Fluid Dynamics

, Volume 52, Issue 4, pp 516–525 | Cite as

Investigation of time-dependent two-dimensional displacement in a porous medium in the self-similar formulation of the problem



Two-dimensional flow through a porous medium when a gas is injected into a permeable aquifer of infinite extension is investigated. The self-similar asymptotic solutions which describe the early stage of the time-dependent two-dimensional process of gas spreading along the caprock over the aquifer are constructed. The asymptotics are constructed on the assumption of the considerable aquifer thickness when the processes in the neighborhood of the aquifer base have no effect on flow along the caprock. Two-dimensional wave patterns describing the gas saturation distribution are investigated by means of the direct numerical simulation. The dimensions of the gas accumulation region are estimated as functions of the similarity parameters.


flow through a porous medium gas injection self-similar solution the Buckley–Leverett problem fractional-flow theory 


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  1. 1.
    G.I. Barenblatt, V.M. Entov, and V.M. Ryzhik, Motion of Liquids and Gases in Natural Formations (Nedra, Moscow, 1984) [in Russian].Google Scholar
  2. 2.
    M.J. Bickle, “Geological Carbon Storage,” Nature Geosci. 2, 815–818 (2009).ADSCrossRefGoogle Scholar
  3. 3.
    K. Michael, A. Golab, V. Shulakova et al., “Geological Storage of CO2 in Saline Aquifers. A Review of the Experience from Existing Storage Operations,” Int. J. Greenhouse Gas Contr. 4, No. 4, 659–667 (2010).CrossRefGoogle Scholar
  4. 4.
    S. Lyle, H.E. Huppert, M. Hallworth, M. Bickle, and A. Chadwick, “Axisymmetric Gravity Currents in a Porous Medium,” J. Fluid Mech. 543, 293–302 (2005).ADSCrossRefMATHGoogle Scholar
  5. 5.
    J.N. Norborten and M.A. Celia, “Similarity Solutions for Fluid Injection into Confined Aquifers,” J. Fluid Mech. 561, 307–327 (2006).ADSMathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    B. Guo, Z. Zheng, M.A. Celia, and H.A. Stone, “Axisymmetric Flows from Fluid Injection into a Confined Porous Medium,” Phys. Fluids. 28, 022107 (2016).ADSCrossRefGoogle Scholar
  7. 7.
    A.A. Afanasyev and T.V. Sultanova, “Investigation of Hydrodynamic Instability of CO2 Injection into an Aquifer,” Fluid Dynamics 51 (4), 513–523 (2016).MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Y.C. Yortsos, “A Theoretical Analysis of Vertical Flow Equilibrium,” Transp. Porous Media 18, 107–129 (1995).CrossRefGoogle Scholar
  9. 9.
    A.A. Afanasyev, O.E. Melnik, and Yu.D. Tsvetkova, “Simulation of Flow through a Porous Medium for Underground CO2 Storagewith the Use of Highly Productive Computational Systems,” Vychisl. Mekhanika Sploshnykh Sred 6, No. 4, 420–429 (2013).Google Scholar
  10. 10.
    S.E. Buckley and M.C. Leverett, “Mechanism of Fluid Displacement in Sands,” Trans. AIME 146, 107–116 (1942).CrossRefGoogle Scholar
  11. 11.
    A.N. Brooks and A.T. Corey, Hydraulic Properties of Porous Media. Hydrology Papers 3 (Colorado: State Univ., 1964).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Institute of MechanicsLomonosov Moscow State UniversityMoscowRussia

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