ФИЛЬТРАЦИЯ В ПОРИСТОЙ СРЕДЕ С ДВУМЯ МЕХАНИЗМАМИ ЗАХВАТА

Промышленное и гражданское строительство. 2022. Т. 7. С. 48–53.

Kuzmina L., ОСИПОВ Ю. В., СОСЕДКА М. Г.

When constructing underground storage facilities for hazardous waste, watertight walls in the ground are
required. A liquid solution is pumped into the porous rock, which is filtered in the pores of the rock and, when
solidified, clogs them. During deep bed filtration, some particles are retained on the framework of the porous medium
and form a stable precipitate. A model is considered with two mechanisms of particle capture acting simultaneously:
particle blocking at the entrance of narrow pores and adhesion to the walls of wide pores. Each capture mechanism has
its own filtration function. The problem is reduced to a standard model with one implicitly defined aggregated filtration
function. For simplification, approximate models with explicit filtration functions are studied. The linearly constant
filtration function admits an explicit solution, but it has a kink and does not optimally approximate the aggregated
filtration function. The hyperbolic filtration function contains a free parameter, the value of which is selected from the
condition of the best approximation to the aggregated function. It is shown that the model with a hyperbolic filtration
function better approximates the exact solution.

Keywords: взвешенные и осажденные частицы, фильтрация в пористой среде, механизм захвата частиц, гиперболическая функция фильтрации, математическая модель фильтрации