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  • Instability in Displacement of Viscous Fluids from Helt-Shaw Cell

    Paper number



    Prof. Nickolay N. Smirnov, Moscow Lomonosov State University, Russia


    Dr. Oleg Ivashnyov, Moscow Lomonosov State University, Russia


    Prof. Jean Claude Legros, University of Brussels, Belgium


    Dr. Valeriy Nikitin, Moscow Lomonosov State University, Russia


    M.Sc. Mohammad Shakhmardan, Moscow Lomonosov State University, Russia



    Frontal  displacement of a more viscous fluid by a less viscous
    one  is an unstable process: the Rayleigh-Taylor or Saffman-Taylor
    instability of the interface could bring to formation  and  growth
    of  "fingers"  of gas penetrating the bulk fluid.  The  growth  of
    fingers  and  their further coalescence could not be described  by
    the  linear analysis. Growth of fingers causes irregularity of the
    mixing zone.
       The  problem  arises in a frontal displacement of  fluids  from
    subterranean  environment,  which is  relevant  to  enhancing  oil
    recovery   and  groundwater  pollution  problems.  Entrapment   of
    residual  fluid by the displacing one lowers down the displacement
    quality leaving most of residual viscous fluid in porous matrix.
       The  goal of the present study was to investigate analytically,
    numerically and experimentally the instability of the displacement
    of  viscous  fluid  by  a less viscous one  in  a  two-dimensional
    channel,  and to determine characteristic size of viscous  fingers
    based  on microgravity experiments and theoretical investigations.
    Both  miscible  and immiscible displacement was investigated.  The
    main accent in the investigations was placed on non-linear effects
    being  of major importance for the quantitative evaluation of  the
    process.   Extensive  direct  numerical  simulations  allowed   to
    investigate  the  sensitivity  of  the  displacement  process   to
    variation  of values of the main governing parameters.  Validation
    of  the  code  was  performed by comparing the  results  of  model
    problems  simulations  with experimental data  and  with  existing
    solutions published in literature.
       Theoretical  analysis  showed that in the  absence  of  surface
    tension  at phase interface one could not determine the  width  of
    viscous fingers, as the model had one free parameter. Taking  into
    account inertia (non-linear) effects allows to get rid of  a  free
    model  parameter  and  to  determine the  characteristic  size  of
    viscous  fingers arising due to displacement instability.  It  was
    proved  theoretically, that viscous fingers have the  tendency  to
    acquire  a  pear shape with their heads being separated  from  the
    main flow forming viscous bubbles floating in the Hele-Shaw cell.
       Taking  into  account non-linear effects in fluids displacement
    allowed  to explain new experimental results on the pear-shape  of
    fingers  and periodical separation of their tip elements from  the
    main  body  of  displacing fluid. Those separated  blobs  of  less
    viscous fluid move much faster then the mean flow of the displaced
    viscous fluid.
       The  present  investigation was supported by the grant  of  the
    President  of  Russian Federation (19.2003.1) and  Schlumberger
    (CRDF RM0-1229A).
    Abstract document


    Manuscript document

    IAC-05-A2.4.09.pdf (🔒 authorized access only).

    To get the manuscript, please contact IAF Secretariat.