressure drop is 5.44 atm, filter medium resistance is 1.5 X 10 fr , and fluid viscosity is same as water. 

Fiber Bed Alist Filtration. In-depth fiber bed filters are used for the collection of Hquid droplets, fogs, and mists. Horizontal pads of knitted metal wire (or plastic fibers), 100—150 mm thick, and gas updow are used for Hquid entrainment removal. Pressure drop is 250—500 Pa (1.9—3.8 mm Hg). 

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. 

There is an additional pressure drop across the cake, developed by electroosmosis, which leads to increased flow rates through the cake and further dewatering at the end of the filtration cycle. The filtration theory proposed for electrofiltration assumes the simple superposition of electroosmotic pressure on the hydraulic pressure drop. 

It does not matter, from the fundamental point of view, how the pressure drop is generated in the filter. In the case of the centrifugal filters there is an additional phenomenon of the mass forces acting on the Hquid within the cake. The conventional filtration theory must be amended to include this effect (2). 

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. 

Pressure Filtration. High pressure drops have a twofold effect, ie, on capacity and on displacement dewatering which often follows. 

The most important feature of the pressure filters which use hydrauHc pressure to drive the process is that they can generate a pressure drop across the medium of more than 1 x 10 Pa which is the theoretical limit of vacuum filters. While the use of a high pressure drop is often advantageous, lea ding to higher outputs, drier cakes, or greater clarity of the overflow, this is not necessarily the case. Eor compressible cakes, an increase in pressure drop leads to a decrease in permeabiUty of the cake and hence to a lower filtration rate relative to a given pressure drop. 

The fundamental case for pressure filters may be made using equation 10 for dry cake production capacity Y (kg/m s) derived from Darcy s law when the filter medium resistance is neglected. Eor the same cycle time (same speed), if the pressure drop is increased by a factor of four, production capacity is doubled. In other words, filtration area can be halved for the same capacity but only if is constant. If increases with pressure drop, and depending how fast it increases, the increased pressure drop may not give much more capacity and may actually cause capacity reductions. 

In vacuum filters, the driving force for filtration results from the appHcation of a suction on the filtrate side of the medium. Although the theoretical pressure drop available for vacuum filtration is 100 kPa, in practice it is often limited to 70 or 80 kPa. 

Pressure Vessel Filters. The several designs of pressure vessel filters all consist of pressure vessels housing a multitude of leaves or other elements which form the filtration surface and which are mounted either horizontally or vertically. With horizontal leaves most suitable where thorough washing is required, there is no danger of the cake falling off the cloth with vertical elements, a pressure drop must be maintained across the element to... 

The advantage of candle filters is that as the cake grows on the tubular elements the filtration area increases and the thickness of a given volume of cake is therefore less than it would be on a flat element. This is of importance where a thick cake is being formed the rate of increase in the pressure drop is less with tubular elements. 

The test results reported show the advantages of pressure filtration quite clearly, ie, the dry cake production capacity obtained with the test soHds (coal suspensions) was raised 60 or 70% and the final moisture content of the cake reduced by as much as 5 to 7% by increasing the pressure drop from 60 to 200 kPa. Further increases in the operating pressure bring about less and less return in terms of capacity and moisture content. 

The so-called hyperbar vacuum filtration is a combination of vacuum and pressure filtration in a pull—push arrangement, whereby a vacuum pump of a fan generates vacuum downstream of the filter medium, while a compressor maintains higher-than-atmospheric pressure upstream. If, for example, the vacuum produced is 80 kPa, ie, absolute pressure of 20 kPa, and the absolute pressure before the filter is 150 kPa, the total pressure drop of 130 kPa is created across the filter medium. This is a new idea in principle but in practice requires three primary movers a Hquid pump to pump in the suspension, a vacuum pump to produce the vacuum, and a compressor to supply the compressed air. The cost of having to provide, install, and maintain one additional primary mover has deterred the development of hyperbar vacuum filtration only Andrit2 in Austria offers a system commercially. 

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. 

Gas Pressure Drops The filtration, or superficial face, velocities used in fabric filters are generally in the range of 0.3 to 3 iTi/min (1 to 10 ft/min), depending on the types of fabric, fabric supports, and... 

Equation (17-10) indicates that for filtration at a given velocity the pressure drop is a linear function of the fabric dust loading w. In some cases, particularly with smooth-surfaced fabrics, this is at least approx-... 

Dry filters are usually deeper than viscous filters. The dry filter media use finer fibers and have much smaller pores than the viscous media and need not rely on an oil coating to retain collected dust. Because of their greater resistance to air flow, dry filters must use lower filtration velocities to avoid excessive pressure drops. Hence, dry media must have larger surface areas and are usually pleated or arranged in the form of pockets (Fig. 17-64), generally sheets of cellulose pulp, cotton, felt, or spun glass. 

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 ... 

Feed Slurry Temperature Temperature can be both an aid and a limitation. As temperature of the feed slurry is increased, the viscosity of the hquid phase is decreased, causing an increase in filtration rate and a decrease in cake moisture content. The limit to the benefits of increased temperature occurs when the vapor pressure of the hquid phase starts to materially reduce the allowable vacuum. If the hquid phase is permitted to flash within the filter internals, various undesired resiilts may ensue disruption in cake formation adjacent to the medium, scale deposit on the filter internals, a sharp rise in pressure drop within the filter drainage passages due to increased vapor flow, or decreased vacuum pump capacity. In most cases, the vacuum system should be designed so that the liquid phase does not boil. 

Constant-Rate Filtration For substantially incompressible cakes, Eq. (18-51) may be integrated for a constant rate of slurry feed to the filter to give the following equations, in which filter-medium resistance is treated as the equivalent constant-pressure component to be deducted from the rising total pressure drop to... 

For incompressible cake, the pressure distribution and the rate depend on the resistance of the filter medium and the permeability of the cake. Figure L8-150 shows several possible pressure profiles in the cake with increasing filtration rates through the cake. It is assumed that r /i i = 0.8 and /p//i = 0.6. The pressure at / = ri, corresponds to pressure drop across the filter medium Ap, with the ambient pressure taken to be zero. The filtration rate as well as the pressure distribution depend on the medium resistance and that of the cake. High medium resistance or blinding of the medium results in greater penalty on filtration rate. 

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