1D mathematical model of deep bed filtration

A one-dimensional mathematical model representing the behavior of the deep bed filter was developed. This model involves the solution of the mass conservation equation for the inclusions and accounts for the change of bed porosity with inclusion deposition, as a function of bed depth and time. The inclusion deposition and reentrainment processes are represented with a rate expression. The pressure drop is calculated from the Ergun equation. The model validation was carried out by comparing the model predictions with the experimental data from a pilot-scale deep bed filter in which the working fluid was water and the bed was of granular alumina Water containing PVC particles as inclusions was filtered under various conditions. The filtration rate expressions were developed for different sizes of alumina and were used to simulate bed behavior for a given bed configuration. The simulated results were in good agreement with the experimental data, and the behavior of the water-PVC system was successfully predicted.