Depth Filtration:  Fundamental Investigation through Three-Dimensional Trajectory Analysis

A mathematical model (array of spheres or AOS Model) of aqueous depth filtration was developed using trajectory analysis performed on a porous media model comprised of a face-centered cubic packing of spheres. To extend removal efficiency predictions beyond the grain-size scale and take into account the presence of densely and sparsely packed regions in an actual filter bed, a parallel deficit porosity compensation scheme was developed and applied. A correlation for single collector efficiency was developed from trajectory results and, using the parallel deficit porosity compensation scheme, compared to an existing model and experimental results. Although the model discussed herein was developed with the intent of advancing the understanding of depth filtration, this work offers tools for investigating and insights into particle fate and transport in other circumstances, e.g., groundwater aquifers. This model represents the first use of a porous media model that explicitly accounts for grain contact points for trajectory modeling of aqueous depth filtration. Particle collection within the model was strongly associated with grain contact points, a phenomenon due largely to hydrodynamic forces “funneling” particles to trajectories coincident with grain contact points. In comparison to previous trajectory models, this model is less sensitive to particle size and filtration rate and much less sensitive to surface chemistry than other currently available models. At moderate to high filtration rates (on the order of 3.7 mm/s or 5.4 gpm/ft2), the AOS model represented well experimental data for removal of particles less than 5 μm. At lower filtration rates and larger particle sizes, the AOS model tends to overpredict particle removal.