Coning during withdrawal from two fluids of different density in a porous medium
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The steady response of the interface between two fluids with different density in a porous medium is considered during extraction through a line sink. Supercritical withdrawal, or coning as it is often called, in which both fluids are being withdrawn, is investigated using a coupled integral equation formulation. It is shown that for each entry angle of the interface into the sink there is a range of supercritical solutions that depend on the flow rate, and that as the flow rate decreases the cone narrows. As the magnitude of the entry angle increases this range of flow-rate values decreases to a narrow range as the entry becomes vertical. Only one branch of solutions (that with horizontal entry) has the property that the interface levels off at a finite height, and this is investigated as a separate branch of solution.
Journal of Engineering Mathematics
© 2009 Springer. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher. The original publication is available at www.springerlink.com
Water Resources Engineering
Computational Fluid Dynamics