Presenting filtration-wave fields in a layered anisotropic medium as a plane wave (part I)

Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy


Release:

2015, Vol. 1. №1(1)

Title: 
Presenting filtration-wave fields in a layered anisotropic medium as a plane wave (part I)


About the authors:

Aleksandr I. Filippov, Dr. Sci. (Tech.), Professor, Department of General Scientific Disciplines, Ufa State Petroleum Technical University branch in Salavat; Professor, Department of General and Theoretical Physics, Sterlitamak branch of the Bashkir State University; eLibrary AuthorID, filippovai@rambler.ru

Oksana V. Akhmetova, Dr. Sci. (Phys.-Math.), Head of the Department of General and Theoretical Physics, Sterlitamak branch of the Bashkir State University; eLibrary AuthorID, ahoksana@yandex.ru

Abstract:

The first part of the article describes the attempt to present the filtration wave process in a three-layered anisotropic medium as an equivalent plane wave in the central layer. A modification of “the average precision” asymptotic method is employed for this purpose. The central area is represented by a semi-infinite layer bounded by two parallel half-planes. At the border of this layer pressure perturbations are set which produce pressure waves in a half-space, while at the borders of the environments no perturbations are observed. Each of the three media is homogeneous as its physical properties are independent of the spatial coordinates. Yet these properties of all the three media depend on the direction and therefore the media are anisotropic. At the boundaries of the contact areas the pressure and flow of the fluid equalities are set. The task is to determine the pressure field in each of the media. To determine the pressure wave fields the unknown functions are presented in the form of asymptotic formulas so the original task of conjugation is reduced to easier tasks for the coefficients of the asymptotic expansion. It is shown that the zero coefficient of the asymptotic expansion describes the dependence of the amplitude of the said plane wave on its spatial coordinates as well as the physical properties of the wave and the medium.

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