Evaluation of scale-up coefficients

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 

In equations (4.70) and (4.72) the average solids concentration in the cake expressed in terms of a volume fraction has been used to represent the cake structure. Several alternative expressions for cake structure are found in the literature, the two most coimnon involve the cake porosity (s ) and the voids ratio (e) 

The use of scale-up coefficients in filter simtdations is demonstrated in Chapters 6 and 7 while Appendix E illustrates their use in predicting filter performance. 

A sequence of constant pressure piston press experiments have been performed over the pressure range Ap = 0.33 - 20.56 MPa using samples of a mineral suspension. Each experiment comprised a filtration phase followed by a consolidation phase and the results of individual analyses are shown in Table 4.6. Determine the scale-up coefficients that characterise the suspension. 

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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. 

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