On the horizontal pressure filtration of the mixture through a porous medium with clogging
DOI:
https://doi.org/10.17072/1994-3598-2016-3-12-21Abstract
The problem under consideration is the slow filtration of the mixture, which consists of the carrier fluid and heavy solute into the horizontal channel of the porous medium. The pressure drop is prescribed on the side walls of the channel, which determines the filtration flow. The solutes distributes into the channel by the gravitational distribution because the solute is the heavier than fluid. The solute concentration near the bottom wall is greater than near the top. We take into account that the transfer of any solutes into the porous medium is accompanied by the process of its deposition to the solid matrix of media. This process is frequently named immobilization. Immobilization slows the transport by removing the solute from the flow. The immobilized solute occupies part of the pore volume, thus it reduces the porosity and permeability of the medium, i.e. the solute clogs the media. It is obtained that the flat front of solute propagation is observed at weak influence of gravity (a narrow channel or a small difference between the fluid density and impurities). The speed of propagation decreases with decreasing pressure drops and increasing the influence of immobilization. In this case, the flow of the mixture homogeneous and uniform concentration field is formed quickly. In the case of significant influence of gravity the front of solute propagation becomes curved. The large part of solute accumulates at the bottom of the channel. Solute intensively immobilizes in the solid matrix of porous media and thereby the speed of flow through channel is decreased. This effect results to significant heterogeneity of concentration field and the reducing of mixture flow through the filter.Received 17.10.2016; accepted 28.10.2016References
Darcy H. P. Les fontaines publiques de la Ville de Dijon. Paris: Dalmont, 1856. 657 p.
Gershuni G. Z., Zhukhovitskii E. M. Convective stability of incompressible fluids. Jerusalem: Keter Publishing House, 1976, 330 p.
Birikh R. V. Thermocapillary convection in a horizontal layer of liquid. Journal of Applied Mechanics and Technical Physics, 1966, vol. 7, no. 3, pp. 43–44.
Gershuni G. Z., Zhukhovitskii E. M., Myznikov V. M. Stability of a plane-parallel convective flow of a liquid in a horizontal layer. Journal of Applied Mechanics and Technical Physics, 1974, vol. 15, no. 1, pp. 78–82.
Gershuni G. Z.. Zhukhovitskii E. M., Myznikov V. M. Stability of plane-parallel convective fluid flow in a horizontal layer relative to spatial perturbations. Journal of Applied Mechanics and Technical Physics, 1974, vol. 15, no. 5, pp. 706–708.
Kirdyashkin A. G., Polezhaev V. I., Fedyushkin A. I. (Thernal convection in horizontal layer with heating from one side). In: Avduevskii V. S. (Ed.) Gidroaeromekhanika i kosmicheskie issledo-vaniia (Hydroaeromechanics and cosmic studies). Moscow: Nauka, 1985, pp. 170–187 (In Russian).
Gershuni G. Z.. Zhukhovitskii E. M., Tarunin E. L. Numerical investigation of convective motion in closed cavity. Fluid Dynamics, 1966, vol. 1, no. 5, pp. 38–42.
Vertgeim I. I., Lyubimov D. V. Konvektsiia v iacheike Khele–Shou pri nagreve sboku (Convection in Hele–Shaw cell heated from one side). In: Issledovanie teplovoi konvektsii i teploperedachi (Study of thermal convection and heat transfer). Sverdlovsk: Ural Scientific Center of USSR Academy of Science, 1981, pp. 32–35 (In Russian).
Walker K. L., Homsy G. M. Convection in a porous cavity. Journal of Fluid Mechanics, 1978, vol. 87, pp. 449–474.
Bejan A., Tien C. L. Natural convection in a horizontal porous medium subjected to an end-to-end temperature difference. ASME Journal of Heat Transfer, 1978, vol. 100, pp. 191–198.
Blythe P. A., Simpkins P. G., Daniels P. G. Thermal convection in a cavity filled with a porous medium: a classification of limiting behaviours. International Journal of Heat and Mass Transfer, 1983, vol. 26, pp. 701–708.
Bejan A., Tien C. L. Natural convection in horizontal space bounded by two concentric cylinders with different end temperatures. International Journal of Heat and Mass Transfer, 1979, vol. 22, pp. 919–927.
Nield D. A., Bejan A. Convection in porous media. New York: Springer, 2006. 654 p.
Latrille C., Cartalade A. New experimental device to study transport in unsaturated porous media. In.: Birkle P., Torres I. S. (Eds.) Water–rock interaction. Leiden: CRC Press, 2010, pp. 299–302.
Agaoglu B., Scheytt T., Copty N. K., Laboratory-scale experiments and numerical modeling of cosolvent flushing of multi-component NAPLs in saturated porous media. Journal of Contaminant Hydrology, 2012, vol. 140, pp. 80–94.
van Genuchten M. Th., Wierenga P. J. Mass transfer studies in sorbing porous media I. Analytical solutions. Soil Science Society of America Journal, 1976, vol. 40, pp. 473–480.
Einstein A. The theory of the Brownian movement. Annalen der Physik, 1905, vol. 17, pp. 549.
Deans H. A. A mathematical model for dispersion in the direction of flow in porous media. SPE Journal, 1963, vol. 3, pp. 49–52.
Barry D. A., Parker J. C. Approximations for solute transport through porous media with flow transverse to layering. Transport in Porous Media. 1987. vol. 2, no. 4, pp. 65–82.
Bosma W. J. P., van der Zee S. E. A. T. M. Analytical approximations for nonlinear adsorbing solute transport in layered soils. Journal of Contaminant Hydrology, 1992, vol. 10, no. 2, pp. 99–118.
Selim H. M., Davidson J. M., Rao P. S. C. Transport of reactive solutes through multilayered soils. Soil Science Society of America Journal, 1977, vol. 41, no. 1, pp. 3–10.
Wu, Y. S., Kool J. B., Huyakorn P. S An analytical model for nonlinear adsorptive transport through layered soils. Water Resources Research, 1997, vol. 33, no. 1, pp. 21–29.
Bromly M., Hinz C. Non-Fickian transport in homogeneous unsaturated repacked sand. Water Resources Research, 2004, vol. 40, W07402.
Harter R. D., Baker D. E. Applications and misapplications of the Langmuir equation to soil adsorption phenomena. Soil Science Society of America Journal, 1977, vol. 41, pp. 1077–1080.
Selim H. M., Amacher M. C. Reactivity and transport of heavy metals in soils. Boca Raton: CRC, 1997. 240 p.
Kozeny J. Über kapillare Leitung des Wassers im Boden. Sitzungsbericht Akademie der Wissenschaften Wien, 1927, vol. 136, pp. 271–306.
Gruesbeck C., Collins R. E. Entrainment and deposition of fine particles in porous media. SPE Journal, 1982, vol. 22, pp. 847–856.
Kalitkin N. N. Chislennye metody (Numerical methods). Saint-Petersburg: BKhV-Peterburg, 2011, 592 p. (In Russian).
Tarunin E. L. The method of a sequence of nets for free convection problems. USSR Computational Mathematics and Mathematical Physics, 1975, vol. 15, no. 2, pp. 148–156.
Downloads
Published
How to Cite
Issue
Section
License
Автор предоставляет Издателю журнала (Пермский государственный национальный исследовательский университет) право на использование его статьи в составе журнала, а также на включение текста аннотации, полного текста статьи и информации об авторах в систему «Российский индекс научного цитирования» (РИНЦ).
Автор даёт своё согласие на обработку персональных данных.
Право использования журнала в целом в соответствии с п. 7 ст. 1260 ГК РФ принадлежит Издателю журнала и действует бессрочно на территории Российской Федерации и за её пределами.
Авторское вознаграждение за предоставление автором Издателю указанных выше прав не выплачивается.
Автор включённой в журнал статьи сохраняет исключительное право на неё независимо от права Издателя на использование журнала в целом.
Направление автором статьи в журнал означает его согласие на использование статьи Издателем на указанных выше условиях, на включение статьи в систему РИНЦ, и свидетельствует, что он осведомлён об условиях её использования. В качестве такого согласия рассматривается также направляемая в редакцию справка об авторе, в том числе по электронной почте.
Редакция размещает полный текст статьи на сайте Пермского государственного национального исследовательского университета: http://www.psu.ru и в системе OJS на сайте http://press.psu.ru
Плата за публикацию рукописей не взимается. Гонорар за публикации не выплачивается. Авторский экземпляр высылается автору по указанному им адресу.
