Instability in Displacement of Viscous Fluids from Helt-Shaw Cell

Paper number

IAC-05-A2.4.09

Author

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

Coauthor

Dr. Oleg Ivashnyov, Moscow Lomonosov State University, Russia

Coauthor

Prof. Jean Claude Legros, University of Brussels, Belgium

Coauthor

Dr. Valeriy Nikitin, Moscow Lomonosov State University, Russia

Coauthor

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

Year

2005

Abstract

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

IAC-05-A2.4.09.pdf

Manuscript document

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

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