Cake filtration dynamics

Scott Wells. .. processes. Research includes modeling the dynamics of cake filtration and the dynamics of liquid/particle flow in water and wastewater... 

Preprint 2000-041. .. which together with initial and boundary conditions determines a dynamic cake filtration... 

Mechanical Cake Removal. This method is used in the American version of the dynamic filter described under cross-flow filtration with rotating elements, where turbine-type rotors are used to limit the cake thickness at low speeds. The Exxflow filter, introduced in the United Kingdom, is described in more detail under cross-flow filtration in porous pipes. It uses, among other means, a roUer cleaning system which periodically roUs over a curtain of flexible pipes and dislodges any cake on the inside of the pipes. The cake is then flushed out of the curtain by the internal flow. 

Vacuum filters are usually simulated with a Buchner funnel test or filter leaf test (54). The measured parameters are cake weight, cake moisture, and filtration rate. Retention aids are usually evaluated using the Britt jar test, also called the Dynamic Drainage Jar, which simulates the shear conditions found on the paper machine and predicts performance (55). 

To understand the dynamics of the filtration process, a conceptual analysis is applied in two parts. The first half considers the mechanism of flow within the cake, while the second examines the external conditions imposed on the cake and pumping system, which brings the results of the analysis of internal flow in accordance with the externally imposed conditions throughout. 

The dynamics of variable-rate and -pressure filtrations can be illustrated by pressure profiles that exist across the filter medium. Figure 7 shows the graphical representation of those profiles. According to this plot, the compressed force in the cake section is ... 

The invasion of particles can be eliminated either by using solids-free systems or by formation of a competent filter cake on the rock surface. If the components forming the filter cake are correctly chosen and blended, they will form a very effective downhole filter element. This ensures that colloidal sized clays or polymeric materials are retained within the filter cake and do not enter the formation. Further protection is provided by ensuring that a thin filter cake is formed due to low dynamic and static filtrate losses. Thus, the cake may be easily removed when the well is brought into production. Additionally, the filter cake can be soluble in acid or oil. 

Therefore, when operating in the filter cake mode, the axial velocity should be maintained at a level such that an adequate shear force exists along the filter media to prevent excessive caking of the catalyst that could cause a blockage in the down-comer circuit. For the separation of ultrafine catalyst particles from FT catalyst/wax slurry, the filter medium can easily become plugged using the dynamic membrane mode filtration. Also, small iron carbide particles (less than 3 nm) near the filter wall are easily taken into the pores of the medium due to their low mass and high surface area. Therefore, pure inertial filtration near the filter media surface is practically ineffective. 

Figure 37 shows a schematic of the dynamic filtration of a drilling fluid. The drilling fluid is filtered across the filter medium at the pressure difference APfd while being subjected to flow (assumed laminar in the following discussion), which gives rise to a shear stress rc at the cake-fluid interface where the shear rate is yc. 

At longer times, the cumulative filtrate volume Vflinear dependence on time, indicating that the filter cake has reached a constant thickness. The limiting (constant) dynamic filtration rate is a marked function of 7C and rc. The limiting dynamic filtration rate Qm (= dVfa/ Adt as t - oo) has been scaled by 7C and rc by (135)... 

Figure 42. Dependence of (a) limiting dynamic filtration rate (Q/d) and (b) inverse of filter cake thickness (l/hc) on shear rate of drilling fluid. (Muds 2 and 3 from reference 139 with Fordham and Ladva s data from reference 135.) Lines show least squares fit to data from muds 2 and 3.

The dynamic filtration theory of Outmans (127) requires experimental terms such as particle-particle stresses, particle friction factors, and thickness of a shear zone within the filter cake that would be difficult to determine. However, the qualitative picture of dynamic filtration presented by Outmans, namely, irreversible adhesion of solid particles up to a certain thickness that is determined by the shear stress (or shear rate) at the surface of the cake, accords with the experiments of Fordham and co-workers (129,135). Once a filter cake has formed under dynamic conditions, it is difficult to remove it by subsequent changes in yc or vm. Figure 44 shows the effect of changes in the flow rate on cumulative filtrate volume. The limiting filtration rate obtained when the initial flow rate of the drilling fluid was 1.8 m3/h remained unaltered when the flow rate of the drilling fluid was increased to 7.0 m3/h in a step-... 

A serious limitation in the data collected by these researchers was the ct that a was measured in permeation rather than in filtration conditions the packing (porosity) and the resistance of newly formed filter cake under the dynamic ccmditions obtaining during filtration may be e ected (in general) to be different fi om those applying after prolonged rotation The latter results in the densest packing and hipest a values. 

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