ANZIAM J.
45 (2004), 401-422
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Maximising output from oil reservoirs without water breakthrough
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S. K. Lucas
School of Mathematics and Statistics
University of South Australia
Mawson Lakes SA 5095
Australia
stephen.lucas@unisa.edu.au
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Abstract
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Often in oil reservoirs a layer of water lies
under the layer of oil. The suction pressure due
to a distribution of oil wells will cause the
oil-water interface to rise up towards the wells.
Given a particular distribution of oil wells, we
are interested in finding the flow rates of each
well that maximise the total flow rate without
the interface breaking through to the wells. A
method for finding optimal flow rates is
developed using the Muskat model to approximate
the interface height, and a version of the
Nelder-Mead simplex method for optimisation. A
variety of results are presented, including the
perhaps nonintuitive result that it is better to
turn off some oil wells when they are
sufficiently close to one another.
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