Pressure, Variable-Rate 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. 

Variable-Pressure, Variable-Rate Filtration The pattern of this categoiy comphcates the use of the basic rate equation. The method of Tiller and Crump (loc. cit.) can be used to integrate the equation when the characteristic curve of the feed pump is available. 

We now turn attention towards the ease of eonstant-rate filtration. When sludge is fed to a filter by means of a positive displaeement pump, the rate of filtration is nearly constant, i.e., dV/dx = constant. During constant-rate filtration, pressure increases with cake thickness. As sueh, the principal filtration variables are pressure ind filtrate volume, or pressure and filtration time. Integrating the filtration equation for a constant-rate process, we find that the derivative dV/dx ean simply be replaeed by V/x, and we obtain ... 

Where particularly dirty water is encountered, special filter bags are available that contain variable micron rating media to provide true depth filtration, low initial pressure drop, and longer life. 

Variable-pressure, variable-rate filtration. The use of a centrifugal pump results in this pattern the discharge rate decreases with increasing back pressure. 

Constant-Rate Filtration For substantially incompressible cakes, Eq. (18-54) 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 give the variable pressure through the filter cake [Ruth, Ind. Eng. Chem., 27, 717 (1935)] ... 

Table 2.2 Illustrative table headings for time required to effect a variable rate and variable pressure filtration...

Constant-pressure cake filtration with non-Newtonian suspending fiuids has received considerable attention [Kozicld, 1990]. The average ecific resistance has been found to vary considerably as a fimction of the flow behaviour index N even during the filtration of apparently incompressible materials [Shirato et al, 1977], Later papers extended the analysis to compressible filter cakes and constant rate and variable pressure and rate filtrations [Shirato et al, 1980a, b]. 

The typical sequence of operations in horizontal diaphragm and filter presses is shown schematically in Figure 6.3 (see also Sections 1.4.2.5 and 1.4.2.3). Suspension is fed into the chambers of the press, with either a positive displacement or centrifugal pump to initiate respectively constant rate/variable pressure or variable rate/variable pressure filtration. Cakes are usually formed simultaneously on the two opposing sides of each chamber. In plate... 

If filtration takes place at constant pressure then the equations presented for the tube press in Section 6.2.1.3 are also valid for the multi-element candle filter noting that = n,ndh where n, is the total number of candles in the filter. When filtration takes place at variable pressure then it is necessary to impose the pump curve characteristics to relate Ap and q and a numerical solution to equation (6.17) is generally required. For the special case of variable pressure/constant rate filtration with a positive displacement pump... 

Tiller F.M., 1958. The role of porosity in filtration 3 Variable pressure-variable rate filtration, AIChEJ, 2, 171-174. 

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