Viscous Fingering in Radially-Tapered Fluidic Cells

• Author / Creator

  Bongrand, Gregoire

• This thesis work concerns the viscous fingering instability occurring during immiscible fluid-fluid displacement experiments using a novel radially-tapered fluidic cell. We use modified Hele-Shaw cells where a negative depth gradient is introduced by tapering the upper plate, so that the gap thickness linearly decreases in the flow direction. We experimentally show that when a less viscous fluid displaces a more viscous one in a converging cell, the classic Saffman-Taylor instabilities can be suppressed and surprisingly the possibility of achieving a full sweep.

  Inspired by these observations, we study the feasibility of controlling such instabilities in non-uniform narrow passages with Newtonian fluids. In particular, we investigate the impact of gap gradient, α, on the stability, for different flow configurations. The injection flow rate, Q, has revealed to be a critical parameter manipulating the viscous fingering instability. For a fixed cell gradient (α), our experimental results show that a full sweep is achieved at low Q, whereas a partial displacement with fingering is obtained when Q overcomes a threshold. By using various cells of different α, we observe the variation of the critical threshold between stable and unstable displacements in terms of flow rate, Q, and the capillary number, Ca, characterizing the effects of viscous forces to surface tension. The comparison of our experimental results of critical Ca* with the theoretical predictions by a recent linear stability analysis showed good agreement.

  Numerous applications of the viscous fingering problem take place in rock formations, such as groundwater hydrology, soil remedy, and enhanced oil recovery. In such porous formations, there is a high chance of finding solid grains, mineral or debris in the fluid flows. Hence, we extended our study on the viscous fingering instability in inhomogeneous passages by considering the displacement of a suspension. The interplay between the destabilizing effect of the particles and the stabilizing effect of the depth gradient is investigated for different particle concentrations, cp. For a fixed α and cp, surprisingly, it is still possible to achieve stable displacements when the injection pressure of gas, p, is smaller than a critical value. Finally, by systematically varying the particle concentration and/or the depth gradient, we characterize the variation of that critical threshold, in terms of critical gas pressure and interface velocity, delineating the full and partial sweep. By considering the influence of the micro-particles and the particle concentration, the establishment of a more complete and multi-dimensional viscous fingering stability diagram is revealed for the first time.

• Subjects / Keywords

  • Interfacial instabilities
  • Porous media flow
  • Hele-Shaw cell
  • Viscous fingering
  • Gap gradient

• Graduation date

  Fall 2018

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/R3J679C7K

• License

  Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.