The role of Pi, Po, and Pf in constitutive equations and new boundary conditions in cake filtration

The constitutive equations proposed by Tiller and Shirato were analyzed and a new constitutive equation originating from the sediment thickness was proposed. A new boundary condition of the filter cake based on the solid compressive pressure of the first solid layer,p _f , was also proposed. Accurate average specific cake resistances at various pressures and the thickness of cake were calculated with the new constitutive equation and boundary conditions. The influence ofp _f on the cake thickness and average porosity was studied theoretically. Using three constitutive equations, it was proved that the compressibility n obtained from filtration results instead of CPC (compression-permeability cell) of very compressible cake could not have an exact value.