Filtration compressibility coefficient

The following example helps to illustrate the use of the equations presented up to this point. An aqueous slurry was filtered in a small laboratory filter press with a pressure drop of 0.5 atm and at a temperature of 20 C. After 10 minutes, 4.7 liters of filtrate were obtained after 20 minutes, 7.0 liters were collected. From experiments at other pressures, it was determined that the cake compression coefficient was s = 0.4. We wish to determine the volume of filtrate expected after 30 minutes from a filter press having a filtering area 10 times greater than the laboratory press if the filtration is to be performed at 1.5 atm pressure. The liquid temperature will be 55 °C. We also wish to determine the rate of filtration at the end of the process. 

Parameters q and W are variables when filtration conditions are changed. Coefficient (rj, is a function of pressure (rj, = f(P). The exact relationship can be derived from experiments in a device called a compression-permeability cell. Once this relationship is defined, the integral of the right hand side of the above equation may be evaluated analytically. Or, if the relationship is in the form of a curve, the evaluation may be made graphically. The interrelation between W and P, is established by the pump characteristics, which define q = f(W) in the integral. Filtration time may then be determined from dq/dt = W, from which we may state ... 

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. 

While valuable information on settling, filtration and cake post-treatments such as washing and gas deliquoring can be obtained from individual tests, in order to subsequently simulate filter performance it is usually necessary to evaluate so-called scale-up coefficients from sequences of tests. These empirical coefficients principally relate to cake formation (compressibility) and compression dehquoring (consolidation), as it is currently impossible to predict either from a knowledge of fundamental solid and liquid properties. Many filter cakes are compressible to some extent, and increases in filtering pressure lead to less porous and more resistant cakes. For these systems data are needed which relate the specific resistance, oc, a measure of cake structure such as solids volume fraction, and where appropriate the modified consolidation coefficient, Q, to variations in the plied pressure difference Ap. It is conventional practice to assume that Q and Q are solely functions of Ap. 

If tests are performed with a piston press and compression deUquoring takes place after filtration has been completed then it is possible to determine further scale-up coefficients that are characteristic of cake consolidation. In a similar maimer to that described above the modified consolidation coefficient, Cg, and the cake solids volume fraction at the end of consolidation, (C X or (C )oo, can be related to the consolidation pressure, Ap, according to... 

Figure 4.20 Example of the plots used to evaluate scale-up coefficients for filtration and cake consolidation (compression deliquoring).

Sometimes thickness and porosity may be necessary for the permeability criterion. In the permeability criteria referred to in terms of permittivity, thickness is included in the permeability coefficient because some geotextUes used for filtration (such as needlepunched nonwoven geotextiles) are thick and compressible. Therefore, for non woven geotextiles, it is important to know the geotextile s thickness and its variation with the applied vertical stress. 

Kinetic study of the filtration and establishment of mass balances during this unit operation allow the determination of the specific resistance, the compressibility and the filtrability coefficients of the filtration cakes (16). The optimisation of pilot filter operation can be deduced from these determinations. 

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