Resistance filter medium

Also from (7.3.1.1), rm is the filter media resistance and a is the average specific cake resistance. If the filter cake is incompressible, a is constant for compressible cake a is defined as ... 

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. 

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... 

Not uncommonly / is found to be only slightly dependent on pressure. When this is true and especially when the filter-medium resistance is, as it should be, relatively small, an average value may be used for all pressures. 

Filtration experiments in a prototype machine at constant pressure or constant rate permit determination of ax , as well as s and Rf, for a given sludge and filtering medium. Consequently, it is possible to predict the time required for the pressure drop to reach the desired level for a specified set of operating conditions. In the initial stages of filtration, the filter medium has no cake. Furthermore, AP is not zero but has a certain value corresponding to the filter medium resistance for a given rate. This initial condition is ... 

In principle, filter bed permeabilities can be calculated using the Carman-Kozeny equation 2.53. For slurries containing irregular particles, however, cake filtrabilities together with filter medium resistance are determined using the Leaf Test (Figure 4.13). In this technique, a sample of suspended slurry is drawn through a sample test filter leaf at a fixed pressure drop and the transient volumetric flowrate of clear filtrate collected determined. 

A rotary drum filter is used to filter a slurry. The drum rotates at a rate of 3 min/cycle, and 40% of the drum surface is submerged in the slurry. A constant pressure drop at 3 psi is maintained across the filter. If the drum is 5 ft in diameter and 10 ft long, calculate the total net filtration rate in gpm that is possible for a slurry having properties as determined by the following lab test. A sample of the slurry was pumped at a constant flow rate of 1 gpm through 0.25 ft2 of the filter medium. After 10 min, the pressure difference across the filter had risen to 2.5 psi. The filter medium resistance may be neglected. 

The cake resistance R K is directly proportional to the cake thickness /, and the filter-medium resistance R F can be assumed to be directly proportional to a fictitious cake thickness l F. Designating C as the proportionality constant,... 

The filter press is to be replaced by a rotary vacuum-drum filter with negligible filter-medium resistance. This rotary filter can deliver the filtrate at a rate of 1000 lb/h when the drum speed is 0.3 r/min. Assuming the fraction submerged and the pressure drop are unchanged, what drum speed in r/min is necessary to make the amount of filtrate delivered in 24 h from the rotary filter exactly equal to the maximum amount of filtrate obtainable per 24 h from the plate-and-frame filter ... 

In cake filtration the liquid passes through two resistances in series that of the cake and that of the filter medium. The filter-medium resistance, which is the only resistance in clarifying filters, is normally important only during the early stages of cake filtration. The cake resistance is zero at the start and increases with time as filtration proceeds. If the cake is washed after it is filtered, both resistances are constant during the washing period and that of the filter medium is usually negligible. 

FILTER-MEDIUM RESISTANCE. A filter-medium resistance R by analogy with the cake resistance amJA. The equation is... 

The filter-medium resistance R includes that of any cake not removed by the discharge mechanism and carried through the next cycle. When the... 

Example 30.3. A rotary drum filter with 30 percent submergence is to be used to filter a concentrated aqueous slurry of CaCOj containing 14.7 lb of solids per cubic foot of water (236 kg/ra ). The pressure drop is to be 20 in. Hg. If the filter cake contains 50 percent moisture (wet basis), calculate the filter area required to filter 10 gal/min of slurry when the filter cycle time is 5 min. Assume that the specific cake resistance is the same as in Example 30.2 and that the filter-medium resistance R is negligible. The temperature is 20°C. 

Again, the simplest method of correcting the overall pressure drop for the pressure drop through the filter medium is to assume the filter medium resistance is constant during a given constant-rate filtration. Then, by Eq. (30.17), Ap is also constant in Eq. (30.38). Since the only variables in Eq. (30.38) are Ap and t, the equation can be written... 

The slurry of Prob. 30.3 is to be filtered in a press having a total area of 8 m and operated at a constant pressure drop of 2 atm. The frames are 36 mm thick. Assume that the filter-medium resistance in the large press is the same as that in the laboratory filter. Calculate the filtration time required and the volume of filtrate obtained in one cycle. 

Unfortunately the use of such a relation other than illustrating first principles is extremely limited in industrial applications because both the specific area of the particles Sq and the porosity 8 are extremely difficult to characterize when dealing with agglomerated solids that are also compressible. A more useful analysis can be made to characterize the filterability of a slurry by the use of the filtration equation as defined by equation (2) below, that shows how the filtration rate is affected by the filter operating parameters (pressure drop AP, filtration area A, filter medium resistance and also slurry related parameters (viscosity p, solids concentration w, specific cake resistance rj ... 

The mutual effects of the operating variables can be seen in Equation 58.1. When the cake is composed of hard granular particles that make it rigid and incompressible, an increase in pressure results in no deformation of the particles or their interstices, i.e., n = 0. If filter medium resistance is neglected. Equation 58.1 becomes... 

In this expression, the differential or instantaneous rate of filtration per unit area dVIAdO) is given as the ratio of a driving force, pressure p, to the product of viscosity p, and the sum of cake resistance a(W/A) and filter medium resistance R. The mass of dry cake W is related to the volume of filtrate V by a simple material balance, thus ... 

When the cake consists of extremely soft, easily deformed particles, such as metal hydroxides, n approaches 1.0. Equation 58.1, with the filter-medium resistance again neglected, reduces to... 

Thus if the liquid viscosity, filter area, filtration pressure and mass of dry cake per unit volume of filtrate, either from Equation (2.17) or (2.18), are known, the graphical values can be used to calculate the cake specific resistance and filter medium resistance. 

Thus, at the start of a crossflow menoibrane filtration the inverse flux rate is proportional to the cumulative fihrate volume, in much the same way as described in Section 2.6.1. The intercept of such a plot can be used to provide an in situ value for the membrane resistance, via Equation (10.15). This resistance is usually much greater than the clean water permeation st value for the same membrane. This is due to the effect of the interaction of the initial layers of deposit within the membrane structure. These layers add substantially to the effective membrane resistance, ie. additional resistances due to adsorption and blocldng, see Section 10.4. This situation is again very similar to that for conventional filtration, where the filter medium resistance increases at the start of the filtration. If the membrane was a true surface filter this would not happen, but almost all membrane filters do permit some initial penetration of particulates. 

Accordingly, the filtration rate is directly proportional to the pressure drop across the cake and the filtration area, and inversely proportional to the filtrate viscosity and the sum of cake and filter medium resistance. 

The filter medium resistance was determined by measuring the time of filtering 350 ml isopropanol at room temperature. The viscosity was monitored by Ubbelohde Viscometer. 

---