FILTWASH - Filter Washing

The washing of filter cake is carried out to remove liquid impurities from valuable solid product or to increase recovery of valuable filtrates from the cake. Wakeman (1990) has shown that the axial dispersion flow model, as developed in Sec. 4.3.6, provides a fundamental description of cake washing. It takes into account such situations as non-uniformities in the liquid flow pattern, non-uniform porosity distributions, the initial spread of washing liquid onto the topmost surface of the filter cake and the desorption of solute from the solid surfaces. 

As shown by Wakeman, the solute material balance for the flowing liquid phase, allowing for axial dispersion and desorption of solute is given by the following defining partial differential equation 

The concentration of the solute adsorbed on to the particles is related to the concentration of the solute in the liquid by an equilibrium relationship of the form 

Expressing the model equations in dimensionless form gives 

For solution by digital simulation, the depth of filter cake is divided into nine segments, each of which has an equivalent dimensionless thickness Ax. For any element n, the form of the resulting difference differential equation is given by 

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Program FILTWASH models the dimensionless filtration wash curves for the above case of a filter cake with constant porosity, axial dispersion in the liquid flow and desorption of solute from the solid particles of the filter bed (Boyd, 1993). 

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