Filtration operations—basic equations, compressible cakes

4 Filtration operations—basic equations, compressible cakes 

The compressibility of cakes, i.e. the increasing resistance of cakes with pressure, can be tested in various ways. As was briefly mentioned in section 9.2.2, one way of testing the relationship a =/(Apc) is in the compression-permeability cell. The solids compression is created by the mechanical action of the piston—an obvious assumption made is that hydraulic pressime can be simulated by mechanical compression. 

An obvious way of dealing with compressible cakes is to use the concept of average cake resistance Oav as defined in equation 9.6. This is of course only possible if the final pressure is known, otherwise a solution can only be obtained by a series of iterative calculations. 

however, an analytical relationship such as equation 9.7 is applicable, usually over a limited range of pressure drops, the function a = f(Ap) can be employed directly as shown in the following. 

For an analytical solution of the filtration of compressible cakes which satisfy equation 9.7, pressure drops across the medium Ap and across the cake Apc have to be treated separately. 

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