ON THE SOLUTIONS OF SOME PROBLEMS OF THE THEORY OF FILTRATION

In terms of the application of the law Darcy considered the problem of constructing complex potentials filtration flows with discontinuities in the form of concentric circles, and filtration areas with boundaries in the form of a square and isosceles rectangular triangle. The method of images singular points (the method of reflections)

MATHEMATICAL MODELING OF UNSTEADY FILTRATION OF ELASTIC LIQUID IN AN INHOMOGENEOUS RESERVOIR

The article considers the possibility of numerical solution of two-dimensional problem of unsteady filtration in an inhomogeneous elastic liquid reservoir. The problem of finding the distribution of the pressure p(x,y,t) in the process of exploitation of deposits is reduced to the solution of a differential equation of parabolic type with variable coefficients. The problem is solved approximately by using the method of finite differences

MATHEMATICAL MODELING OF SALTS LEACHING WITH ONEDIMENSIONAL FILTRATION OF WATER IN SOILS OF FINITE THICKNESS

Abstract. In the article is considered and solved the problem of dissolution and leaching of salts from saline strata of homogeneous soil of the first type with onedimensional steady-state and uniform water filtration. This problem is reduced to the solution of the differential equation in partial derivatives, with initial and boundary conditions.Derived is the resulting equation of convective diffusion that determines the change in the concentration of the salt solution during filtration of water in saline soils, provided that water filtration in saline soil is steady and uniform, all the salts contained in the pores of the soil are completely dissolved, the coefficient of convective diffusion does not depend on speed of filtration.Determined are the change in concentration in time at the lower boundary of the washing out ground thickness.Derived are the formulae using of which allows to determine convective diffusion and dissolution of salts factors