## Water And Wastewater Treatment Technologies Constant Rate Filtration

Filtration with gradual pore blocking is most frequently encountered in industrial practice. This process is typically studied under the operating mode of constant rate. We shall assume a unit area of medium which has Np pores, whose average radius and length are rp and 5p, respectively. The pore walls have a uniform layer of particles that build up with time and decrease the pore passage flow area. Filtration must be performed in this case with an increasing pressure difference to compensate for the rise in flow resistance due to pore blockage. If the pores are blocked by a compressible cake, a gradual decrease in porosity occurs, accompanied by an increase in the specific resistance of the deposited particles and a decrease in the ratio of cake-to-filtrate volumes. The influence of particle compressibility on the controlling mechanism may be neglected. The reason for this is that the liquid phase primarily flows through the available flow area in the pores, bypassing deposited solids. Thus, the ratio of cake volume to filtrate volume (x0) is not sensitive to the pressure difference even for highly compressible cakes. From the Hagen-Poiseuille relation (Equation 39) replacing Win in Equation 40 with constant filtration rate W and substituting APin for constant pressure drop AP we obtain:

The mass of particles deposited on the pore walls will be xGdq, and the thickness of this particle layer in each pore is dr. Hence

where

x0dq = -Np2itrtpdz

Integration over the limits of 0, q from rp to r yields

Radii rp and r are defined by Equations 83 and 85, respectively, from which we obtain the following expressions:

where

It is important to note that pore blocking occurs when suspensions have the

Both particle size and the liquid viscosity affect the rate of particle settling. The rate of settling due to gravitational force decreases with decreasing particle size and increasing viscosity. The process mechanisms are sensitive to the relative rates of

Examination of the manner in which particles accumulate onto a horizontal filter medium assists in understanding the influences that the particle settling velocity and particle concentration have on the controlling mechanisms. "Dead zones" exist on the filter medium surface between adjacent pores. In these zones, particle settling onto the medium surface prevails. After sufficient particle accumulation, solids begin to move under the influence of fluid jets in the direction of pore entrances. This leads to favorable conditions for bridging. The conditions for bridge formation become more favorable as the ratio of particle settling to filtration rate increases. An increase in the suspension's particle concentration also enhances accumulation in "dead zones" with subsequent bridging. Hence, both high particle settling velocity increases and higher solids concentrations create favorable conditions for cake filtration. In contrast, low settling velocity and concentration results in

The transition from pore-blocked filtration to more favorable cake filtration can therefore be achieved with a suspension of low settling particles by initially feeding it to the filter medium at a low rate for a time period sufficient to allow surface accumulation. This is essentially the practice that is performed with filter aids.

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