Advertisement

Doklady Earth Sciences

, Volume 484, Issue 1, pp 105–108 | Cite as

Theory of Filtration in a Double Porosity Medium

  • L. I. LobkovskiiEmail author
  • M. M. RamazanovEmail author
GEOPHYSICS
  • 9 Downloads

Abstract

This paper defines a generalized mathematical model of filtration in a double porosity medium, taking into account recent ideas on liquid and gas flow in rocks with an anomalously low permeability (including nanoporous rocks). The obtained generalized equation takes into consideration, in contrast to the classical model, the integral effects of direct filtration of an energy (or heat) carrier in low-permeable inclusions. The laws of gas flow variations at the discharge point are compared with the classical double porosity model and with the Boussinesq–Leibenzon model.

Notes

ACKNOWLEDGMENTS

The general problem setting and the analytical constructions were supported by the Russian Science Foundation, project no. 14-50-00095. The numerical analysis was performed under a state assignment, project no. 0149-2019-005.

REFERENCES

  1. 1.
    G. I. Barenblatt, L. I. Lobkovsky, and R. I. Nigmatulin, Dokl. Earth Sci. 470 (2), 1046–1049 (2016).CrossRefGoogle Scholar
  2. 2.
    P. M. Monteiro, C. H. Rycroft, and G. I. Barenblatt, Proc. Natl. Acad. Sci. U. S. A. 109 (50), 20309–20313 (2012).CrossRefGoogle Scholar
  3. 3.
    G. I. Barenblatt, V. M. Entov, and V. M. Ryzhik, Theory of Nonstationary Filtration of Liquid and Gas (Nedra, Moscow, 1972) [in Russian].Google Scholar
  4. 4.
    L. I. Lobkovskii and M. M. Ramazanov, Fluid Dyn. 52 (4), 536–546 (2017).CrossRefGoogle Scholar
  5. 5.
    L. I. Lobkovskii and M. M. Ramazanov, Izv. Akad. Nauk, Mekh. Zhidk. Gaza, No. 4 (2018).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Shirshov Institute of Oceanology, Russian Academy of SciencesMoscowRussia
  2. 2.Institute for Geothermal Research, Dagestan Scientific Center, Russian Academy of SciencesMakhachkalaRussia

Personalised recommendations