Darcy filter cake resistance

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. 

Results from constant differential pressure filtration tests have been analyzed according to traditional filtration science techniques with some modifications to account for the cross-flow filter arrangement.11 Resistivity of the filter medium may vary over time due to the infiltration of the ultrafine catalyst particles within the media matrix. Flow resistance through the filter cake can be measured and correlated to changes in the activation procedure and to the chemical and physical properties of the catalyst particles. The clean medium permeability must be determined before the slurries are filtered. The general filtration equation or the Darcy equation for the clean medium is defined as... 

The fundamental case for pressure filters may be made using the following equation for dry cake production capacity, T(kgm s ), derived from Darcy s law when the filter medium resistance is neglected (for the full derivation see appendix I in Svarovsky ) ... 

A test method called the modified fouling index (MFI or MFI-0.45) is gaining popularity and has been used in Europe for 25 years. The test was developed based on Darcy s Taw that relates flux (dV/dt) to the thickness of the cake layer, which is the sum of the filter resistance (R ) and the cake resistance (R) ... 

The development of the MFI is consistent with Darcy s law in that the thickness of the cake layer formed on the membrane surface is assumed to be directly proportional to the filtrate volume. The total resistance is the sum of the filter and cake resistance. 

A schematic of the flow through the cake and filter medium is shown in Fig. 13-6. The slurry flow rate is Q, and the total volume of filtrate that passes through the filter is V. The flow through the cake and filter medium is inevitably laminar, so the resistance can be described by Darcy s law and the permeability of the medium (K) ... 

The first advantage of any continuous filter is the absence of or reduction in down-times which means gains in capacity. Bearing in mind the effects of compressibility of cakes discussed in section 12.2.1.1, the effect of higher driving force on capacity can be seen in equation 12.1 which is derived for constant-pressure filtration from the well-known law of Darcy. The effect of resistance of the filter medium is neglected here and the cake is assumed to be incompressible. 

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