ASYMPTOTICALLY AVERAGING SOLVING THE PROBLEM OF THE PRESSURE FIELD IN LAYERED POROUS MEDIUM

Abstract

Solved the problem of the quasi-steady pressure fields in layered orthotropic porous medium in the mode of constant depression. Statement of the problem carried out on the basis of the diffusion equation for the three layers with a plane interface perpendicular to the vertical axis, the different physical characteristics and the equality of pressures and flows at the interface between layers. The original problem is parameterized by adding a factor e -1 before the first and second derivatives of the function of the pressure in the middle of crosspieces along the vertical coordinate. In this administration, the formal parameter e, aspiration it to zero corresponds to an increase of the vertical component of permeability average interlayer indefinitely. This tends to equalize the pressure in the middle of the front vertical coordinate inter layers. Using the asymptotic formula of the parameterized problem highlighted mathematical formulation of the problem of the pressure field in a layered – inhomogeneous porous medium to zero coefficient of the asymptotic expansion. It is shown that the formulation of the problem for zero expansion coefficient up to notation coincides with the integral averaged over the thickness of the core layer of the original formulation of the parameterized problem that causes the physical meaning of zero-order approximation. By using the asymptotic method of analytical expressions, allowing to build a spatial - temporal dependence with the physical properties of the porous medium and a fluid filling. An exact solution of the original problem parameterized using the Laplace transform - Carson and sine Fourier transform. The validity of the asymptotic solutions checked by comparing them with the Maclaurin expansion of the exact solution of the problem. Constructed spatial - temporal distribution of pressure perturbations in the three-layer formation.