Transport of Non-Brownian Particles in Porous Media

Fluid in porous media flows through tortuous paths. When the fluid velocities are large enough, this tortuosity and inertial effects cause suspended particles to collide with pore walls. After each collision, a particle loses momentum and needs to be accelerated again by hydrodynamic forces. As a result, the average velocity of suspended particles may be smaller than that of the fluid. In addition, if the fluid velocity field is not macroscopically homogeneous, the retardation of the particles with respect to the fluid leads to an increase of the concentration of particles in certain regions which may eventually result in the clogging of the porous medium. This effect is of importance in flows near wells where the flow has circular symmetry and thus it is not macroscopically homogeneous. In this paper, we study the physical effect described above. We first develop a mathematical model that takes into account tortuosity and inertial effects at the pore scale. This model provides us with the average particle velocities as a function of the fluid velocity. We use this function in a second model, a macroscopic scale model, to study the evolution of concentration of particles and the development of clogging when the flow has circular symmetry.