(440a) Modeling of Particle Retention and Penetration Depth in Deep Bed Filtration

Authors: 
Zhang, S., University of Pittsburgh
McCarthy, J. J., University of Pittsburgh
A mathematical model that describes the transport and deposition of both nano- and micro-particles through porous media is important in industrial applications, such as oil exploration, water purification and pollutant treatment; however, existing experimental studies and mathematical models of deep depth filtration often fail to accurately quantify the particle retention and penetration depth. This is due, in part, to the fact that most existing models depend heavily on empirical parameters; inaccurately describe pore structure of the filter medium and particle size distribution of contaminants; and neglect the probability of deposition when dparticle < dpore.

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.

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