The effect of buoyant convection on the buoyancy-driven spreading and draining of porous media gravity currents along a permeability jump

  • Author / Creator
    Khan, Md Imran
  • We investigate theoretically the impact of introducing convective dissolution along the interface of a (dense) miscible gravity current propagating up- and downdip along a permeability jump in a saturated, layered porous medium.
    Emphasis is placed on three different dissolution scenarios, namely constant dissolution, dissolution with simultaneous shutdown and dissolution with sequential shutdown. The last two modes are book-end opposite cases that make different assumptions concerning the mixing that arises along the gravity current-ambient interface. In the case of simultaneous shutdown, all portions of the interface experience the same rate of convective dissolution. Thus the point of shutdown, the instant at which the rate of dissolution begins to decrease,
    is everywhere the same. Simultaneous shutdown is associated with a rapid mixing of ambient fluid contaminated through dissolution in both the horizontal and vertical directions. By contrast, and in sequential shutdown, we neglect horizontal mixing in the ambient such that, in general, the rate of
    dissolution depends on position. In all three dissolution scenarios, we apply a sharp interface model and consider that the permeability jump separating the upper and lower layer of the porous medium makes an angle to the
    horizontal. To gauge the effectiveness of dissolution as a long-term trapping mechanism, e.g. for supercritical CO2 or acid-gas, we consider the temporal evolution of the storage efficiency and examine the impact of changing the dissolution strength, the (possibly infinite) time, t1, for the onset of shutdown and, for t1 < ∞, the e-folding decay time, t2, which prescribes the rate at which dissolution terminates. The along-jump distances traveled by the up- and downdip gravity currents fall as the dissolution strength increases. This observation has special importance when characterizing gravity current intermediate run-out lengths, defined (for not small t1) as the along-jump propagation distances where there exists a balance between the fluid supplied to the gravity current vs. that lost by a combination of dissolution and basal draining. The run-out lengths so defined are classified as intermediate because, for t > t1, shutdown decreases the rate of dissolution. The associated readjustment leads to a remobilization of previously-arrested gravity current fronts and the subsequent
    (though not indefinite) elongation of these along-jump flows. In turn, the distances traveled between intermediate and terminal run-out are shown to depend on the dissolution strength and t1. Contrasting sequential vs. simultaneous
    dissolution models, the former is associated with a high degree of injectate retention in the upper layer and is therefore associated with comparatively
    large storage efficiencies, E∗h. A more general comparison between dissolution models reveals regions of the parameter space where horizontal mixing in the ambient fluid plays a dynamically significant vs. minor role.

  • Subjects / Keywords
  • Graduation date
    Spring 2022
  • Type of Item
  • Degree
    Master of Science
  • DOI
  • 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.