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Stability analysis for a multi-layer Hele-Shaw displacement

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Abstract

A well known approximation for the displacement of two immiscible fluids in a porous medium is the Hele-Shaw model. In experiments it was observed that a liquid with variable viscosity, introduced between the two initial fluids, can minimize the Saffman-Taylor instability. In some works an attempt was made to replace the variable viscosity liquid with a sequence of several immiscible liquids with constant viscosities. We prove that the linear stability analysis of this multi-layer Hele-Shaw model leads us to an ill-posed problem.

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References

  1. Bear, J.: Dynamics of Fluids in Porous Media. Elsevier, New York (1972)

    MATH  Google Scholar 

  2. Daripa, P.: Hydrodynamic stability of multi-layer Hele-Shaw flows. J. Stat. Mech. Theory Exp. P12005, 1–32 (2008)

    MathSciNet  MATH  Google Scholar 

  3. Daripa, P., Ding, X.: A numerical study of instability control for the design of an optimal policy of enhanced oil recovery by tertiary displacement processes. Tran. Porous Media 93, 675–703 (2012)

    Article  MathSciNet  Google Scholar 

  4. Daripa, P.: On stabilization of multi-layer Hele-Shaw and porous media flows in the presence of gravity. Tran. Porous Media 95, 349–371 (2012)

    Article  MathSciNet  Google Scholar 

  5. Daripa, P., Ding, X.: Universal stability properties for multi-layer Hele-Shaw flows and application to instability control. SIAM J. Appl. Math. 72, 1667–1685 (2012)

    Article  MathSciNet  Google Scholar 

  6. Daripa, P., Ding, X.: Selection principle of optimal profiles for multi-layer Hele-Shaw flows and stabilization. Tran. Porous Media 96, 353–367 (2013)

    Article  Google Scholar 

  7. Gorell, S.B., Homsy, G.M.: A theory of the optimal policy of oil recovery by secondary displacement process. SIAM J. Appl. Math. 43, 79–98 (1983)

    Article  MathSciNet  Google Scholar 

  8. Gorell, S.B., Homsy, G.M.: A theory for the most stable variable viscosity profile in graded mobility displacement process. AIChE J. 31, 1503–1598 (1985)

    Article  Google Scholar 

  9. Hele-Shaw, H.S.: Investigations of the nature of surface resistence of water and of streamline motion under certain experimental conditions. Inst. Naval Architects Trans. 40, 21–46 (1898)

    Google Scholar 

  10. Lamb, H.: Hydrodynamics. Dower Publications, New York (1933)

    MATH  Google Scholar 

  11. Pasa, G.: A paradox in Hele-Shaw displacements. Ann. Univ. Ferrara 66, 99–111 (2020)

    Article  MathSciNet  Google Scholar 

  12. Saffman, P.G., Taylor, G.I.: The penetration of a fluid in a porous medium or Helle-Shaw cell containing a more viscous fluid. Proc. R. Soc. A 245, 312–329 (1958)

    MATH  Google Scholar 

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  1. Simion Stoilow Institute of Mathematics of Romanian Academy, Calea Griviţei 21, Bucharest, 010702, Romania

    Gelu Paşa

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  1. Gelu Paşa
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Correspondence to Gelu Paşa.

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Paşa, G. Stability analysis for a multi-layer Hele-Shaw displacement. Ann Univ Ferrara 68, 1–9 (2022). https://doi.org/10.1007/s11565-021-00371-9

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  • DOI: https://doi.org/10.1007/s11565-021-00371-9

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