Cake formation filtration phase

Process design calculations for filtration are based on the general filtration equation which is usually stated as 

The cake thickness (L ) is related to the cumulative volume of filtrate and the cake properties through a mass balance  

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As previously described, the cycle for a continuous filter typically comprises a cake formation phase followed by a combination of sequential displacement washing and gas deliquoring phases, potentially in any order. If a cycle is assumed to comprise the sequence filtration-washing-deliquoring and the subscripts /, d and w, respectively denote values for these phases, then the total time (tj) devoted to a cycle is given by... 

The concept of the specific resistance used in equation 4 is based on the assumptions that flow is one-dimensional, growth of cake is unrestricted, only soHd and Hquid phases are present, the feed is sufficiently dilute such that the soHds are freely suspended, the filtrate is free of soHds, pressure losses in feed and filtrate piping are negligible, and flow is laminar. Laminar flow is a vaHd assumption in most cake formation operations of practical interest. 

Feed Slurry Temperature Temperature can be both an aid and a limitation. As temperature of the feed slurry is increased, the viscosity of the hquid phase is decreased, causing an increase in filtration rate and a decrease in cake moisture content. The limit to the benefits of increased temperature occurs when the vapor pressure of the hquid phase starts to materially reduce the allowable vacuum. If the hquid phase is permitted to flash within the filter internals, various undesired resiilts may ensue disruption in cake formation adjacent to the medium, scale deposit on the filter internals, a sharp rise in pressure drop within the filter drainage passages due to increased vapor flow, or decreased vacuum pump capacity. In most cases, the vacuum system should be designed so that the liquid phase does not boil. 

The theoretical description of the cake formation in the constant pressure filtration is based on Darcy s Permeation Law, which describes the single-phase laminar flow of an incompressible fluid through a porous incompressible system due to an applied pressure difference. It can be written as follows (2, 3) ... 

In filtration unit operation, especially in microfiltration, one usually differentiates between dead-end filtration (with cake formation) and cross-flow filtration [25] (Fig. 5). The cross-flow filter can have different geometries (Fig. 6) phase membranes, tubular membranes, or pleated membranes, of which the tubular and pleated ones are already accepted as cross-flow geometries in reactor technology, as mentioned above. In filtration engineering the cross-flow term means that the filtrate flows perpendicularly to the suspension stream. Cross-flow may not be considered a sufficiently illustrative term here [25]. A better term would be parallel filtration, but the term cross-flow filtration has been accepted generally and may be difficult to change at present. 

Filtration on a laboratory scale is usually performed with relatively small amounts of API and thus relatively small filter cake heights. Because the time for cake formation scales quadraticaUy with cake height, potential filtration issues on a large scale are often unforeseen in early phase process development. The filtration time of a suspension on plant scale, tp, as a function of filtration time, tp, and cake height, hp, on a laboratory scale is determined by Equation 18.3 ... 

The principal objective of an expression test is to determine the compression deliquoring characteristics of a cake. However, the nature of the test allows both filtration and compression characteristics to be determined when the starting mixture is a suspension (i.e. where the solids are not networked or they are interacting to a significant extent). Cake formation rate, specific resistance and solids volume fraction data can be determined for the filtration phase while analysis of a subsequent consolidation phase allows the calculation of parameters such as consolidation coefficient, consolidation index and ultimate solids concentration in the cake. Repeated use of the expression test over a range of constant pressures allows the evaluation of scale-up coefficients for filter sizing and simulation as described in Section 4.7. 

Other parameters that characterise the filtration phase include the average cake porosity (8 /, solids volume fraction (C ) and moisture content (M ) at the end of filtration, mass of dry cake per unit filter area (w) and average cake formation rate (L ) as given respectively by equations (4.50), (4.13), (4.51), (4.19) and (4.20)... 

All feature an Initial cake formation (filtration) phase(s). 

The moisture content is calculated hy equation (6.16). The end of the primary filtration phase, represented hy the final row of values in Table 6.5, is determined from the specification that cake formation with the pump stops when the cake thickness on each filtration surface reaches 20 mm. Although the value is calculated hy equation (6.92), in reality, a point on the pump... 

Figure 7.6 Mass balance schematic for solids, liquid and solute (from FDS). The values shown for filtrate include the throughputs of liquid and solute from both the cake formation and gas deliquoring phases.

Area of cloth used in a constant pressure filtration that follows cake formation with a pump or area of cloth used in a consolidation phase, m ... 

In the diafiltration method [23], which uses the Nucleopore membranes, the dispersion is filtered under pressure through the membrane. Like the dialysis method, diafiltration can be used not only to separate the aqueous phase, but also to purify a polymer dispersion, that is to separate all the water-soluble components. When used for the latter purpose, the dispersion is continuously rinsed with water during the diafiltration process. Filter cake formation is prevented by adopting a cross-flow filtration arrangement in which, for example, a stirrer is used to create a convective current parallel to the surface of the membrane. 

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