Flow of water suspension in unsaturated-saturated porous media and determination of its filtration property

The transportation of water suspension in unsaturated-saturated porous media is considered. Numerical modelling of silt deposition is characterized by a filtration function. Mathematical model includes a coupled system for the water suspension infiltration, silt (uniformly mixed in the water) transport with dispersion and its deposition in porous media. The filtration function expresses the rate of silt deposition depending on the amount of (immobile) deposited silt. The determination of filtration function is based on measurements of inflow/outflow characteristics in column experiments. The transportation and deposition of silt significantly influence the porosity and hydraulic conductivity which in unsaturated porous media leads to a strongly coupled and non-linear systems. This yields numerical difficulties in the construction of correct and efficient numerical approximation, which could be used in solution of an ill-posed inverse problem. In the paper, three different methods are presented and compared. Their applicability is demonstrated by solving inverse problem with determination of filtration function.