Solid compressive pressure specific cake resistance

Unfortunately the use of such a relation other than illustrating first principles is extremely limited in industrial applications because both the specific area of the particles Sq and the porosity 8 are extremely difficult to characterize when dealing with agglomerated solids that are also compressible. A more useful analysis can be made to characterize the filterability of a slurry by the use of the filtration equation as defined by equation (2) below, that shows how the filtration rate is affected by the filter operating parameters (pressure drop AP, filtration area A, filter medium resistance and also slurry related parameters (viscosity p, solids concentration w, specific cake resistance rj ... 

For incompressible cakes, the filtration rate is directly proportional to the specific cake resistance and the pressure/vacuum, and inversely proportional to the viscosity and cake thickness. The filtration rate is inversely proportional to the ratio of solids to filtrate, while the rate of cake formation is directly related to this ratio. For compressible cakes, the filtration rate is relatively independent of pressure. The more flocculated the solids, the more compressible will be the filter cake. 

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. 

If a cake is composed of rigid nondeformable solid particles a is independent of -AP and does not vary throughout the depth of the cake, and is known as incompressible cake. However, if the cake contains nonrigid, deformable solid particles or agglomerates of particles the resistance to flow will depend on the pressure drop and will vary throughout the depth of the cake. In this case the cake is called compressible and an average value of the specific resistance for the entire cake must be used in Equation 10.89. This average specific resistance must be measured experimentally for any particular slurry. 

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. 

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