﻿ Fluid filtration in an inhomogeneous porous layer with permeability coefficient that varies according to a quadratic law | Engineering Journal: Science and Innovation
Engineering Journal: Science and InnovationELECTRONIC SCIENCE AND ENGINEERING PUBLICATION
Certificate of Registration Media number Эл #ФС77-53688 of 17 April 2013. ISSN 2308-6033. DOI 10.18698/2308-6033
Article

### Fluid filtration in an inhomogeneous porous layer with permeability coefficient that varies according to a quadratic law

Published: 21.04.2017

Authors: Algazin O.D., Kopaev A.V.

Published in issue: #6(66)/2017

Category: Mechanics | Chapter: Mechanics of Liquid, Gas, and Plasma

The paper considers a model problem of fluid filtration in an inhomogeneous porous layer with the permeability coefficient which decreases with depth as the square of the distance to the bottom. We obtained exact solutions of the corresponding boundary value problems for two-dimensional and three-dimensional cases. As an example of applying the obtained formulas we give the solutions of filtering problems under the spot dam and a cascade of two spot dams in an inhomogeneous layer with aquiclude, the solutions being expressed in elementary functions. Moreover, we examined the source and the vertical well in the three-dimensional inhomogeneous layer. The velocity potential in these cases is recorded in the form of integrals of elementary functions. The solutions of the boundary value problems discussed in this article can be applied when considering the steady electrical and thermal fields in inhomogeneous media, in which, respectively, the dielectric constant and coefficient of thermal conductivity change according to a quadratic law.

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