January 31, 2008
Dr. Stephen Lucas, JMU
Maximizing output from oil wells without water breakthrough

ABSTRACT:   A layer of oil often lies under the layer of oil within the porous rock that makes up an oil reservoir. A distribution of operating oil wells in the oil layer will cause a pressure gradient throughout the fluids, which causes the interface to rise. This is balanced by gravitational forces due to density differences, and a steady state shape for the interface may exist. Given a distribution of oil wells, our aim is to establish the individual well flow rates to maximize total flow without water breakthrough. This talk will outline an approximate method for finding the interface position due to Muskat, and explain why previous accurate BEM methods will not be used. An optimization method will be described, and result presented on optimal flow rates.

Opportunities for undergraduate research in this and other areas will also be briefly described, and no previous knowledge in the area is assumed.


BIOGRAPHICAL SKETCH:  Steve Lucas received a 1st Class honours degree with University Medal in Mathematics from Wollongong University in 1989, and a PhD in Mechanical Engineering from Sydney University in 1994. He did a Postdoctoral Research Fellowship in the Division of Applied Sciences, Harvard University during the period 1993-1995. From 1996-2006 he was employed by the School of Mathematics in the University of South Australia, including a visiting position 2005-2006 at the Department of Mathematics, University of Tennessee. He is currently a visiting associate professor within the Department of Mathematics and Statistics, James Madison University. Steve's research interests include analysis, fluid and solid mechanics, signal processing, control theory, number theory, graph theory and industrial mathematics, but the majority of his research has a numerical flavor. In February 2002, Steve received the Michell Medal for the outstanding new researcher in Applied Mathematics in Australia and New Zealand, awarded by the Australia New Zealand Industrial and Applied Mathematics division of the Australian Mathematical Society.