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Filling box flows in porous media

  • Author / Creator
    Sahu, Chunendra K.
  • Drawing on ideas from turbulent plume theory, a novel solution is presented for buoyant convection from an isolated source in uniform and non-uniform porous media of finite extents. In the former case, the problem is divided into three flow regimes: (i) a negatively-buoyant plume, (ii) rectilinear or axisymmetric gravity current comprising discharged plume fluid that forms when the plume reaches the bottom (impermeable) boundary, and, (iii) the subsequent ascending motion of this discharged plume fluid towards the source after the gravity current reaches the vertical side walls. We derive analytical solutions for all three regimes in a rectilinear geometry with a line source and in an axisymmetric geometry with a point source. By synthesizing the above three flow regimes, a ``filling box" model is developed that can predict the time needed for a source of dense fluid to fill the control volume up to the point of overflow as a function of the source and reservoir parameters. For purposes of corroborating our model predictions, complimentary rectilinear laboratory experiments were performed with fresh water and salt water as the working fluids. Images were recorded during the experiments and later post-processed in Matlab by employing an interface detection algorithm to determine the height profiles of the gravity current and the first front. We find good agreement between the measured and predicted height profiles. Extending the above results to a nonuniform porous medium, the effects of sudden permeability changes in a filling box flow are studied for the case of rectilinear geometry. The porous medium consists of two thick horizontal layers of different permeabilities. Two configurations are examined: a lower permeable medium on top of the higher permeability layer and vice-versa. While the flow dynamics observed in the first configuration are qualitatively similar to the case of a uniform porous medium, a significantly different flow behavior is observed in the latter configuration. Here not all of the plume fluid enters the lower layer. Rather some significant fraction propagates along the (horizontal) interface between the upper and lower layers as an intrusive gravity current exhibiting fingering instabilities along its bottom surface. Depending on the source parameters and permeability ratio, the gravity current can reach only a certain length before draining completely into the lower layer. Analytical solutions are presented for this runout length and the corresponding filling box time. Similitude experiments were then also performed to verify these predictions. While we find a good agreement in case of the filling box time, for the runout length an underprediction is observed. Reasons for this discrepancy are carefully examined.

  • Subjects / Keywords
  • Graduation date
    2016-06:Fall 2016
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/R3WM14747
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Doctoral
  • Department
    • Department of Mechanical Engineering
  • Supervisor / co-supervisor and their department(s)
    • Flynn, Morris R. (Mechanical Engineering)
  • Examining committee members and their departments
    • Lange, Carlos (Mechanical Engineering)
    • Sutherland, Bruce (Earth and Atmospheric Sciences)
    • Flynn, Morris R. (Mechanical Engineering)
    • Hejazi, Hossein (University of Calgary)
    • Secannel, Marc (Mechanical Engineering)