About a topological dependence of the permeability factor in Darcy rule

The permeability factor in Darcy rule has the dimension of a square of length ; where – an effective diameter of the particles composing the porous environment; – a dimensionless factor (Slikhter’s number), depending on the porosity of a rock and parameter of the pore space structure (which in its turn depends on the form of the particles composing the rock, and on so-called "tortuosity factor " ξ); – vector of the average speed; μ – factor of the dynamic viscosity of a liquid; P – average pressure. Permeability factors can differ on 9 orders and, for example, for clay, they are characterized by values in an interval 10–3–10–11 mkm2. From average equations of the heterogeneous environment of R. I. Nigmatulin the authors of the paper offer a dependence of the permeability factor ; where – specific surface of pores; – dimensionless factors – close to the order of the value depending on the form of the particles composing the porous environment. The dependence of the permeability factor on the absolute value of pressure upon surfaces of pores is given. The permeability factors of porous environments, formed by particles with simple geometrical forms are calculated as examples.