Predicting the wash behaviour of filter cakes with inhomogeneous cake geometry on a macroscopic scale

Displacement washing of isotropic filter cakes with inhomogeneous cake geometry is investigated theoretically. Fluid flow is described by Darcy's law, while the advection–dispersion equation is used to describe solute transport within the cake. An additional mass transfer term is taken into account to describe mass transfer from non-permeated to permeated domains of the filter cake. The equations are solved numerically in three spatial dimensions. Model predictions are compared to experimental data from preceding publications of the authors and show good agreement. An explorative case study demonstrates the negative impact of typical inhomogeneous cake geometries on displacement washing.