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Filling box flows in porous media

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Motivated from buoyancy/density-driven flows in confined sub-surface environment, e.g. carbon sequestration and geothermal energy recovery, 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) 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. Analytical solutions are derived 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 “fi lling box” model is developed that can predict the time needed for a source of dense fluid to fi ll the control volume up to the point of overflow as a function of the source and reservoir parameters.

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 con figurations are examined: a lower permeable medium on top of the higher permeability layer and vice-versa. While the flow dynamics observed in the fi rst con figuration are qualitatively similar to the case of a uniform porous medium, a signi ficantly different flow behaviour is observed in the latter con figuration. 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.

This talk is part of the Institute for Energy and Environmental Flows (IEEF) series.

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