Application of the Method of Multiple Scales to the Problem of Occurrence of Solute Convection in Rectangular Region of Porous Medium
- 作者: Khabin M.R.1,2, Maryshev B.S.1,2
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隶属关系:
- Institute of Continuous Media Mechanic, Ural Branch of the Russian Academy of Sciences
- Perm State University
- 期: 编号 1 (68) (2025)
- 页面: 79-90
- 栏目: Mechanics
- URL: https://journal-vniispk.ru/1993-0550/article/view/326434
- DOI: https://doi.org/10.17072/1993-0550-2025-1-79-90
- EDN: https://elibrary.ru/alqwze
- ID: 326434
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详细
Concentration convection has a significant effect on the transport of impurity in porous media. Such transport processes can occur in a variety of geophysical systems. Concentration convection is often considered by analogy with thermogravitational convection in porous media without taking into account the fact that the impurity can be adsorbed on the skeleton of the porous medium. One of the approaches allowing to take this fact into account is the MIM (mobile-immobile media) approach. The paper studies the occurrence of concentration convection in an elongated rectangular region filled with porous medium in the field of gravity at a constant pressure and concentration drop. The Darcy-Boussinesq law is used as a filtration model. The problem is solved analytically by the method of many scales in the approximation of weak buoyancy force. Analytical expressions of concentration and pressure fields for the ground state (the case of no gravity) and the first order of smallness are obtained. The results of numerical calculation are compared with the analytical solution. It is shown that the convective-free case is unstable at any small concentration drop, and the resulting flow is a solitary convective cell. The position of the region of the largest concentration inhomogeneity depends on the ratio of the Peclet and Rayleigh-Darcy numbers.
作者简介
M. Khabin
Institute of Continuous Media Mechanic, Ural Branch of the Russian Academy of Sciences; Perm State University
Email: khabin.m@icmm.ru
Postgraduate, Research Engineer, Institute of Continuous Media Mechanics Ural Branch of the Russian Academy of Sciences (1, Academican Korolev St., Perm, Russia, 614018) Perm, Russia; Perm, Russia
B. Maryshev
Institute of Continuous Media Mechanic, Ural Branch of the Russian Academy of Sciences; Perm State University
Email: bmaryshev@icmm.ru
Candidate of Physical and Mathematical Sciences, Associate Professor, Researcher, Institute of Continuous Media Mechanics Ural Branch of the Russian Academy of Sciences (1, Academican Korolev St., Perm, Russia, 614018) Perm, Russia; Perm, Russia
参考
- Schincariol R.A., Schwartz F.W. An experimental investigation of variable density flow and mixing in homogeneous and heterogeneous media // Water Resources Re-search. 1990. Vol. 26, No 10. P. 2317-2329. doi: 10.1029/WR026i010p02317.
- Maryshev B.S., Khabin M.R., Evgrafova A.V. Identification of transport parameters for the solute filtration through porous media with clogging // Journal of Porous Media, 2023. Vol. 26, No 6. P. 31-35. doi: 10.1615/JPorMedia.2022044645 EDN: RAEQIQ.
- Deans H.A. A mathematical model for dispersion in the direction of flow in porous media // Society of Petroleum Engineers Journal, 1963. Vol. 3, No 01. P. 49-52. doi: 10.2118/493-PA.
- van Genuchten M.T., Wierenga P.J. Mass transfer studies in sorbing porous media I. Analytical solutions 1 // Soil Science Society of America Journal. 1976. Vol. 40, No4. P. 473-480.
- Schumer R., Benson D.A., Meerschaert M.M., Baeumer B. Fractal mobile/immobile solute transport // Water Resources Research, 2003. Vol. 39, No 10. doi: 10.1029/2003 WR002141 EDN: LRUGJB.
- Gouze P., Le Borgne T., Leprovost R., Lods G., Poidras T., Pezard P. Non-Fickian dispersion in porous media: 1. Multiscale measurements using single-well injection withdrawal tracer tests // Water Resources Research, 2008. Vol. 44, No 6, W06426. doi: 10.1029/2007WR006278.
- Selim H.M. Prediction of contaminant retention and transport in soils using kinetic multireaction models // Environmental Health Perspectives. 1989. Vol. 83. P. 69-75. doi: 10.2136/sssaj2006.0422.
- Nield D., Bejan A. Convection in Porous Media. Cham, Switzerland: Springer, 2017. 988 p. doi: 10.1007/978-3-319-49562-0.
- Найфэ A. Введение в методы возмущений. М.: Наука, 1984. 535 с.
- Хабин М.Р., Марышев Б.С. Возникновение концентрационной конвекции в длинной прямоугольной области пористой среды // Вестник Пермского университета. Физика, 2023. No 4. С. 10-21. doi: 10.17072/1994-3598-2023-4-10-21 EDN: BFWVXA.
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