(440a) Modeling of Particle Retention and Penetration Depth in Deep Bed Filtration
We develop a deep bed filtration model that is able to predict the migration of micro- and sub- micro- particles in porous media. The model couples the transport and deposition characteristics of particles. A transport probability function P(i) is proposed to predict the probability of flow through a pore based on the analysis of pore resistance. The model also includes a deposit probability function P*(i) that captures the likelihood of particle deposition within a pore. The P*(i) is measured experimentally using the change of concentrations during filtration tests with different pore structures and particle sizes, including cases where dparticle < dpore. The empirical P*(i) shows the probability of particle deposit/ pore capture is highly related with the size ratio (dparticle/dpore) and flow velocity (i.e., P*(i) is positively correlated with the size ratio and is negatively correlated with the flow velocity). This model can predict both the particle retention concentration in a pore and the approximate penetration depth of contaminants within a filter bed. By combining this new model with our earlier macroscopic description of filter flow, we can predict the filtrate concentration, flow dynamics and the penetration-scale of the filter medium from first principles.