Modelagem matemática para o transporte de partículas sujeitas a múltiplos mecanismos de retenção

Discrepancies between classical model predictions and experimental data for deep bed filtration have been reported by various authors. In order to understand these discrepancies, an analytic continuum model for deep bed filtration is proposed. In this model, a filter coefficient is attributed to each distinct retention mechanism (straining, diffusion, gravity interception, etc.). It was shown that these coefficients generally cannot be merged into an effective filter coefficient, as considered in the classical model. Furthermore, the derived analytic solutions for the proposed model were applied for fitting experimental data, and a very good agreement between experimental data and proposed model predictions were obtained. Comparison of the obtained results with empirical correlations allowed identifying the dominant retention mechanisms. In addition, it was shown that the larger the ratio of particle to pore sizes, the more intensive the straining mechanism and the larger the discrepancies between experimental data and classical model predictions. The classical model and proposed model were compared via statistical analysis. The obtained p values allow concluding that the proposed model should be preferred especially when straining plays an important role. In addition, deep bed filtration with finite retention capacity was studied. This work also involves the study of filtration of particles through porous media with a finite capacity of filtration. It was observed, in this case, that is necessary to consider changes in the boundary conditions through time evolution. It was obtained a solution for such a model using different functions of filtration coefficients. Besides that, it was shown how to build a solution for any filtration coefficient. It was seen that, even considering the same filtration coefficient, the classic model and the one here propposed, show different predictions for the concentration of particles retained in the porous media and for the suspended particles at the exit of the media