Depth filtration: Fundamental investigation through three dimensional trajectory analysis

A mathematical model (array of spheres or AOS Model) of aqueous depth filtr ation was developed using trajectory analysis performed on a porous media m odel comprised of a face-centered cubic packing of spheres. To extend remov al efficiency predictions beyond the grain-size scale and take into account the presence of densely and sparsely packed regions in an actual filter be d, a parallel deficit porosity compensation scheme was developed and applie d. A correlation for single collector efficiency was developed from traject ory results and, using the parallel deficit porosity compensation scheme, c ompared to an existing model and experimental results. Although the model d iscussed herein was developed with the intent of advancing the understandin g of depth filtration, this work offers tools for investigating and insight s into particle fate and transport in other circumstances, e.g., groundwate r aquifers. This model represents the first use of a porous media model tha t explicitly accounts for grain contact points for trajectory modeling of a queous depth filtration. Particle collection within the model was strongly associated with grain contact points, a phenomenon due largely to hydrodyna mic forces "funneling" particles to trajectories coincident with grain cont act 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 hig h filtration rates (on the order of 3.7 mm/s or 5.4 gpm/ft(2)), the AOS mod el represented well experimental data for removal of particles less than 5 mu m. At lower filtration rates and larger particle sizes, the AOS model te nds to overpredict particle removal.