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Maximising output from oil reservoirs without water breakthrough

Published online by Cambridge University Press:  17 February 2009

S. K. Lucas
S. K. Lucas
Affiliation:
School of Mathematics and Statistics, University of South Australia, Mawson Lakes, SA 5095, Australia; e-mail: [email protected].
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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.

Type
Research Article
Information
The ANZIAM Journal , Volume 45 , Issue 3 , January 2004 , pp. 401 - 422
Copyright
Copyright © Australian Mathematical Society 2004

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