Almost all theoretical studies on solid-liquid separation are either dedicated to depth filtration or cake filtration regimes, just a few are considering the case, when depth filtration is followed by cake filtration. At the same time, very little attention is paid to a case, which often occurs for polydisperse dust, namely combined depth and cake filtration. This study is devoted to the macroscopic modeling of such filtration processes. The flow resistivity and the filtration efficiency are studied in the case of a relatively dilute suspension of polydisperse spherical particles. Constant flow rate filtration is considered, which leads to an increase of the pressure drop. A mathematical model based on macroscopic equations for depth filtration is used. The concentration of dissolved dirt is modeled with a convection-diffusion-reaction equation and the concentration of deposited dirt with a kinetic expression. The cake thickness is computed with an evolution equation.

A first effort is made to couple this model with a flow simulation for two-dimensional problems. One starts with computing the flow through a clean filtering medium. The resulting flow field is taken as an input to the combined depth-cake filtration model. Since the model is one-dimensional, it is adjusted to the direction normal to the filtering medium surface. The equations are solved and, based on the deposited amount of dirt, the porosity and permeability of the filtering medium are updated. The permeability is modified in each layer with an approach similar to a hybrid permeability model in the depth filtration regime and with a modified Kozeny Carman model in the cake filtration regime. Here an average diameter, computed from the number of different sized deposited particles, is used. Based on this information, the flow field is either updated (if the permeability change fulfills a given criterion or after a prescribed number of time steps) or the simulation continues with the already computed flow field. The cake on the surface starts to grow, when the porosity of the top layer reaches a prescribed value. In our case the cake growth is assumed to be uniform in normal direction to the filtering medium and is considered as incompressible. Numerical simulations of single-pass experiments are conducted and both, filtration efficiency and pressure curves are shown. Initially, we start with the simulation of a flat filtering medium, where also the flow can be considered as one-dimensional. Then the method is tested for a more complex geometry. A single round filter pleat of a cartridge filter is simulated and the influence of the change in permeability on the flow field is shown.

In summary, a first step in the direction of coupling a one-dimensional cake filtration model with a two-dimensional flow solver is made. It is shown that this model can predict the pressure curve and the filtration efficiency in a proper way...

**Session: **L12 - Depth and Cake Filtration - Numerical Simulation

**Day:** 12 October 2016

**Time: ** 16:45 - 18:00 h