Solutions of the Model of Liquid and Gas Filtration in the Elastic Mode with Dynamic Filtration Law
DOI:
https://doi.org/10.15407/ujpe64.1.19Keywords:
porous medium, generalized Darcy’s law, invariant solutions, relaxationAbstract
A filtration model with the generalized Darcy’s law making allowance for nonlocal and nonlinear effects has been developed. The expression for the law was derived within the relaxation formalizm of nonequilibrium thermodynamics. The developed model is applied to analyze the influence of relaxation effects on the phase velocity of small wave-like perturbations. The character of nonlinear traveling waves is determined. The properties of polynomial and self-similar solutions are analyzed.
References
U. Hornung. Homogenization and Porous Media (Springer, 1997). https://doi.org/10.1007/978-1-4612-1920-0
V.N. Nikolaevskii, K.S. Basniev, A.T. Gorbunov, G.A. Zotov. Mechanics of Saturated Porous Media (Nedra, 1970) (in Russian).
Yu.P. Zheltov. Mechanics of Oil-Gas-Bearing Stratum (Nedra, 1975) (in Russian).
M.G. Alishaev. Modeling and Calculation in Applied Mechanics and Oil Production (ALEF,2015) (in Russian).
G.I. Barenblatt, V.M. Entov, V.M. Ryzhik. The Motion of Liquids and Gases in Natural Strata (Nedra, 1984) (in Russian).
M.M. Khasanov, G. T. Bulgakova. Nonlinear and Nonequilibrium Effects in Rheologically Complex Media (Institute of Computer Sciences, Moscow-Izhevsk, 2003) (in Russian).
C.H. Brinkman. A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl. Sci. Res. A1, 27 (1947).
S.M. Hassanizadeh, W.G. Gray. High velocity flow in porous media. Transp. Por. Media 2, 521 (1987). https://doi.org/10.1007/BF00192152
M.G. Alishaev, A.Kh. Mirzadzhanzade. To account of delay phenomena in filtration theory. Izv. Vyssh. Ucheb. Zaved. Neft Gas. 6, 71 (1975) (in Russian).
V.A. Danylenko, T.B. Danevych, O.S. Makarenko et al., Self-Organization in Nonlocal Non-Equilibrium Media (Inst. of Geophysics, Kyiv, 2011).
O.S. Makarenko. Model equations and formation of structures in media with memory. Ukr. Fiz. Zh. 57, 408 (2012).
A. Cemal Eringen. Vistas of nonlocal continuum physics. Int. J. Eng. Sci. 30, 1551 (1992). https://doi.org/10.1016/0020-7225(92)90165-D
R. Helmig. Multiphase Flow and Transport Processes in the Subsurface (Springer, 1997). https://doi.org/10.1007/978-3-642-60763-9
B.A. Suleimanov. Specific Features of Filtration in Heterogeneous Systems (Institute of Computer Sciences, Moscow-Izhevsk, 2006) (in Russian).
D. A. Nield. The limitations of the Brinkman–Forchheimer equation in modeling flow in a saturated porous medium and at an interface. Int. J. Heat Fluid Flow 12, 269 (1991). https://doi.org/10.1016/0142-727X(91)90062-Z
Yu.A. Buevich, G.P. Yasnikov. Relaxation methods in transfer process studies. Inzh. Fiz. Zh. 44, 489 (1983) (in Russian).
G. Rehbinder. Measurement of the relaxation time in Darcy flow. Transp. Por. Media 8, 263 (1992). https://doi.org/10.1007/BF00618545
A. Cemal Eringen. Nonlocal Continuum Field Theories (Springer, 2002).
X. Hu, J. H. Cushman. Nonequilibrium statistical mechanical derivation of a nonlocal Darcy's law for unsaturated/saturated flow. Stochast. Hydrol. Hydraul. 8, 109 (1994). https://doi.org/10.1007/BF01589892
N.N. Bautin, E.A. Leontovich, Methods and Techniques for Qualitative Study of Dynamical Systems on the Plane (Nauka, 1990) (in Russian).
V.I. Lagno, S.V. Spichak, V.I. Stognii. Symmetry Analysis of Evolution Equations (Institute of Computer Sciences, Moscow-Izhevsk, 2004) (in Russian).
Downloads
Published
How to Cite
Issue
Section
License
Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4. Duration.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5. Loyalty.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.
.png){kind=small}
