Fluid extraction from porous media by a slender permeable prolate-spheroid

Fluid extraction from porous media by a slender permeable prolate-spheroid is analyzed. It is found that the flux density along the spheroid-reservoir surface increases with the sharpness of the spheroid tip; and the fluid production rate is significantly higher than that predicted by the cylinder model used in the literature. It is shown that the flow in the reservoir is a superposition of a confocal flow and a redistributive flow, with only the confocal flow being productive. For high spheroid-to-reservoir permeability ratios, there exists an optimum length-to-radius ratio that maximizes fluid production rate for a given spheroid body volume.