Mathematical Averaging of the Coefficients of a System of Elliptic and Parabolic Equations in Continuum Mechanics
- Authors: Plohotnikov S.P.1, Bogomolov V.A.1, Nizayev R.K.2, Bogomolova O.I.1, Malov P.V.1
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Affiliations:
- Kazan National Research Technological University
- The Tatar Oil Research and Design Institute
- Issue: Vol 40, No 5 (2019)
- Pages: 681-689
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/204530
- DOI: https://doi.org/10.1134/S1995080219050160
- ID: 204530
Cite item
Abstract
The problem of averaging the physical parameters (the coefficients of a system of elliptic and parabolic equations) of the continuum mechanics is studied. As an example, we consider the mathematical model of two-phase filtration. A comparative analysis of a numerical solution of the two-phase filtration in two known models averaged over the thickness of oil bed and in three-dimensional reference models is performed. The calculations are made using the linear, quadratic, and cubic initial permeability. All the calculations are performed for five-point and nine-point flooding systems.
About the authors
S. P. Plohotnikov
Kazan National Research Technological University
Author for correspondence.
Email: belova-elena-n@mail.ru
Russian Federation, Kazan, Tatarstan, 420015
V. A. Bogomolov
Kazan National Research Technological University
Author for correspondence.
Email: bogomolov@kfti.knc.ru
Russian Federation, Kazan, Tatarstan, 420015
R. Kh. Nizayev
The Tatar Oil Research and Design Institute
Author for correspondence.
Email: nizaev@tatnipi.ru
Russian Federation, Bugul’ma, Tatarstan, 423236
O. I. Bogomolova
Kazan National Research Technological University
Author for correspondence.
Email: boikfti@yandex.ru
Russian Federation, Kazan, Tatarstan, 420015
P. V. Malov
Kazan National Research Technological University
Author for correspondence.
Email: pavel.malov@mail.ru
Russian Federation, Kazan, Tatarstan, 420015