SpringerLink
Log in

Mathematical Model of Filtration of Solutions in a Porous Medium with Semipermeable Inclusions. Osmotic Convection

  • Published:
Journal of Engineering Physics and Thermophysics Aims and scope

The author gives generalized equations of filtration of solutions in porous media containing semipermeable inclusions, that take account of the osmotic effect. Corrections describing this effect are usually small, but in some cases they play a key role, since osmosis is the main or only reason for the motion of a solution. With the developed model, the author has solved a new problem on osmotic convection.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. K. Mitchell, Fundamentals of Soil Behavior, John Wiley, New York (1993).

    Google Scholar 

  2. B. F. Rel′tov and N. A. Novistkaya, Osmotic phenomena in cohesive soils with their nonuniform salinization, Izv. Vseross. Nauch.-Issled. Inst. Gidrotekhniki, 51, 94–122 (1954).

  3. C. Dirksen, Thermo-osmosis through compacted saturated clay membranes, Soil Sci. Soc. Am. J., 33, No. 6, 821–826 (1969).

    Article  Google Scholar 

  4. T. Grundl and P. Michalski, Electroosmotically driven water flow in sediments, Water Res., 30, 811–818 (1996).

    Article  Google Scholar 

  5. N. I. Gamayunov and S. N. Gamayunov, Mass transfer and osmotic phenomena in swelling organic substances, J. Eng. Phys. Thermophys., 76, No. 6, 1325–1333 (2003).

    Article  Google Scholar 

  6. N. B. Pleshchinskii, M. G. Khramchenkov, and É. M. Khramchenkov, Model of water influx to a perfect well with allowance for the water loss by the overlying clay layer, J. Eng. Phys. Thermophys., 80, No. 3, 511–516 (2007).

    Article  Google Scholar 

  7. A. V. Luikov, Heat and Mass Transfer in Capillary-Porous Bodies [in Russian], Gostekhizdat, Moscow (1954).

    MATH  Google Scholar 

  8. S. D. Voronkevich, V. I. Sergeev, and S. N. Emel′yanov, Investigation into the fi ltration-osmotic processes in creating dense protective screens, in: Problems of the Mechanics of Natural Processes [in Russian], NII Mekhaniki MGU, Moscow (1983), pp. 47–63.

  9. J. M. Soler, The effect of coupled transport phenomena in the Opalinus Clay and implications for radionuclide transport, J. Contam. Hydrol., 53, 63–84 (2001).

    Article  Google Scholar 

  10. P. Glansdorff and I. Prigogine (Yu. A. Chizmadjev Ed.), Thermodynamic Theory of Structure, Stability, and Fluctuations [Russian translation], Mir, Moscow (1973).

  11. S. R. de Groot and P. Mazur (D. P. Zubarev Ed.), Nonequilibrium Thermodynamics [Russian translation], Mir, Moscow (1964).

  12. N. V. Churaev, Physicochemistry of the Processes of Mass Transfer in Porous Media [in Russian], Khimiya, Moscow (1990).

    Google Scholar 

  13. J. Graham, N. Tanaka, T. Crilly, and M. Alfaro, Modifi ed Cam-Clay modeling of temperature effects in clays, Can. Geotech. J., 38, 608–621 (2001).

    Article  Google Scholar 

  14. R. C. Srivastava and P. K. Avasthi, Non-equilibrium thermodynamics of thermo-osmosis of water through kaolinite, J. Hydrol., 24, 111–120 (1975).

    Article  Google Scholar 

  15. Th. J. S. Keijzer and J. P. G. Loch, Chemical osmosis in compacted dredging sludge, Soil Sci. Soc. Am. J., 65, 1045–1055 (2001).

    Article  Google Scholar 

  16. M. M. Ramazanov, A. V. Karakin, and L. I. Lobkovskii, Mathematical model of motion of solutions with account of the osmotic effect, Dokl. Akad. Nauk, 489, No. 1, 75–79 (2019).

    Google Scholar 

  17. Th. J. S. Keijzer, Chemical Osmosis in Natural Clayey Materials, Ph. D. Thesis, Utrecht University (2000).

  18. M. A. Malusis, C. D. Shackelford, and H. W. Olsen, A laboratory apparatus to measure chemico-osmotic efficiency coefficients for clay soils, Geotech. Test. J., 24, No. 3, 229–242 (2001).

    Article  Google Scholar 

  19. A. P. Vlasyuk and P. N. Martynyuk, Mathematical Modeling of the Consolidation of Grounds in Filtration of Saline Solutions under Nonisothermal Conditions [Russian translation], Nats. Univ. Vodn. Khoz. i Prirodopol′zovan., Rovno (2008).

  20. K. Terzaghi, Die Berechnung der Durchlassigkeitsziffer des Tones aus dem Verlauf der hydrodynamischem Spannungserscheinungen, Mathematish-Naturwissenschaftiliche Klasse, Vienna, 132, 125–138 (1923).

    Google Scholar 

  21. K. Magara, Compaction, Ion fi ltration, and osmosis in shale and their signifi cance in primary migration, The Am. Assoc. Pet. Geol. Bullet., 58, No. 2, 283–290 (1974).

    Google Scholar 

  22. C. E. Neuzil, Osmotic generation of "anomalous" fluid pressures in geological environments, Nature, 40, 182–184 (2000).

    Article  Google Scholar 

  23. B. B. Hanshaw, Membrane Properties of Compacted Clays, Ph. D. Thesis, Harvard University (1962).

  24. S. J. Fritz, Ideality of clay membranes in osmotic processes: A review, Clays Clay Miner., 34, 214–223 (1986).

    Article  Google Scholar 

  25. H. W. Olsen, Liquid movement through kaolinite under hydraulic, electric and osmotic gradients, Soil Sci. Soc Am. Bull., 56, 2022–2028 (1972).

    Google Scholar 

  26. W. M. Benzel and D. L. Graf, Studies of smectite membrane behavior: Importance of latter thickness and fabric at 200°C, Geochim. Cosmochim. Acta, 48, 1769–1778 (1984).

    Article  Google Scholar 

  27. A. Young and P. F. Low, Osmosis in agrillaceous rocks, AAPG Bull., 49, 1004–1008 (1965).

    Google Scholar 

  28. I. W. Marine and S. J. Fritz, Os motic model to explain anomalous hydraulic heads, Water Resour. Res., 17, 73–82 (1981).

    Article  Google Scholar 

  29. F. A. F. Berry and B. B. Hanshaw, Geological fi eld evidence suggesting membrane properties of shales, Proc. 21st Int. Geol. Congress, Copenhagen (1960), p. 209.

  30. G. H. Bolt, Electrochemical phenomena in soil and clay systems, Soil Chem.: B. Phys.-Chem. Models, 5b, 387–432 (1982).

  31. A. Kh. Mirzajanzade and V. M. Entov, Hydrodynamics in Drilling [in Russian], Nedra, Moscow (1985).

    Google Scholar 

  32. M. M. Ramazanov and A. V. Karakin, The effect of "flooding" of concretions at the ocean floor, Fizika Zemli, No. 2, 205–210 (2018).

    Google Scholar 

  33. G. I. Barenblatt and G. N. Baturin, On the "flooding" of ferromanganese concretions and certain features of the benthic ocean, Dokl. Akad. Nauk, 308, No. 1, 183–188 (1989).

    Google Scholar 

  34. G. N. Baturin, Geochemistry of Ferromanganese Concretions of the Ocean [in Russian], Nauka, Moscow (1968).

    Google Scholar 

  35. L. D. Landau and E. M. Lifshits, Theoretical Physics. Vol. 6. Hydrodynamics [in Russian], Nauka, Moscow (1986).

  36. L. D. Landau and E. M. Lifshits, Theoretical Physics. Vol. 5. Statistical Physics [in Russian], Nauka, Moscow (1976).

Download references

Author information

Authors and Affiliations

  1. Institute of Geothermal and Renewable Energy Problems — Branch of the Joint Institute for High Temperatures of the Russian Academy of Sciences, 39a I. Shamil Ave., Makhachkala, 367030, Russia

    M. M. Ramazanov

Authors
  1. M. M. Ramazanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. M. Ramazanov.

Additional information

Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 96, No. 3, pp. 823–833, May–June, 2023.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ramazanov, M.M. Mathematical Model of Filtration of Solutions in a Porous Medium with Semipermeable Inclusions. Osmotic Convection. J Eng Phys Thermophy 96, 823–833 (2023). https://doi.org/10.1007/s10891-023-02744-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10891-023-02744-7

Keywords

Search

Navigation