Abstract. A population balance model for a particulate suspension transport with size 6 exclusion capture of particles by porous rock is derived. The model accounts for particle 7 flux reduction and pore space accessibility due to restriction for large particles to move 8 through smaller pores -a particle is captured by a smaller pore and passes through a 9 larger pore. Analytical solutions are obtained for a uniform pore size medium, and also 10 for a medium with small pore size variation. For both cases, the equations for averaged 11 concentrations significantly differ from the classical deep bed filtration model. 12

Abstract. A population balance model for a particulate suspension transport with size 6 exclusion capture of particles by porous rock is derived. The model accounts for particle 7 flux reduction and pore space accessibility due to restriction for large particles to move 8 through smaller pores -a particle is captured by a smaller pore and passes through a 9 larger pore. Analytical solutions are obtained for a uniform pore size medium, and also 10 for a medium with small pore size variation. For both cases, the equations for averaged 11 concentrations significantly differ from the classical deep bed filtration model. 12

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A statistical model for filtration in porous media is proposed and analytical solutions for particle concentrations are derived. The proposed model takes multiple particle capture mechanisms into account and allows a fundamental physical interpretation of the filtration coefficients. Considering two distinct particle capture mechanisms, the inverse problem solution was discussed and applied to determine the filtration coefficients by fitting experimental data from the literature. Finally, a comparison between the classic and proposed model predictions led to the conclusion that the proposed model showed better agreement with experimental data.