A note on axisymmetric supercritical coning in a porous medium

Graeme Charles Hocking, H. Zhang

Abstract


The steady response of a fluid with two layers of different density in a porous medium is considered during extraction through a point sink. Supercritical withdrawal in which both layers are being withdrawn is investigated using a spectral method. We show that for each withdrawal rate, there is a single entry angle of the interface into the point sink. As the flow rate decreases the angle of entry steepens until it becomes almost vertical, at which point the method fails. This limit is shown to correspond to the upper bound on sub-critical (single-layer) flow.

doi:10.1017/S1446181114000170

Keywords


porous media, point sink, axisymmetric flow, coning



DOI: http://dx.doi.org/10.21914/anziamj.v55i0.7907



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.