IN-PLANE MOTION OF INCOMPRESSIBLE FLUID CONSIDERING AN INTERNAL SMALL BOUNDARY

Abstract

We consider plane-radial motion, where the filtration velocity vectors are directed along the radii toward the borehole axis. As the borehole is approached, the pressure and filtration rate gradients sharply increase [1]. In this case, the radii change in geometric progression, while the pressure on the isobars changes in arithmetic progression [15]. At the same time, the mathematical model of such filtration flow movement can be described using Laplace’s equation. For example, A.N. Chekalin [5] by way of a mathematical experiment based on solving the simplest problems, introduced a correction coefficient for the Laplace difference equation and studies the movement of filtration flow in the Cartesian coordinate system. A.A. Andreev [2], [4] experiments with the application of the Dirac delta function. Based on the theory of distributions functions, this paper proves the modeling of plane-radial motion in a Cartesian coordinate grid based on the Dirac delta function. An analysis of the results of the numerical and analytical solution of the problem is performed.