Deep bed filtration is a process used to separate small solid particles suspended in a fluid by using granular solids as the collecting medium. The filter efficiency depends on many parameters such as the Reynolds number, particle drag coefficient, the ratio of the diameter of injected, and filter particles, etc.

In the present work we model the porous media flow (solution of the Navier-Stokes equations) by using a computer code developed by Dr. P. Singh and we restrict our analysis to the case of two dimensional periodic porous media. The computational domain is discretized using the finite element method. In our simulation, the fluid is passing through the periodic porous medium.

One of our objectives is to estimate the range of the drag force that can effect filter efficiency. We study in detail, a range of drag coefficients depending on the Reynolds number, the fitter efficiency depending on the size of particle injected, and the number of particles. Last, we study the evolution of the distribution of trapped particles in the filter.

In our model, we find that the filter efficiency is not changed until the drag coefficient, C_D is 10. But in the range of drag coefficient from 10 to 100, the filter efficiency is changed. We find that the fitter efficiency is not effected by the number of particles injected and the time step, Δt in the range of 0.0001 - 0.1. We found that about 40% of the particles were trapped in top part of the filter. And we can find very similar results when the Reynolds number is 1, 16.556, or 100. The particle distribution results are in qualitative agreement with the available experimental data by Ghidaglia, Arcangelis, Hinch, and Guazzelli [1].