Deep bed filtration rate in porous media

Filtration problems are investigated when calculating foundation fortifying in free soil, when planning tunnels and underground structures to make watertight dividers in porous rock. Amid the filtering of a liquid with tiny particles through a porous frame, some of the particles are trapped in the little pores and form immovable sediment. A 1D model of filtration of similar particles transported by the carrier fluid in a homogeneous porous structure is considered, the filtration function is presumed to be nonlinear. A suspension or colloid is injected into a porous sample filled with clean water and gradually displaced. The growth rate in time of the particles concentrations at a given point of the porous sample is studied. Depending on the particle size, the growth rate of the trapped particles concentration either decreases monotonically with time, or first increases and then decreases. For the nonlinear filtration function, the conditions for the existence of an inflection point on the graphs of the suspended and trapped particles dynamics are obtained.